Classifications

• • G—PHYSICS
  • G07—CHECKING-DEVICES
  • G07F—COIN-FREED OR LIKE APPARATUS
  • G07F17/00—Coin-freed apparatus for hiring articles; Coin-freed facilities or services
  • G07F17/32—Coin-freed apparatus for hiring articles; Coin-freed facilities or services for games, toys, sports, or amusements
  • G07F17/3286—Type of games
  • G07F17/3288—Betting, e.g. on live events, bookmaking
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
  • G06Q40/04—Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q30/00—Commerce
  • G06Q30/06—Buying, selling or leasing transactions
  • G06Q30/08—Auctions
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
  • G06Q40/02—Banking, e.g. interest calculation or account maintenance
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q40/00—Finance; Insurance; Tax strategies; Processing of corporate or income taxes
  • G06Q40/08—Insurance
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
  • G06Q50/34—Betting or bookmaking, e.g. Internet betting
• • G—PHYSICS
  • G07—CHECKING-DEVICES
  • G07F—COIN-FREED OR LIKE APPARATUS
  • G07F7/00—Mechanisms actuated by objects other than coins to free or to actuate vending, hiring, coin or paper currency dispensing or refunding apparatus
  • G07F7/08—Mechanisms actuated by objects other than coins to free or to actuate vending, hiring, coin or paper currency dispensing or refunding apparatus by coded identity card or credit card or other personal identification means
  • G07F7/10—Mechanisms actuated by objects other than coins to free or to actuate vending, hiring, coin or paper currency dispensing or refunding apparatus by coded identity card or credit card or other personal identification means together with a coded signal, e.g. in the form of personal identification information, like personal identification number [PIN] or biometric data

Definitions

• This invention relates to systems and methods for demand-based trading. More specifically, this invention relates to methods and systems for trading financial products, including digital options, having demand-based adjustable returns, and systems and methods for determining those returns. BACKGROUND OF THE INVENTION
• Financial products such as stocks, bonds, foreign exchange contracts, exchange traded futures and options, as well as contractual assets or liabilities such as reinsurance contracts or interest-rate swaps, all involve some measure of risk.
• the risks inherent in such products are a function of many factors, including the uncertainty of events, such as the Federal Reserve's determination to increase the discount rate, a sudden increase in commodity prices, the change in value of an underlying index such as the Dow Jones Industrial Average, or an overall increase in investor risk aversion.
• financial economists often treat the real-world financial products as if they were combinations of simpler, hypothetical financial products. These hypothetical financial products typically are designed to pay one unit of currency, say one dollar, to the trader or investor if a particular outcome among a set of possible outcomes occurs.
• Possible outcomes may be said to fall within "states,” which are typically constructed from a distribution of possible outcomes (e.g., the magnitude of the change in the Federal Reserve discount rate) owing to some real-world event (e.g., a decision of the Federal Reserve regarding the discount rate).
• states typically constructed from a distribution of possible outcomes (e.g., the magnitude of the change in the Federal Reserve discount rate) owing to some real-world event (e.g., a decision of the Federal Reserve regarding the discount rate).
• a set of states is typically chosen so that the states are mutually exclusive and the set collectively covers or exhausts all possible outcomes for the event. This arrangement entails that, by design, exactly one state always occurs based on the event outcome.
• Derivatives are traded on exchanges, such as the option and futures contracts traded on the Chicago Board of Trade (“CBOT”), as well as off-exchange or over-the- counter (“OTC”) between two or more derivative counterparties.
• CBOT Chicago Board of Trade
• OTC over-the- counter
• orders are typically either transmitted electronically or via open outcry in pits to member brokers who then execute the orders.
• member brokers then usually balance or hedge their own portfolio of derivatives to suit their own risk and return criteria. Hedging is customarily accomplished by trading in the derivatives' underlying securities or contracts (e.g., a futures contract in the case of an option on that future) or in similar derivatives (e.g., futures expiring in different calendar months).
• brokers or dealers customarily seek to balance their active portfolios of derivatives in accordance with the trader's risk management guidelines and profitability criteria.
• Order matching is a model followed by exchanges such as the CBOT or the Chicago Mercantile
• the exchange coordinates the activities of buyers and sellers so that "bids" to buy (i.e., demand) can be paired off with "offers” to sell (i.e., supply). Orders may be matched both electronically and through the primary market making activities of the exchange members.
• the exchange itself takes no market risk and covers its own cost of operation by selling memberships to brokers. Member brokers may take principal positions, which are often hedged across their portfolios.
• principal market making a bank or brokerage firm, for example, establishes a derivatives trading operation, capitalizes it, and makes a market by maintaining a portfolio of derivatives and underlying positions.
• the market maker usually hedges the portfolio on a dynamic basis by continually changing the composition of the portfolio as market conditions change.
• the market maker strives to cover its cost of operation by collecting a bid-offer spread and through the scale economies obtained by simultaneously hedging a portfolio of positions.
• the market maker takes significant market risk, its counterparties are exposed to the risk the* it may go bankrupt.
• the principal market making activity could be done over a wide area network, in practice derivatives trading is today usually accomplished via the telephone. Often, trades are processed laboriously, with many manual steps required from the front office transaction to the back office processing and clearing.
• the return to a trader of a traditional derivative product is, in most cases, largely determined by the value of the underlying security, asset, liability or claim on which the derivative is ba ⁇ ed.
• the value of a call option on a stock which gives the holder the right to buy the stock at some future date at a fixed strike price, varies directly with the price of the underlying stock.
• the value of the reinsurance contract is affected by the loss experience on the underlying portfolio of insured claims.
• the prices of traditional derivative products are usually determined by supply and demand for the derivative based on the value of the underlying security (which is itself usually determined by supply and demand, or, as in the case of insurance, by events insured by the insurance or reinsurance contract).
• a counterparty to a derivatives (or insurance contract) transaction typically assumes the risk that its counterparty will go bankrupt during the life of the derivatives (or insurance) contract.
• Margin requirements, credit monitoring, and other contractual devices, which may be costly, are customarily employed to manage derivatives and insurance counterparty credit risk.
• Regulatory bodies such as the Federal Reserve, Comptroller of the Currency, the Commodities Futures Trading Commission, and international bodies that promulgate regulations affecting global money center banks (e.g., Basle Committee guidelines) generally require institutions dealing in derivatives to meet capital requirements and maintain risk management systems. These requirements are considered by many to increase the cost of capital and barriers to entry for some entrants into the derivatives trading business, and thus to increase the cost of derivatives transactions for both dealers and end users.
• state insurance regulations also impose requirements on the operations of insurers, especially in the property-casualty lines where capital demands may be increased by the requirement that insurers reserve for future losses without regard to interest rate discount factors.
• Liquidity Derivatives traders typically hedge their exposures throughout the life of the derivatives contract. Effective hedging usually requires that an active or liquid market exist, throughout the life of the derivative contract, for both the underlying security and the derivative. Frequently, especially in periods of financial market shocks and. disequilibria, liquid markets do not exist to support a well-functioning derivatives market.
• Dynamic hedging of derivatives often requires continual transactions in the market over the life of the derivative in order to reduce, eliminate, and manage risk for a derivative or portfolio of derivative securities. This usually means paying bid-offers spreads for each hedging transaction, which can add significantly to the price of the derivative security at inception compared to its theoretical price in absence of the need to pay for such spreads and similar transaction costs.
• Event Risk Most traders understand effective hedging of derivatives transactions to require markets to be liquid and to exhibit continuously fluctuating prices without sudden and dramatic "gaps.” During periods of financial crises and disequilibria, it is not uncommon to observe dramatic repricing of underlying securities by 50% or more in a period of hours. The event risk of such crises and disequilibria are therefore customarily factored into derivatives prices by dealers, which increases the cost of derivatives in excess of the theoretical prices indicated by derivatives valuation models. These costs are usually spread across all derivatives users.
• Model Risk Derivatives contracts can be quite difficult to value, especially those involving interest rates or features which allow a counterparty to make decisions throughout the life of the derivative (e.g., American options allow a counterparty to realize the value of the derivative at any time during its life). Derivatives dealers will typically add a premium to derivatives prices to insure against the possibility that the valuation models may not adequately reflect market factors or other conditions throughout the life of the contract. In addition, risk management guidelines may require firms to maintain additional capital supporting a derivatives dealing operation where model risk is determined to be a significant factor. Model risk has also been a large factor in well-known cases where complicated securities risk management systems have provided incorrect or incomplete information, such as the Joe Jett/Kidder Peabody losses of 1994.
• Asymmetric Information Derivatives dealers and market makers customarily seek to protect themselves from counterparties with superior information. Bid- offer spreads for derivatives therefore usually reflect a built-in insurance premium for the dealer for transactions with counterparties with superior information, which can lead to unprofitable transactions.
• Traditional insurance markets also incur costs due to asymmetric information.
• the direct writer of the insurance almost always has superior information regarding the book of risks than does the assuming reinsurer. Much like the market maker in capital markets, the reinsurer typically prices its informational disadvantage into the reinsurance premiums.
• Incomplete Markets Traditional capital and insurance markets are often viewed as incomplete in the sense that the span of contingent claims is limited, i.e., the markets may not provide opportunities to hedge all of the risks for which hedging opportunities are sought. As a consequence, participants typically either bear risk inefficiently or use less than optimal means to transfer or hedge against risk. For example, the demand by some investors to hedge inflation risk has resulted in the issuance by some governments of inflation-linked bonds which have coupons and principal amounts linked to Consumer Price Index (CPI) levels. This provides a degree of insurance against inflation risk. However, holders of such bonds frequently make assumptions as to the future relationship between real and nominal interest rates. An imperfect correlation between the contingent claim (in this case, inflation-linked bond) and the contingent event (inflation) gives rise to what traders call "basis risk," which is risk that, in today's markets, cannot be perfectly insured or hedged.
• CPI Consumer Price Index
• the disclosed techniques appear to enhance liquidity at the expense of placing large informational burdens on the traders (by soliciting preferences, for example, over an entire price-quantity demand curve) and by introducing uncertainty as to the exact price at which a trade has been transacted or is "filled.”
• these electronic order matching systems contemplate a traditional counterparty pairing, which means physical securities are frequently transferred, cleared, and settled after the counterparties are identified and matched.
• techniques disclosed in the context of electronic order-matching systems are technical elaborations to the basic problem of how to optimize the process of matching arrays of bids and offers.
• Patents relating to derivatives such as U.S. Patent No. 4,903,201, disclose an electronic adaptation of current open-outcry or order matching exchanges for the trading of futures is disclosed.
• Another recent patent, U.S. Pat. No. 5,806,048, relates to the creation of open-end mutual fund derivative securities to provide enhanced liquidity and improved availability of information affecting pricing.
• This patent does not contemplate an electronic derivatives exchange which requires the traditional hedging or replicating portfolio approach to synthesizing the financial derivatives.
• U.S. Pat. No. 5,794,207 proposes an electronic means of matching buyers' bids and sellers' offers, without explaining the nature of the economic price equilibria achieved through such a market process.
• the present invention is directed to systems and methods of trading, and financial products, having a goal of reducing transaction costs for market participants who hedge against or otherwise make investments in contingent claims relating to events of economic significance.
• the claims are contingent in that their payout or return depends on the outcome of an observable event with more than one possible outcome.
• An example of such a contingent claim is a digital option, such as a digital call option, where the investor receives a payout if the underlying asset, stock or index expires at or above a specified strike price and receives no payout if the underlying asset, stock or other index expires below the strike price.
• Digital options can also be referred to as, for example, "binary options” and "all or nothing options.”
• the contingent claims relate to events of economic significance in that an investor or trader in a contingent claim typically is not economically indifferent to the outcome of the event, even if the investor or trader has not invested in or traded a contingent claim relating to the event.
• Intended users of preferred and other embodiments of the present invention are typically institutional investors, such as financial institutions including banks, investment banks, primary insurers and reinsurers, and co ⁇ orate treasurers, hedge funds and pension funds. Users can also include any individual or entity with a need for risk allocation services.
• the terms "user,” “trader” and “investor” are used interchangeably to mean any institution, individual or entity that desires to trade or invest in contingent claims or other financial products described in this specification.
• the contingent claims pertaining to an event have a trading period or an auction period in order to finalize a return for each defined state, each defined state corresponding to an outcome or set of outcomes for the event, and another period for observing the event upon which the contingent claim is based.
• the price or investment amount for each digital option is finalized at the end of the trading period, along with the return for each defined state.
• the entirety of trades or orders placed and accepted with respect to a certain trading period are processed in a demand- based market or auction.
• the organization or institution, individual or other entity sponsoring, running, maintaining or operating the demand-based market or auction, can be referred to, for example, as an "exchange,” “auction sponsor” and/or "market sponsor.”
• the returns to the contingent claims adjust during the trading period of the market or auction with changes in the distribution of amounts invested in each of the states.
• the investment amounts for the contingent claims can either be provided up front or determined during the trading period with changes in the distribution of desired returns and selected outcomes for each claim.
• the returns payable for each of the states are finalized after the conclusion of each relevant trading period.
• the total amount invested, less a transaction fee to an exchange, or a market or auction sponsor is equal to the total amount of the payouts.
• the returns on all of the contingent claims established during a particular trading period and pertaining to a particular event are essentially zero sum, as are the traditional derivatives markets.
• the investment amounts or prices for each contingent claim are finalized after the conclusion of each relevant trading period, along with the returns payable for each of the states. Since the total amount invested, less a transaction fee to an exchange, or a market or auction sponsor, is equal to the total amount of payouts, an optimization solution using an iteration algorithm described below can be used to determine the equilibrium investment amounts or prices for each contingent claim along with establishing the returns on all of the contingent claims, given the desired or requested return for each claim, the selection of outcomes for each claim and the limit (if any) on the investment amount for each claim.
• the process by which returns and investment amounts for each contingent claim are finalized in the present invention is demand-based, and does not in any substantial way depend on supply.
• traditional markets set prices through the interaction of supply and demand by crossing bids to buy and offers to sell ("bid/offer").
• the demand-based contingent claim mechanism of the present invention sets returns by financing returns to successful investments with losses from unsuccessful investments.
• the returns to successful investments (as well as the prices or investment amounts for investments in digital options) are determined by the total and relative amounts of all investments placed on each of the defined states for the specified observable event.
• Contingent claims thus include, for example, stocks, bonds and other such securities, derivative securities, insurance contracts and reinsurance agreements, and any other financial products, instruments, contracts, assets, or liabilities whose value depends upon or reflects economic risk due to the occurrence of future, real-world events. These events may be financial-related events, such as changes in interest rates, or non- financial-related events such as changes in weather conditions, demand for electricity, and fluctuations in real estate prices. Contingent claims also include all economic or financial interests, whether already traded or not yet traded, which have or reflect inherent risk or uncertainty due to the occurrence of future real-world events.
• contingent claims of economic or financial interest which are not yet traded on traditional markets are financial products having values that vary with the fluctuations in co ⁇ orate earnings or changes in real estate values and rentals.
• the term "contingent claim” as used in this specification encompasses both hypothetical financial products of the Arrow- Debreu variety, as well as any risky asset, contract or product which can be expressed as a combination or portfolio of the hypothetical financial products.
• an "investment” in or “trade” or an “order” of a contingent claim is the act of putting an amount (in the units of value defined by the contingent claim) at risk, with a financial return depending on the outcome of an event of economic significance underlying the group of contingent claims pertaining to that event.
• Derivative security (used interchangeably with “derivative”) also has a meaning customarily ascribed to it in the securities, trading, insurance and economics communities. This includes a security or contract whose value depends on such factors as the value of an underlying security, index, asset or liability, or on a feature of such an underlying security, such as interest rates or convertibility into some other security.
• a derivative security is one example of a contingent claim as defined above. Financial futures on stock indices such as the S&P 500 or options to buy and sell such futures contracts are highly popular exchange-traded financial derivatives.
• An interest-rate swap which is an example of an off-exchange derivative, is an agreement between two counte ⁇ arties to exchange series of cashflows based on underlying factors, such as the
• London Interbank Offered Rate (LIBOR) quoted daily in London for a large number of foreign currencies.
• LIBOR London Interbank Offered Rate
• off-exchange agreements can fluctuate in value with the underlying factors to which they are linked or derived.
• Derivatives may also be traded on commodities, insurance events, and other events, such as the weather.
• DRF Demand Reallocation Function
• a DRF is demand-based and involves reallocating returns to investments in each state after the outcome of the observable event is known in order to compensate successful investments from losses on unsuccessful investments (after any transaction or exchange fee). Since an adjustable return based on variations in amounts invested is a key aspect of the invention, contingent claims implemented using a DRF will be referred to as demand-based adjustable return (DBAR) contingent claims.
• DBAR demand-based adjustable return
• an Order Price Function is a function for computing the investment amounts or prices for contingent claims which are digital options.
• An OPF which includes the DRF, is also demand-based and involves determining the prices for each digital option at the end of the trading period, but before the outcome of the observable event is known. The OPF determines the prices as a function of the outcomes selected in each digital option (corresponding to the states selected by a trader for the digital option to be in-the-money), the requested payout for the digital option if the option expires in-the money, and the limit placed on the price (if any) when the order for the option is placed in the market or auction.
• “Demand-based market,” “demand-based auction” may include, for example, a market or auction which is run or executed according to the principles set forth in the embodiments of the present invention.
• “Demand-based technology” may include, for example, technology used to run or execute orders in a demand-based market or auction in accordance with the principles set forth in the embodiments of the present invention.
• Continuous claims may include, for example, contingent claims that are processed in a demand-based market or auction.
• Continuous claims or “DBAR contingent claims” may include, for example, digital options or DBAR digital options, discussed in this specification.
• demand-based markets may include, for example, DBAR DOEs (DBAR Digital Option Exchanges), or exchanges in which orders for digital options or DBAR digital options are placed and processed.
• Continuous claims or “DBAR contingent claims” may also include, for example, DBAR-enabled products or DBAR-enabied financial products, discussed in this specification.
• Preferred features of a trading system for a group of DBAR contingent claims include the following: (1) an entire distribution of states is open for investment, not just a single price as in the traditional markets; (2) returns are adjustable and determined mathematically based on invested amounts in each of the states available for investment, (3) invested amounts are preferably non-decreasing (as explained below), providing a commitment of offered liquidity to the market over the distribution of states, and in one embodiment of the present invention, adjustable and determined mathematically based on requested returns per order, selection of outcomes for the option to expire in-the-money, and limit amounts (if any), and (4) information is available in real-time across the distribution of states, including, in particular, information on the amounts invested across the distribution of all states (commonly known as a "limit order book").
• an issuer such as a co ⁇ oration, investment bank, underw ⁇ ter or other financial intermediary can create a secu ⁇ ty having returns that are d ⁇ ven in a comparable manner to the DBAR contingent claims of the present invention.
• a co ⁇ oration may issue a bond with returns that are linked to insurance ⁇ sk.
• the issuer can solicit trading and calculate the returns based on the amounts invested in contingent claims corresponding to each level or state of insurance ⁇ sks.
• changes in the return for investments in one state will affect the return on investments in another state in the same dist ⁇ bution of states for a group of contingent claims
• traders' returns will depend not only on the actual outcome of a real-world, observable event but also on trading choices from among the dist ⁇ bution of states made by other traders.
• This aspect of DBAR markets in which returns for one state are affected by changes in investments in another state in the same dist ⁇ bution, allows for the elimination of order-crossing and dynamic market maker hedging P ⁇ ce-discovery in preferred embodiments of the present invention can be supported by a one-way market (i.e., demand, not supply) for DBAR contingent claims.
• a market implemented by systems and methods of the present invention is especially amenable to electronic operation over a wide network, such as the Internet.
• the present invention mitigates de ⁇ vatives transaction costs found in traditional markets due to dynamic hedging and order matching.
• a preferred embodiment of the present invention provides a system for trading contingent claims structured under DBAR p ⁇ nciples, in which amounts invested in on each state in a group of DBAR contingent claims are reallocated from unsuccessful investments, under defined rules, to successful investments after the deduction of exchange transaction fees.
• the operator of such a system or exchange provides the physical plant and electronic infrastructure for trading to be conducted, collects and aggregates investments (or in one embodiment, first collects and aggregates investment information to determine investment amounts per trade or order and then collects and aggregates the investment amounts), calculates the returns that result from such investments, and then allocates to the successful investments returns that are financed by the unsuccessful investments, after deducting a transaction fee for the operation of the system.
• the market-maker which typically has the function of matching buyers and sellers, customarily quotes a price at which an investor may buy or sell. If a given investor buys or sells at the price, the investor's ultimate return is based upon this price, i.e., the price at which the investor later sells or buys the original position, along with the original price at which the position was traded, will determine the investor's return.
• the market-maker may not be able perfectly to offset buy and sell orders at all times or may desire to maintain a degree of risk in the expectation of returns, it will frequently be subject to varying degrees of market risk (as well as credit risk, in some cases).
• dynamic hedging or bid-offer crossing by the exchange is generally not required, and the probability of the exchange or market-maker going bankrupt may be reduced essentially to zero.
• Such a system distributes the risk of bankruptcy away from the exchange or market-maker and among all the traders in the system.
• the system as a whole provides a great degree of self-hedging and substantial reduction of the risk of market failure for reasons related to market risk.
• a DBAR contingent claim exchange or market or auction may also be "self- clearing" and require little clearing infrastructure (such as clearing agents, custodians, nostro/vostro bank accounts, and transfer and register agents).
• a derivatives trading system or exchange or market or auction structured according to DBAR contingent claim principles therefore offers many advantages over current derivatives markets governed by house banking principles.
• the present invention also differs from electronic or parimutuel betting systems disclosed in the prior art (e.g., U.S. Patent Nos. 5,873,782 and 5,749,785).
• betting systems or games of chance in the absence of a wager the bettor is economically indifferent to the outcome (assuming the bettor does not own the casino or the racetrack or breed the racing horses, for example).
• the difference between games of chance and events of economic significance is well known and understood in financial markets.
• a preferred embodiment of a method of the present invention for conducting demand-based trading includes the steps of (a) establishing a plurality of defined states and a plurality of predetermined termination criteria, wherein each of the defined states corresponds to at least one possible outcome of an event of economic significance; (b) accepting investments of value units by a plurality of traders in the defined states; and (c) allocating a payout to each investment.
• the allocating step is responsive to the total number of value units invested in the defined states, the relative number of value units invested in each of the defined states, and the identification of the defined state that occurred upon fulfillment of all of the termination criteria.
• An additional preferred embodiment of a method for conducting demand-based trading also includes establishing, accepting, and allocating steps.
• the establishing step in this embodiment includes establishing a plurality of defined states and a plurality of predetermined termination criteria. Each of the defined states corresponds to a possible state of a selected financial product when each of the termination criteria is fulfilled.
• the accepting step includes accepting investments of value units by multiple traders in the defined states.
• the allocating step includes allocating a payout to each investment. This allocating step is responsive to the total number of value units invested in the defined states, the relative number of value units invested in each of the defined states, and the identification of the defined state that occurred upon fulfillment of all of the termination criteria.
• the payout to each investment in each of the defined states that did not occur upon fulfillment of all of the termination criteria is zero, and the sum of the payouts to all of the investments is not greater than the value of the total number of the value units invested in the defined states. In a further preferred embodiment, the sum of the values of the payouts to all of the investments is equal to the value of all of the value units invested in defined states, less a fee.
• At least one investment of value units designates a set of defined states and a desired retum- on-investment from the designated set of defined states.
• the allocating step is further responsive to the desired retum-on-investment from the designated set of defined states.
• the method further includes the step of calculating Capital-At-Risk for at least one investment of value units by at least one trader.
• the step of calculating Capital-At-Risk includes the use of the Capital-At- Risk Value-At-Risk method, the Capital-At-Risk Monte Carlo Simulation method, or the Capital-At-Risk Historical Simulation method.
• the method further includes the step of calculating Credit-Capital-At-Risk for at least one investment of value units by at least one trader.
• the step of calculating Credit-Capital-At-Risk includes the use of the
• At least one investment of value units is a multi-state investment that designates a set of defined states.
• at least one multi-state investment designates a set of desired returns that is responsive to the designated set of defined states, and the allocating step is further responsive to the set of desired returns.
• each desired return of the set of desired returns is responsive to a subset of the designated set of defined states.
• the set of desired returns approximately corresponds to expected returns from a set of defined states of a prespecified investment vehicle such as, for example, a particular call option.
• the allocating step includes the steps of (a) calculating the required number of value units of the multi-state investment that designates a set of desired returns, and (b) distributing the value units of the multi-state investment that designates a set of desired returns to the plurality of defined states.
• the allocating step includes the step of solving a set of simultaneous equations that relate traded amounts to unit payouts and payout distributions; and the calculating step and the distributing step are responsive to the solving step.
• the solving step includes the step of fixed point iteration.
• the step of fixed point iteration includes the steps of (a) selecting an equation of the set of simultaneous equations described above, the equation having an independent variable and at least one dependent variable; (b) assigning arbitrary values to each of the dependent variables in the selected equation; (c) calculating the value of the independent variable in the selected equation responsive to the currently assigned values of each the dependent variables; (d) assigning the calculated value of the independent variable to the independent variable; (e) designating an equation of the set of simultaneous equations as the selected equation; and (f) sequentially performing the calculating the value step, the assigning the calculated value step, and the designating an equation step until the value of each of the variables converges.
• a preferred embodiment of a method for estimating state probabilities in a demand-based trading method of the present invention includes the steps of: (a) performing a demand-based trading method having a plurality of defined states and a plurality of predetermined termination criteria, wherein an investment of value units by each of a plurality of traders is accepted in at least one of the defined states, and at least one of these defined states corresponds to at least one possible outcome of an event of economic significance; (b) monitoring the relative number of value units invested in each of the defined states; and (c) estimating, responsive to the monitoring step, the probability that a selected defined state will be the defined state that occurs upon fulfillment of all of the termination criteria.
• An additional preferred embodiment of a method for estimating state probabilities in a demand-based trading method also includes performing, monitoring, and estimating steps.
• the performing step includes performing a demand-based trading method having a plurality of defined states and a plurality of predetermined termination criteria, wherein an investment of value units by each of a plurality of traders is accepted in at least one of the defined states; and wherein each of the defined states corresponds to a possible state of a selected financial product when each of the termination criteria is fulfilled.
• the monitoring step includes monitoring the relative number of value units invested in each of the defined states.
• the estimating step includes estimating, responsive to the monitoring step, the probability that a selected defined state will be the defined state that occurs upon fulfillment of all of the termination criteria.
• a preferred embodiment of a method for promoting liquidity in a demand-based trading method of the present invention includes the step of performing a demand-based trading method having a plurality of defined states and a plurality of predetermined termination criteria, wherein an investment of value units by each of a plurality of traders is accepted in at least one of the defined states and wherein any investment of value units cannot be withdrawn after acceptance.
• Each of the defined states corresponds to at least one possible outcome of an event of economic significance.
• a further preferred embodiment of a method for promoting liquidity in a demand-based trading method includes the step of hedging.
• the hedging step includes the hedging of a trader's previous investment of value units by making a new investment of value units in one or more of the defined states not invested in by the previous investment.
• An additional preferred embodiment of a method for promoting liquidity in a demand-based trading method includes the step of performing a demand-based trading method having a plurality of defined states and a plurality of predetermined termination criteria, wherein an investment of value units by each of a plurality of traders is accepted in at least one of the defined states and wherein any investment of value units cannot be withdrawn after acceptance, and each of the defined states corresponds to a possible state of a selected financial product when each of the termination c ⁇ te ⁇ a is fulfilled
• a further preferred embodiment of such a method for promoting liquidity in a demand-based trading method includes the step of hedging.
• the hedging step includes the hedging of a trader's previous investment of value units by making a new investment of value units in one or more of the defined states not invested in by the previous investment.
• a preferred embodiment of a method for conducing quasi-continuous demand- based trading includes the steps of: (a) establishing a plurality of defined states and a plurality of predetermined termination c ⁇ te ⁇ a, wherein each of the defined states corresponds to at least one possible outcome of an event; (b) conducting a plurality of trading cycles, wherein each trading cycle includes the step of accepting, du ⁇ ng a predefined trading pe ⁇ od and p ⁇ or to the fulfillment of all of the termination c ⁇ te ⁇ a, an investment of value units by each of a plurality of traders in at least one of the defined states; and (c) allocating a payout to each investment.
• the allocating step is responsive to the total number of the value units invested in the defined states du ⁇ ng each of the trading pe ⁇ ods, the relative number of the value units invested in each of the defined states du ⁇ ng each of the trading pe ⁇ ods, and an identification of the defined state that occurred upon fulfillment of all of the termination c ⁇ te ⁇ a.
• the predefined trading pe ⁇ ods are sequential and do not overlap
• Another preferred embodiment of a method for conducting demand-based trading includes the steps of: (a) establishing a plurality of defined states and a plurality of predetermined termination c ⁇ te ⁇ a, wherein each of the defined states corresponds to one possible outcome of an event of economic significance (or a financial instrument); (b) accepting, p ⁇ or to fulfillment of all of the termination cnte ⁇ a, an investment of value units by each of a plurality of traders in at least one of the plurality of defined states, with at least one investment designating a range of possible outcomes corresponding to a set of defined states; and (c) allocating a payout to each investment.
• the allocating step is responsive to the total number of value units in the plurality of defined states, the relative number of value units invested in each of the defined states, and an identification of the defined state that occurred upon the fulfillment of all of the termination c ⁇ te ⁇ a. Also in such a preferred embodiment, the allocation is done so that substantially the same payout is allocated to each state of the set of defined states.
• This embodiment contemplates, among other implementations, a market or exchange for contingent claims of the present invention that provides - without traditional sellers - profit and loss scenarios comparable to those expected by traders in derivative securities known as digital options, where payout is the same if the option expires anywhere in the money, and where there is no payout if the option expires out of the money.
• Another preferred embodiment of the present invention provides a method for conducting demand-based trading including: (a) establishing a plurality of defined states and a plurality of predetermined termination criteria, wherein each of the defined states corresponds to one possible outcome of an event of economic significance (or a financial instrument); (b) accepting, prior to fulfillment of all of the termination criteria, a conditional investment order by a trader in at least one of the plurality of defined states; (c) computing, prior to fulfillment of all of the termination criteria a probability corresponding to each defined state; and (d) executing or withdrawing, prior to the fulfillment of all of the termination criteria, the conditional investment responsive to the computing step.
• the computing step is responsive to the total number of value units invested in the plurality of defined states and the relative number of value units invested in each of the plurality of defined states.
• a market or exchange (again without traditional sellers) in which investors can make and execute conditional or limit orders, where an order is executed or withdrawn in response to a calculation of a probability of the occurrence of one or more of the defined states.
• Preferred embodiments of the system of the present invention involve the use of electronic technologies, such as computers, computerized databases and telecommunications systems, to implement methods for conducting demand-based trading of the present invention.
• a preferred embodiment of a system of the present invention for conducting demand-based trading includes (a) means for accepting, prior to the fulfillment of all predetermined termination criteria, investments of value units by a plurality of traders in at least one of a plurality of defined states, wherein each of the defined states corresponds to at least one possible outcome of an event of economic significance; and (b) means for allocating a payout to each investment.
• This allocation is responsive to the total number of value units invested in the defined states, the relative number of value units invested in each of the defined states, and the identification of the defined state that occurred upon fulfillment of all of the termination criteria.
• An additional preferred embodiment of a system of the present invention for conducting demand-based trading includes (a) means for accepting, prior to the fulfillment of all predetermined termination criteria, investments of value units by a plurality of traders in at least one of a plurality of defined states, wherein each of the defined states corresponds to a possible state of a selected financial product when each of ⁇ the termination criteria is fulfilled; and (b) means for allocating a payout to each investment.
• This allocation is responsive to the total number of value units invested in the defined states, the relative number of value units invested in each of the defined states, and the identification of the defined state that occurred upon fulfillment of all of the termination criteria.
• a preferred embodiment of a demand-based trading apparatus of the present invention includes (a) an interface processor communicating with a plurality of traders and a market data system; and (b) a demand-based transaction processor, communicating with the interface processor and having a trade status database.
• the demand-based transaction processor maintains, responsive to the market data system and to a demand- based transaction with one of the plurality of traders, the trade status database, and processes, responsive to the trade status database, the demand-based transaction.
• maintaining the trade status database includes (a) establishing a contingent claim having a plurality of defined states, a plurality of predetermined termination criteria, and at least one trading period, wherein each of the defined states corresponds to at least one possible outcome of an event of economic significance; (b) recording, responsive to the demand-based transaction, an investment of value units by one of the plurality of traders in at least one of the plurality of defined states; (c) calculating, responsive to the total number of the value units invested in the plurality of defined states during each trading period and responsive to the relative number of the value units invested in each of the plurality of defined states during each trading period, finalized returns at the end of each trading period; and (d) determining, responsive to an identification of the defined state that occurred upon the fulfillment of all of the termination criteria and to the finalized returns, payouts to each of the plurality of traders; and processing the demand-based transaction includes accepting, during the trading period, the investment of value units by one of the plurality of traders in
• maintaining the trade status database includes (a) establishing a contingent claim having a plurality of defined states, a plurality of predetermined termination criteria, and at least one trading period, wherein each of the defined states corresponds to a possible state of a selected financial product when each of the termination criteria is fulfilled; (b) recording, responsive to the demand-based transaction, an investment of value units by one of the plurality of traders in at least one of the plurality of defined states; (c) calculating, responsive to the total number of the value units invested in the plurality of defined states during each trading period and responsive to the relative number of the value units invested in each of the plurality of defined states during each trading period, finalized returns at the end of each trading period; and (d) determining, responsive to an identification of the defined state that occurred upon the fulfillment of all of the termination criteria and to the finalized returns, payouts to each of the plurality of traders; and processing the demand-based transaction includes accepting, during the trading period, the investment of value units by
• maintaining the trade status database includes calculating return estimates; and processing the demand-based transaction includes providing, responsive to the demand-based transaction, the return estimates.
• maintaining the trade status database includes calculating risk estimates; and processing the demand-based transaction includes providing, responsive to the demand-based transaction, the risk estimates.
• the demand-based transaction includes a multi-state investment that specifies a desired payout distribution and a set of constituent states; and maintaining the trade status database includes allocating, responsive to the multi-state investment, value units to the set of constituent states to create the desired payout distribution.
• Such demand-based transactions may also include multi-state investments that specify the same payout if any of a designated set of states occurs upon fulfillment of the termination criteria.
• Other demand-based transactions executed by the demand-based trading apparatus of the present invention include conditional investments in one or more states, where the investment is executed or withdrawn in response to a calculation of a probability of the occurrence of one or more states upon the fulfillment of the termination criteria.
• systems and methods for conducting demand-based trading includes the steps of (a) establishing a plurality of states, each state corresponding to at least one possible outcome of an event of economic significance; (b) receiving an indication of a desired payout and an indication of a selected outcome, the selected outcome corresponding to at least one of the plurality of states; and (c) determining an investment amount as a function of the selected outcome, the desired payout and a total amount invested in the plurality of states.
• systems and methods for conducting demand- based trading includes the steps of (a) establishing a plurality of states, each state corresponding to at least one possible outcome of an event (whether or not such event is an economic event); (b) receiving an indication of a desired payout and an indication of a selected outcome, the selected outcome corresponding to at least one of the plurality of states; and (c) determining an investment amount as a function of the selected outcome, the desired payout and a total amount invested in the plurality of states.
• systems and methods for conducting demand- based trading includes the steps of (a) establishing a plurality of states, each state corresponding to at least one possible outcome of an event of economic significance; (b) receiving an indication of an investment amount and a selected outcome, the selected outcome corresponding to at least one of the plurality of states; and (c) determining a payout as a function of the investment amount, the selected outcome, a total amount invested in the plurality of states, and an identification of at least one state corresponding to an observed outcome of the event.
• systems and methods for conducting demand- based trading include the steps of: (a) receiving an indication of one or more parameters of a financial product; and (b) determining one or more of a selected outcome, a desired payout, an investment amount, and a limit on the investment amount for each contingent claim in a set of one or more contingent claims as a function of the one or more financial product parameters.
• systems and methods for conducting demand- based trading include the steps of: (a) receiving an indication of one or more parameters of a financial product; and (b) determining an investment amount and a selected outcome for each contingent claim in a set of one or more contingent claims as a function of the one or more financial product parameters.
• a demand-enabled financial product for trading in a demand-based auction includes a set of one or more contingent claims, the set approximating a financial product, each contingent claim in the sei having an investment amount and a selected outcome, each investment amount being dependent upon one or more parameters of a financial product and a total amount invested in the auction.
• An object of the present invention is to provide systems and methods to support and facilitate a market structure for contingent claims related to observable events of economic significance, which includes one or more of the following advantages, in addition to those described above: 1. ready implementation and support using electronic computing and networking technologies;
• a further object of the present invention is to provide systems and methods for the electronic exchange of contingent claims related to observable events of economic significance, which includes one or more of the following advantages: 1. reduced transaction costs, including settlement and clearing costs, associated with derivatives transactions and insurable claims;
• FIG. 1 is a schematic view of various forms of telecommunications between
• FIG. 2 is a schematic view of a central controller of a preferred embodiment of a DBAR contingent claims exchange network architecture implementing the present invention.
• FIG. 3 is a schematic depiction of the trading process on a preferred embodiment of a DBAR contingent claims exchange.
• FIG. 4 depicts data storage devices of a preferred embodiment of a DBAR contingent claims exchange.
• FIG. 5 is a flow diagram illustrating the processes of a preferred embodiment of
• FIG. 6 is an illustrative HTML interface page of a preferred embodiment of a DBAR contingent claims exchange.
• FIG. 7 is a schematic view of market data flow to a preferred embodiment of a DBAR contingent claims exchange.
• FIG. 8 is an illustrative graph of the implied liquidity effects for a group of DBAR contingent claims.
• FIG. 9a is a schematic representation of a traditional interest rate swap transaction.
• FIG. 9b is a schematic of investor relationships for an illustrative group of DBAR contingent claims.
• FIG. 9c shows a tabulation of credit ratings and margin trades for each investor in to an illustrative group of DBAR contingent claims.
• FIG. 10 is a schematic view of a feedback process for a preferred embodiment of DBAR contingent claims exchange.
• FIG. 11 depicts illustrative DBAR data structures for use in a preferred embodiment of a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 12 depicts a preferred embodiment of a method for processing limit and market orders in a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 13 depicts a preferred embodiment of a method for calculating a multistate composite equilibrium in a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 14 depicts a preferred embodiment of a method for calculating a multistate profile equilibrium in a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 15 depicts a preferred embodiment of a method for converting "sale" orders to buy orders in a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 16 depicts a preferred embodiment of a method for adjusting implied probabilities for demand-based adjustable return contingent claims to account for transaction or exchange fees in a Demand-Based Adjustable Return Digital Options
• FIG. 17 depicts a preferred embodiment of a method for filling and removing lots of limit orders in a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 18 depicts a preferred embodiment of a method of payout distribution and fee collection in a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 19 depicts illustrative DBAR data structures used in another embodiment of a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 20 depicts another embodiment of a method for processing limit and market orders in another embodiment of a Demand-Based Adjustable Return Digital Options Exchange of the present invention.
• FIG. 21 depicts an upward shift in the earnings expectations curve which can be protected by trading digital options and other contingent claims on earnings in successive quarters according to the embodiments of the present invention.
• FIG. 22 depicts a network implementation of a demand-based market or auction according to the embodiments of the present invention.
• FIG. 23 depicts cash flows for each participant trading a principle-protected ECI- linked FRN.
• FIG. 24 depicts an example time line for a demand-based market trading DBAR- enabled FRNs or swaps according to the embodiments of the present invention.
• FIG. 25 depicts an example of an embodiment of a demand-based market or auction with digital options and DBAR-enabled products.
• the first section provides an overview of systems and methods for trading or investing in groups of DBAR contingent claims.
• the second section describes in detail some of the important features of systems and methods for trading or investing in groups of DBAR contingent claims.
• the third section of this Detailed Description of Preferred Embodiments provides detailed descriptions of two preferred embodiments of the present invention: investments in a group of DBAR contingent claims, and investments in a portfolio of groups of such claims.
• the fourth section discusses methods for calculating risks attendant on investments in groups and portfolios of groups of DBAR contingent claims.
• the fifth section of this Detailed Description addresses liquidity and price/quantity relationships in preferred embodiments of systems and methods of the present invention.
• the sixth section provides a detailed description of a DBAR Digital Options Exchange.
• the seventh section provides a detailed description of another embodiment of a DBAR Digital Options Exchange.
• the eighth section presents a network implementation of this DBAR Digital Options Exchange.
• the ninth section presents a structured instrument implementation of a demand-based market or auction.
• the tenth section presents a detailed description of the figures accompanying this specification.
• the eleventh section of the Detailed Description discusses some of the salient advantages of the methods and systems of the present invention.
• the twelfth section is a Technical Appendix providing additional information on the multistate allocation method of the present invention.
• the last section is a conclusion of the Detailed Description. More specifically, this Detailed Description of the Preferred Embodiments is organized as follows:
• a distribution of possible outcomes for an observable event is partitioned into defined ranges or states.
• one state always occurs because the states are mutually exclusive and collectively exhaustive.
• Traders in such an embodiment invest on their expectation of a return resulting from the occurrence of a particular outcome within a selected state. Such investments allow traders to hedge the possible outcomes of real-world events of economic significance represented by the states.
• unsuccessful trades or investments finance the successful trades or investments.
• the states for a given contingent claim preferably are defined in such a way that the states are mutually exclusive and form the basis of a probability distribution, namely, the sum of the probabilities of all the uncertain outcomes is unity.
• states corresponding to stock price closing values can be established to support a group of DBAR contingent claims by partitioning the distribution of possible closing values for the stock on a given future date into ranges.
• the distribution of future stock prices, discretized in this way into defined states forms a probability distribution in the sense that each state is mutually exclusive, and the sum of the probabilities of the stock closing within each defined state at the given date is unity.
• traders can simultaneously invest in selected multiple states within a given distribution, without immediately breaking up their investment to fit into each defined states selected for investment. Traders thus may place multi-state investments in order to replicate a desired distribution of retums from a group of contingent claims. This may be accomplished in a preferred embodiment of a DBAR exchange through the use of suspense accounts in which multi-state investments are tracked and reallocated periodically as retums adjust in response to amounts invested during a trading period. At the end of a given trading period, a multi-state investment may be reallocated to achieve the desired distribution of payouts based upon the final invested amounts across the distribution of states.
• the invested amount allocated to each of the selected states, and the corresponding respective returns, are finalized only at the closing of the trading period.
• An example of a multi-state investment illustrating the use of such a suspense account is provided in Example 3.1.2, below.
• Other examples of multi-state investments are provided in Section 6, below, which describes embodiments of the present invention that implement DBAR Digital Options Exchanges, (b) Allocating Returns:
• returns for each state are specified. In such an embodiment, while the amount invested for a given trade may be fixed, the return is adjustable.
• Determination of the returns for a particular state can be a simple function of the amount invested in that state and the total amount invested for all of the defined states for a group of contingent claims.
• alternate preferred embodiments can also accommodate methods of return determination that include other factors in addition to the invested amounts.
• the returns can be allocated based on the relative amounts invested in each state and also on properties of the outcome, such as the magnitude of the price changes in underlying securities.
• An example in section 3.2 below illustrates such an embodiment in the context of a securities portfolio.
• a group of DBAR contingent claims can be modeled as digital options, providing a predetermined or defined payout if they expire in-the-money, and providing no payout if they expire out-of-the-money.
• the investor or trader specifies a requested payout for a DBAR digital option, and selects the outcomes for which the digital option will expire "in the money," and can specify a limit on the amount they wish to invest in such a digital option.
• payout amount per digital option (or per an order for a digital option) is predetermined or defined
• investment amounts for each digital option are determined at the end of the trading period along with the allocation of payouts per digital option as a function of the requested payouts, selected outcomes (and limits on investment amounts, if any) for each of the digital options ordered during the trading period, and the total amount invested in the auction or market.
• This embodiment is described in Section 7 below, along with another embodiment of demand-based markets or auctions for digital options described in Section 6 below.
• Termination Criteria In a preferred embodiment of a method of the present invention, retums to investments in the plurality of defined states are allocated (and in another embodiment for DBAR digital options, investment amounts are determined) after the fulfillment of one or more predetermined termination criteria. In preferred embodiments, these criteria include the expiration of a "trading period" and the determination of the outcome of the relevant event after an "observation period.” In the trading period, traders invest on their expectation of a return resulting from the occurrence of a particular outcome within a selected defined state, such as the state that IBM stock will close between 120 and 125 on July 6, 1999.
• the duration of the trading period is known to all participants; returns associated with each state vary during the trading period with changes in invested amounts; and returns are allocated based on the total amount invested in all states relative to the amounts invested in each of the states as at the end of the trading period.
• the duration of the trading period can be unknown to the participants.
• the trading period can end, for example, at a randomly selected time. Additionally, the trading period could end depending upon the occurrence of some event associated or related to the event of economic significance, or upon the fulfillment of some criterion.
• the trading period could close after an nth catastrophic natural event (e.g., a fourth hurricane), or after a catastrophic event of a certain magnitude (e.g., an earthquake of a magnitude of 5.5 or higher on the Richter scale).
• the trading period could also close after a certain volume, amount, or frequency of trading is reached in a respective auction or market.
• the observation period can be provided as a time period during which the contingent events are observed and the relevant outcomes determined for the pu ⁇ ose of allocating retums. In a preferred embodiment, no trading occurs during the observation period.
• the expiration date, or "expiration,” of a group of DBAR contingent claims as used in this specification occurs when the termination criteria are fulfilled for that group of DBAR contingent claims.
• the expiration is the date, on or after the occurrence of the relevant event, when the outcome is ascertained or observed. This expiration is similar to well-known expiration features in traditional options or futures in which a future date, i.e., the expiration date, is specified as the date upon which the value of the option or future will be determined by reference to the value of the underlying financial product on the expiration date.
• a trading start date (“TSD”) and a trading end date ('TED”) refer to the beginning and end of a time period ("trading period") during which traders can make investments in a group of DBAR contingent claims.
• TSD trading start date
• 'TED trading end date
• the trading period the time during which a group of DBAR contingent claims is open for investment or trading , i.e., the difference between the TSD and TED, may be referred to as the trading period.
• one trading period's TED may coincide exactly with the subsequent trading period's TSD, or in other examples, trading periods may overlap.
• the relationship between the duration of a contingent claim, the number of trading periods employed for a given event, and the length and timing of the trading periods, can be arranged in a variety of ways to maximize trading or achieve other goals.
• at least one trading period occurs — that is, starts and ends ⁇ prior in time to the identification of the outcome of the relevant event.
• the trading period will most likely temporally precede the event defining the claim. This need not always be so, since the outcome of an event may not be known for some time thereby enabling trading periods to end (or even start) subsequent to the occurrence of the event, but before its outcome is known.
• a nearly continuous or "quasi-continuous" market can be made available by creating multiple trading periods for the same event, each having its own closing returns. Traders can make investments during successive trading periods as the retums change. In this way, profits-and- losses can be realized at least as frequently as in current derivatives markets. This is how derivatives traders currently are able to hedge options, futures, and other derivatives trades. In preferred embodiments of the present invention, traders may be able to realize profits and at varying frequencies, including more frequently than daily, (b) Market Efficiency and Fairness: Market prices reflect, among other things, the distribution of information available to segments of the participants transacting in the market. In most markets, some participants will be better informed than others.
• DBAR contingent claim markets In house-banking or traditional markets, market makers protect themselves from more informed counte ⁇ arties by increasing their bid-offer spreads. In preferred embodiments of DBAR contingent claim markets, there may be no market makers as such who need to protect themselves. It may nevertheless be necessary to put in place methods of operation in such markets in order to prevent manipulation of the outcomes underlying groups of DBAR contingent claims or the retums payable for various outcomes.
• One such mechanism is to introduce an element of randomness as to the time at which a trading period closes.
• Another mechanism to minimize the likelihood and effects of market manipulation is to introduce an element of randomness to the duration of the observation period. For example, a DBAR contingent claim might settle against an average of market closing prices during a time interval that is partially randomly determined, as opposed to a market closing price on a specific day.
• incentives can be employed in order to induce traders to invest earlier in a trading period rather than later.
• a DRF may be used which allocates slightly higher returns to earlier investments in a successful state than later investments in that state.
• an OPF may be used which determines slightly lower (discounted) prices for earlier investments than later investments. Earlier investments may be valuable in preferred embodiments since they work to enhance liquidity and promote more uniformly meaningful price information during the trading period.
• the dealer or exchange is substantially protected from primary market risk by the fundamental principle underlying the operation of the system ⁇ that returns to successful investments are funded by losses from unsuccessful investments. The credit risk in such preferred embodiments is distributed among all the market participants. If, for example, leveraged investments are permitted within a group of DBAR contingent claims, it may not be possible to collect the leveraged unsuccessful investments in order to distribute these amounts among the successful investments.
• One way to address this risk is to not allow leveraged investments within the group of DBAR contingent claims, which is a preferred embodiment of the system and methods of the present invention.
• traders in a DBAR exchange may be allowed to use limited leverage, subject to real-time margin monitoring, including calculation of a trader's impact on the overall level of credit risk in the DBAR system and the particular group of contingent claims.
• These risk management calculations should be significantly more tractable and transparent than the types of analyses credit risk managers typically perform in conventional derivatives markets in order to monitor counte ⁇ arty credit risk.
• An important feature of preferred embodiments of the present invention is the ability to provide diversification of credit risk among all the traders who invest in a group of DBAR contingent claims.
• traders make investments (in the units of value as defined for the group) in a common distribution of states in the expectation of receiving a return if a given state is determined to have occurred.
• all traders through their investments in defined states for a group of contingent claims, place these invested amounts with a central exchange or intermediary which, for each trading period, pays the retums to successful investments from the losses on unsuccessful investments.
• a given trader has all the other traders in the exchange as counte ⁇ arties, effecting a mutualization of counte ⁇ arties and counte ⁇ arty credit risk exposure. Each trader therefore assumes credit risk to a portfolio of counte ⁇ arties rather than to a single counte ⁇ arty.
• DBAR contingent claim and exchange of the present invention present four principal advantages in managing the credit risk inherent in leveraged transactions.
• a preferred form of DBAR contingent claim entails limited liability investing.
• Investment liability is limited in these embodiments in the sense that the maximum amount a trader can lose is the amount invested.
• the limited liability feature is similar to that of a long option position in the traditional markets.
• a short option position in traditional markets represents a potentially unlimited liability investment since the downside exposure can readily exceed the option premium and is, in theory, unbounded.
• a group of DBAR contingent claims of the present invention can easily replicate returns of a traditional short option position while maintaining limited liability.
• the limited liability feature of a group of DBAR contingent claims is a direct consequence of the demand-side nature of the market. More specifically, in preferred embodiments there are no sales or short positions as there are in the traditional markets, even though traders in a group of DBAR contingent claims may be able to attain the return profiles of traditional short positions. Second, in preferred embodiments, a trader within a group of
• DBAR contingent claims should have a portfolio of counte ⁇ arties as described above. As a consequence, there should be a statistical diversification of the credit risk such that the amount of credit risk borne by any one trader is, on average (and in all but exceptionally rare cases), less than if there were an exposure to a single counte ⁇ arty as is frequently the case in traditional markets. In other words, in preferred embodiments of the system and methods of the present invention, each trader is able to take advantage of the diversification effect that is well known in portfolio analysis.
• the entire distribution of margin loans, and the aggregate amount of leverage and credit risk existing for a group of DBAR contingent claims can be readily calculated and displayed to traders at any time before the fulfillment of all of the termination criteria for the group of claims.
• traders themselves may have access to important information regarding credit risk.
• DBAR contingent claim exchange provides more information about the distribution of possible outcomes than do traditional market exchanges.
• traders have more information about the distribution of future possible outcomes for real-world events, which they can use to manage risk more effectively.
• a significant part of credit risk is likely to be caused by market risk.
• the ability through an exchange or otherwise to control or at least provide information about market risk should have positive feedback effects for the management of credit risk.
• the trader can invest in the depreciate state, in proportion to the amount that had been invested in that state not counting the trader's "new" investments.
• a market or exchange for groups of DBAR contingent claims market according to the invention is not designed to establish a counte ⁇ arty-driven or order-matched market. Buyers' bids and sellers' offers do not need to be "crossed.” As a consequence of the absence of a need for an order crossing network, preferred embodiments of the present invention are particularly amenable to large-scale electronic network implementation on a wide area network or a private network (with, e.g., dedicated circuits) or the public Internet, for example.
• Preferred embodiments of an electronic network-based embodiment of the method of trading in accordance with the invention include one or more of the following features.
• (b) Interest and Margin Accounts Trader accounts are maintained using electronic methods to record interest paid to traders on open DBAR contingent claim balances and to debit trader balances for margin loan interest. Interest is typically paid on outstanding investment balances for a group of DBAR contingent claims until the fulfillment of the termination criteria. Interest is typically charged on outstanding margin loans while such loans are outstanding. For some contingent claims, trade balance interest can be imputed into the closing returns of a trading period.
• Suspense Accounts These accounts relate specifically to investments which have been made by traders, during trading periods, simultaneously in multiple states for the same event. Multi-state trades are those in which amounts are invested over a range of states so that, if any of the states occurs, a return is allocated to the trader based on the closing return for the state which in fact occurred.
• DBAR digital options of the present invention, described in Section 6, provide other examples of multi-state trades.
• a trader can, of course, simply break-up or divide the multi-state investment into many separate, single-state investments, although this approach might require the trader to keep rebalancing his portfolio of single state investments as returns adjust throughout the trading period as amounts invested in each state change.
• Multi-state trades can be used in order to replicate any arbitrary distribution of payouts that a trader may desire. For example, a trader might want to invest in all states in excess of a given value or price for a security underlying a contingent claim, e.g., the occurrence that a given stock price exceeds 100 at some future date. The trader might also want to receive an identical payout no matter what state occurs among those states.
• Suspense accounts can be employed so that the exchange, rather than the trader, is responsible for rebalancing the portfolio of single-state investments so that, at the end of the trading period, the amount of the multi-state investment is allocated among the constituent states in such a way so as to replicate the trader's desired distribution of payouts.
• Example 3.1.2 below illustrates the use of suspense accounts for multi-state investments.
• Each trader may have an account that may be authenticated using authenticating data.
• Real-Time Market Data Server Real-time market data may be provided to support frequent calculation of returns and to ascertain the outcomes during the observation periods.
• (g) Real-Time Calculation Engine Server Frequent calculation of market returns may increase the efficient functioning of the market. Data on coupons, dividends, market interest rates, spot prices, and other market data can be used to calculate opening returns at the beginning of a trading period and to ascertain observable events during the observation period. Sophisticated simulation methods may be required for some groups of DBAR contingent claims in order to estimate expected retums. at least at the start of a trading period, (h) Real-Time Risk Management Server: In order to compute trader margin requirements, expected retums for each trader should be computed frequently. Calculations of "value-at-risk" in traditional markets can involve onerous matrix calculations and Monte Carlo simulations.
• Risk calculations in preferred embodiments of the present invention are simpler, due to the existence of information on the expected returns for each state. Such information is typically unavailable in traditional capital and reinsurance markets, (i) Market Data Storage: A DBAR contingent claims exchange in accordance with the invention may generate valuable data as a byproduct of its operation. These data are not readily available in traditional capital or insurance markets. In a preferred embodiment of the present invention, investments may be solicited over ranges of outcomes for market events, such as the event that the 30-year U.S. Treasury bond will close on a given date with a yield between 6.10% and 6.20%. Investment in the entire distribution of states generates data that reflect the expectations of traders over the entire distribution of possible outcomes.
• (j) Market Evaluation Server Preferred embodiments of the method of the present invention include the ability to improve the market's efficiency on an ongoing basis. This may readily be accomplished, for example, by comparing the predicted returns on a group of DBAR contingent claims retums with actual realized outcomes. If investors have rational expectations, then DBAR contingent claim returns will, on average, reflect trader expectations, and these expectations will themselves be realized on average. In preferred embodiments, efficiency measurements are made on defined states and investments over the entire distribution of possible outcomes, which can then be used for statistical time series analysis with realized outcomes.
• the network implementation of the present invention may therefore include analytic servers to perform these analyses for the pu ⁇ ose of continually improving the efficiency of the market. 2.
• a group of a DBAR contingent claims related to an observable event includes one or more of the following features:
• the events are events of economic significance.
• the possible outcomes can typically be units of measurement associated with the event, e.g., an event of economic interest can be the closing index level of the S&P 500 one month in the future, and the possible outcomes can be entire range of index levels that are possible in one month.
• the states are defined to correspond to one or more of the possible outcomes over the entire range of possible outcomes, so that defined states for an event form a countable and discrete number of ranges of possible outcomes, and are collectively exhaustive in the sense of spanning the entire range of possible outcomes.
• possible outcomes for the S&P 500 can range from greater than 0 to infinity (theoretically), and a defined state could be those index values greater than 1000 and less than or equal to 1100. In such preferred embodiments, exactly one state occurs when the outcome of the relevant event becomes known.
• a DBAR contingent claim group defines the acceptable units of trade or value for the respective claim. Such units may be dollars, barrels of oil, number of shares of stock, or any other unit or combination of units accepted by traders and the exchange for value.
• DBAR contingent claims defines the means by which the outcome of the relevant events is determined. For example, the level that the S&P 500
• Index actually closed on a predetermined date would be an outcome observation which would enable the determination of the occurrence of one of the defined states.
• a closing value of 1050 on that date, for instance, would allow the determination that the state between 1000 and 1100 occurred.
• (4) The specification of a DRF which takes the traded amount for each trader for each state across the distribution of states as that distribution exists at the end of each trading period and calculates payouts for each investments in each state conditioned upon the occurrence of each state. In preferred embodiments, this is done so that the total amount of payouts does not exceed the total amount invested by all the traders in all the states.
• DRF can be used to show payouts should each state occur during the trading period, thereby providing to traders information as to the collective level of interest of all traders in each state.
• contract is typically associated with one distribution of states.
• the distribution will typically be defined for events of economic interest for investment by traders having the expectation of a return for a reduction of ⁇ sk ("hedging"), or for an increase of ⁇ sk ("speculation").
• the dist ⁇ bution can be based upon the values of stocks, bonds, futures, and foreign exchange rates. It can also be based upon the values of commodity indices, economic statistics (e.g., consumer p ⁇ ce inflation monthly reports), property-casualty losses, weather patterns for a certain geographical region, and any other measurable or observable occurrence or any other event in which traders would not be economically indifferent even in the absence of a trade on the outcome of the event.
• DBAR Claim Notation The following notation is used in this specification to facilitate further desc ⁇ ption of DBAR contingent claims: m represents the number of traders for a given group of DBAR contingent claims n represents the number of states for a given dist ⁇ bution associated with a given group of DBAR contingent claims
• A represents a mat ⁇ x with m rows and n columns, where the element at the I- th row and j-th column, ⁇ , ⁇ , is the amount that trader I has invested in state j in the expectation of a return should state j occur
• LI represents a mat ⁇ x with n rows and n columns where element ⁇ , j is the payout per unit of investment in state l should state j occur ("unit payouts")
• P represents a mat ⁇ x with m rows and n columns, where the element at the I- th row and j-th column, p, j , is the payout to be made to trader I should state j occur, i.e., P is equal to the mat ⁇ x product A*FI
• T represents the total traded amount over thitrid entire distribution of states, i.e.,
• f(A,X) represents the exchange's transaction fee, which can depend on the entire distribution of traded amounts placed across all the states as well as other factors, X, some of which are identified below. For reasons of brevity, for the remainder of this specification unless otherwise stated, the transaction fee is assumed to be a fixed percentage of the total amount traded over all the states.
• c p represents the interest rate charged on margin loans.
• c r represents the interest rate paid on trade balances
• t represents time from the acceptance of a trade or investment to the fulfillment of all of the termination criteria for the group of DBAR contingent claims, typically expressed in years or fractions thereof.
• X represents other information upon which the DRF or transaction fee can depend such as information specific to an investment or a trader, including for example the time or size of a * trade.
• a DRF is a function that takes the traded amounts over the distribution of states for a given group of DBAR contingent claims, the transaction fee schedule, and, conditional upon the occurrence of each state, computes the payouts to each trade or investment placed over the distribution of states. In notation, such a DRF is:
• the m traders who have placed trades across the n states, as represented in matrix A, will receive payouts as represented in matrix P should state i occur, also, taking into account the transaction fee f and other factors X.
• the payouts identified in matrix P can be represented as the product of (a) the payouts per unit traded for each state should each state occur, as identified in the matrix fL and (b) the matrix A which identifies the amounts traded or invested by each trader in each state.
• the following notation may be used to indicate that, in preferred embodiments, payouts should not exceed the total amounts invested less the transaction fee, irrespective of which state occurs:
• a preferred embodiment of a group of DBAR contingent claims of the present invention is self-financing in the sense that for any state, the payouts plus the transaction fee do not exceed the inputs (i.e., the invested amounts).
• the DRF may depend on factors other than the amount of the investment and the state in which the investment was made. For example, a payout may depend upon the magnitude of a change in the observed outcome for an underlying event between two dates (e.g., the change in price of a security between two dates).
• the DRF may allocate higher payouts to traders who initiated investments earlier in the trading period than traders who invested later in the trading period, thereby providing incentives for liquidity earlier in the trading period.
• the DRF may allocate higher payouts to larger amounts invested in a given state than to smaller amounts invested for that state, thereby providing another liquidity incentive.
• a preferred embodiment of a DRF should effect a meaningful reallocation of amounts invested across the distribution of states upon the occurrence of at least one state.
• Groups of DBAR contingent claims of the present invention are discussed in the context of a canonical DRF, which is a preferred embodiment in which the amounts invested in states which did not occur are completely reallocated to the state which did occur (less any transaction fee).
• the present invention is not limited to a canonical DRF, and many other types of DRFs can be used and may be preferred to implement a group of DBAR contingent claims.
• another DRF preferred embodiment allocates half the total amount invested to the outcome state and rebates the remainder of the total amount invested to the states which did not occur.
• a DRF would allocate some percentage to an occurring state, and some other percentage to one or more "nearby" or "adjacent" states with the bulk of the non-occurring states receiving zero payouts.
• Section 7 decribes an OPF for DBAR digital options which includes a DRF and determines investment amounts per investment or order along with allocating returns.
• Other DRFs will be apparent to those of skill in the art from review of this specification and practice of the present invention.
• the units of investments and payouts in systems and methods of the present invention may be units of currency, quantities of commodities, numbers of shares of common stock, amount of a swap transaction or any other units representing economic value.
• the investments or payouts be in units of currency or money (e.g., U.S. dollars) or that the payouts resulting from the DRF be in the same units as the investments.
• the same unit of value is used to represent the value of each investment, the total amount of all investments in a group of DBAR contingent claims, and the amounts invested in each state.
• OPF OPF
• traded amounts and payouts may be some combination of units, such as, for example, a combination of commodities, currencies, and number of shares.
• traders need not physically deposit or receive delivery of the value units, and can rely upon the DBAR contingent claim exchange to convert between units for the pu ⁇ oses of facilitating efficient trading and payout transactions.
• a DBAR contingent claim might be defined in such a way so that investments and payouts are to be made in ounces of gold.
• a trader can still deposit currency, e.g., U.S.
• the exchange and the exchange can be responsible for converting the amount invested in dollars into the correct units, e.g., gold, for the pu ⁇ oses of investing in a given state or receiving a payout.
• a U.S. dollar is typically used as the unit of value for investments and payouts.
• This invention is not limited to investments or payouts in that value unit.
• the exchange preferably converts the amount of each investment, and thus the total of the investments in a group of DBAR contingent claims, into a single unit of value
• Example 3.1.20 illustrates a group of DBAR contingent claims in which investments and payouts are in units of quantities of common stock shares.
• Example 3.1.20 illustrates a group of DBAR contingent claims in which investments and payouts are in units of quantities of common stock shares.
• Example 3.1.20 illustrates a group of DBAR contingent claims in which investments and payouts are in units of quantities of common stock shares.
• a canonical DRF is a type of DRF which has the following property: upon the occurrence of a given state i, investors who have invested in that state receive a payout per unit invested equal to (a) the total amount traded for all the states less the transaction fee, divided by (b) the total amount invested in the occurring state.
• a canonical DRF may employ a transaction fee which may be a fixed percentage of the total amount traded, T, although other transaction fees are possible. Traders who made investments in states which not did occur receive zero payout. Using the notation developed above:
• the unit payout matrix is:
• the payout matrix is the total amount invested less the transaction fee, multiplied by a diagonal matrix which contains the inverse of the total amount invested in each state along the diagonal, respectively, and zeroes elsewhere.
• T the total amount invested by all m traders across all n states, and T;
• T the total amount invested in state i
• A the matrix A, which contains the amount each trader has invested in each state:
• T i [ T m m * A* B n (i) *
• B n (i) is a column vector of dimension n which has a 1 at the i-th row and zeroes elsewhere.
• n 5 as an example, the canonical DRF described above has a unit payout matrix which is a function of the amounts traded across the states and the transaction fee: 1
• the actual payout matrix in the defined units of value for the group of DBAR contingent claims (e.g., dollars), is the product of the m x n traded amount matrix A and the n x n unit payout matrix ⁇ , as defined above:
• payout matrix as defined above is the matrix product of the amounts traded as contained in the matrix A and the unit payout matrix 11, which is itself a function of the matrix A and the transaction fee, f.
• the expression is labeled CDRF for
• any change to the matrix A will generally have an effect on any given trader's payout, both due to changes in the amount invested, i.e., a direct effect through the matrix A in the CDRF, and changes in the unit payouts, i.e., an indirect effect since the unit payout matrix ⁇ is itself a function of the traded amount matrix A.
• DBAR digital options described in Section 6, are an example of an investment with a desired payout distribution should one or more specified states occur.
• Such a payout distribution could be denoted Pi,*, which is a row corresponding to trader i in payout matrix P.
• Such a trader may want to know how much to invest in contingent claims corresponding to a given state or states in order to achieve this payout distribution.
• the amount or amounts to be invested across the distribution of states for the CDRF, given a payout distribution can be obtained by inverting the expression for the CDRF and solving for the traded amount matrix A:
• the -1 superscript on the unit payout matrix denotes a matrix inverse.
• CDRF 2 does not provide an explicit solution for the traded amount matrix A, since the unit payout matrix ⁇ is itself a function of the traded amount matrix.
• CDRF 2 typically involves the use of numerical methods to solve m simultaneous quadratic equations. For example, consider a trader who would like to know what amount, ⁇ , should be traded for a given state i in order to achieve a desired payout of p. Using the "forward" expression to compute payouts from traded amounts as in CDRF above yields the following equation:
• a simplified example illustrates the use of the CDRF with a group of DBAR contingent claims defined over two states (e.g., states "1" and "2") in which four traders make investments.
• states e.g., states "1" and "2”
• the following assumptions are made: (1) the transaction fee, f, is zero; (2) the investment and payout units are both dollars; (3) trader 1 has made investments in the amount of $5 in state 1 and $10 state 2; and (4) trader 2 has made an investment in the amount of $7 for state 1 only.
• the traded amount matrix A which as 4 rows and 2 columns, and the unit payout matrix FI which has 2 rows and 2 columns, would be denoted as follows: 5 10
• the payout matrix P which contains the payouts in dollars for each trader should each state occur is, the product of A and FI:
• the first row of P corresponds to payouts to trader 1 based on his investments and the unit payout matrix. Should state 1 occur, trader lwill receive a payout of $9,167 and will receive $22 should state 2 occur. Similarly, trader 2 will receive $12,833 should state 1 occur and $0 should state 2 occur (since trader 2 did not make any investment in state 2). In this illustration, traders 3 and 4 have $0 payouts since they have made no investments. In accordance with the expression above labeled "DRF Constraint," the total payouts to be made upon the occurrence of either state is less than or equal to the total amounts invested.
• the CDRF in this example is self-financing so that total payouts plus the transaction fee (assumed to be zero in this example) do not exceed the total amounts invested, irrespective of which state occurs.
• payouts are made based upon the invested amounts A, and therefore are also based on the unit payout matrix ri(A,f(A)), given the distribution of traded amounts as they exist at the end of the trading period.
• ri(A,f(A) unit payout matrix
• the suspense account can be used to solve CDRF 2, for example:
• the solution of this expression will yield the amounts that traders 3 and 4 need to invest in for contingent claims corresponding to states 1 and 2 to in order to achieve their desired payout distributions, respectively. This solution will also finalize the total investment amount so that traders 1 and 2 will be able to determine their payouts should either state occur.
• This solution can be achieved using a computer program that computes an investment amount for each state for each trader in order to generate the desired payout for that trader for that state. In a preferred embodiment, the computer program repeats the process iteratively until the calculated investment amounts converge, i.e., so that the amounts to be invested by traders 3 and 4 no longer materially change with each successive iteration of the computational process.
• the resulting payout matrix P is the product of A and Y ⁇ and is equal to:
• returns which represent the percentage return per unit of investment are closely related to payouts. Such returns are also closely related to the notion of a financial return familiar to investors. For example, if an investor has purchased a stock for $100 and sells it for $110, then this investor has realized a return of 10% (and a payout of $110).
• the unit return, r hail should state i occur may be expressed as follows:
• the return per unit investment in a state that occurs is a function of the amount invested in that state, the amount invested in all the other states and the exchange fee.
• the unit return is -100% for a state that does not occur, i.e., the entire amount invested in the expectation of receiving a return if a state occurs is forfeited if that state fails to occur.
• a -100% return in such an event has the same return profile as, for example, a traditional option expiring "out of the money.” When a traditional option expires out of the money, the premium decays to zero, and the entire amount invested in the option is lost.
• a payout is defined as one plus the return per unit invested in a given state multiplied by the amount that has been invested in that state.
• the sum of all payouts P s , for a group of DBAR contingent claims corresponding to all n possible states can be expressed as follows:
• the payout Ps may be found for the occurrence of state i by substituting the above expres ions for the unit return in any state:
• the aggregate payout to all of the traders as a whole is one minus the transaction fee paid to the exchange (expressed in this preferred embodiment as a percentage of total investment across all the states), multiplied by the total amount invested across all the states for the group of DBAR contingent claims.
• transaction fees can be implemented.
• the transaction fee might have a fixed component for some level of aggregate amount invested and then have either a sliding or fixed percentage applied to the amount of the investment in excess of this level.
• Other methods for determining the transaction fee are apparent to those of skill in the art, from this specification or based on practice of the present invention.
• the total distribution of amounts invested in the various states also implies an assessment by all traders collectively of the probabilities of occurrence of each state.
• the expected return E(r, ) for an investment in a given state i may be expressed as the probability weighted sum of the retums:
• the expected return E(r,) across all states is equal to the transaction costs of trading, i.e., on average, all traders collectively earn returns that do not exceed the costs of trading.
• E(r,) equals the transaction fee, -f
• the probability of the occurrence of state i implied by matrix A is computed to be:
• the implied probability of a given state is the ratio of the amount invested in that state divided by the total amount invested in all states. This relationship allows traders in the group of DBAR contingent claims (with a canonical DRF) readily to calculate the implied probability which traders attach to the various states.
• Information of interest to a trader typically includes the amounts invested per state, the unit return per state, and implied state probabilities.
• An advantage of the DBAR exchange of the present invention is the relationship among these quantities. In a preferred embodiment, if the trader knows one, the other two can be readily determined.
• the payout to state i may be expressed as: p - — ⁇ * *a
• the amount to be invested to generate a desired payout is approximately equal to the ratio of the total amount invested in state i to the total amount invested in all states, multiplied by the desired payout. This is equivalent to the implied probability multiplied by the desired payout.
• a DBAR Range Derivative is a type of group of DBAR contingent claims implemented using a canonical DRF described above (although a DBAR range derivative can also be implemented, for example, for a group of DBAR contingent claims, including DBAR digital options, based on the same ranges and economic events established below using, e.g., a non-canonical DRF and an OPF).
• a range of possible outcomes associated with an observable event of economic significance is partitioned into defined states.
• the states are defined as discrete ranges of possible outcomes so that the entire distribution of states covers all the possible outcomes — that is, the states are collectively exhaustive.
• states are preferably defined so as to be mutually exclusive as well, meaning that the states are defined in such a way so that exactly one state occurs. If the states are defined to be both mutually exclusive and collectively exhaustive, the states form the basis of a probability distribution defined over discrete outcome ranges. Defining the states in this way has many advantages as described below, including the advantage that the amount which traders invest across the states can be readily converted into implied probabilities representing the collective assessment of traders as to the likelihood of the occurrence of each state.
• the system and methods of the present invention may also be applied to determine projected DBAR RD returns for various states at the beginning of a trading period. Such a determination can be, but need not be, made by an exchange.
• the distribution of invested amounts at the end of a trading period determines the returns for each state, and the amount invested in each state is a function of trader preferences and probability assessments of each state. Accordingly, some assumptions typically need to be made in order to determine preliminary or projected returns for each state at the beginning of a trading period.
• An illustration is provided to explain further the operation of DBAR RDs. In the following illustration, it is assumed that all traders are risk neutral so that implied probabilities for a state are equal to the actual probabilities, and so that all traders have identical probability assessments of the possible outcomes for the event defining the contingent claim.
• the event forming the basis for the contingent claims is taken to be a closing price of a security, such as a common stock, at some future date; and the states, which represent the possible outcomes of the level of the closing price, are defined to be distinct, mutually exclusive and collectively exhaustive of the range of (possible) closing prices for the security.
• ⁇ represents a given time during the trading period at which traders are making investment decisions
• ⁇ represents the time corresponding to the expiration of the contingent claim
• V ⁇ represents the price of underlying security at time ⁇
• V 0 represents the price of underlying security at time ⁇
• Z( ⁇ , ⁇ ) represents the present value of one unit of value payable at time ⁇ evaluated at time ⁇
• D( ⁇ , ⁇ ) represents dividends or coupons payable between time ⁇ and ⁇ ⁇ t represents annualized volatility of natural logarithm retums of the underlying security dz represents the standard normal variate Traders make choices at a representative time, ⁇ , during a trading period which is open, so that time ⁇ is temporally subsequent to the current trading period's TSD.
• the defined states for the group of contingent claims for the final closing price V ⁇ are constructed by discretizing the full range of possible prices into possible mutually exclusive and collectively exhaustive states. The technique is similar to forming a histogram for discrete countable data.
• the endpoints of each state can be chosen, for example, to be equally spaced, or of varying spacing to reflect the reduced likehood of extreme outcomes compared to outcomes near the mean or median of the distribution. States may also be defined in other manners apparent to one of skill in the art.
• the lower endpoint of a state can be included and the upper endpoint excluded, or vice versa.
• the states are defined (as explained below) to maximize the attractiveness of investment in the group of DBAR contingent claims, since it is the invested amounts that ultimately determine the retums that are associated with each defined state.
• the procedure of defining states can be accomplished by assuming lognormality, by using statistical estimation techniques based on historical time series data and cross-section market data from options prices, by using other statistical distributions, or according to other procedures known to one of skill in the art or learned from this specification or through practice of the present invention. For example, it is quite common among derivatives traders to estimate volatility parameters for the pu ⁇ ose of pricing options by using the econometric techniques such as GARCH. Using these parameters and the known dividend or coupons over the time period from ⁇ to ⁇ , for example, the states for a DBAR RD can be defined.
• a lognormal distribution is chosen for this illustration since it is commonly employed by derivatives traders as a distributional assumption for the pu ⁇ ose of evaluating the prices of options and other derivative securities. Accordingly, for pu ⁇ oses of this illustration it is assumed that all traders agree that the underlying distribution of states for the security are lognormally distributed such that:
• the assumptions and calculations reflected in the expressions presented above can also be used to calculate indicative returns ("opening retums"), r, at a beginning of the trading period for a given group of DBAR contingent claims.
• the calculated opening returns are based on the exchange's best estimate of the probabilities for the states defining the claim and therefore may provide good indications to traders of likely retums once trading is underway.
• a very small number of value units may be used in each state to initialize the contract or group of contingent claims.
• DBAR range derivatives and other contingent claims serve to illustrate their operation, their usefulness in connection with a variety of events of economic significance involving inherent risk or uncertainty, the advantages of exchanges for groups of DBAR contingent claims, and, more generally, systems and methods of the present invention.
• Sections 6 and 7 also provide examples of DBAR contingent claims of the present invention that provide profit and loss scenarios comparable to those provided by digital options in conventional options markets, and that can be based on any of the variety of events of economic signficance described in the following examples of DBAR RDs.
• a state is defined to include a range of possible outcomes of an event of economic significance.
• the event of economic significance for any DBAR auction or market can be, for example, an underlying economic event (e.g., price of stock) or a measured parameter related to the underlying economic event (e.g., a measured volatility of the price of stock).
• a curved brace “(" or ")” denotes strict inequality (e.g., "greater than” or “less than,” respectively ) and a square brace “]” or “[” shall denote weak inequality (e.g., "less than or equal to” or “greater than or equal to,” respectively).
• the exchange transaction fee, f is zero.
• MSFT Microsoft Co ⁇ oration Common Stock
• the predetermined termination criteria are the investment in a contingent claim during the trading period and the closing of the market for Microsoft common stock on 8/19/99.
• the amount invested for any given state is inversely related to the unit return for that state.
• traders can invest in none, one or many states. It may be possible in preferred embodiments to allow traders efficiently to invest in a set, subset or combination of states for the pu ⁇ oses of generating desired distributions of payouts across the states. In particular, traders may be interested in replicating payout distributions which are common in the traditional markets, such as payouts corresponding to a long stock position, a short futures position, a long option straddle position, a digital put or digital call option. If in this Example 3.1.1 a trader desired to hedge his exposure to extreme outcomes in MSFT stock, then the trader could invest in states at each end of the distribution of possible outcomes.
• a trader might decide to invest $100,000 in states encompassing prices from $0 up to and including $83 (i.e., (0,83]) and another $100,000 in states encompassing prices greater than $86.50 (i.e., (86.5, ⁇ ]).
• the trader may further desire that no matter what state actually occurs within these ranges (should the state occur in either range) upon the fulfillment of the predetermined termination criteria, an identical payout will result.
• a multi-state investment is effectively a group of single state investments over each multi-state range, where an amount is invested in each state in the range in proportion to the amount previously invested in that state.
• each multi-state investment may be allocated to its constituent states on a pro-rata or proportional basis according to the relative amounts invested in the constituent states at the close of trading. In this way, more of the multi-state investment is allocated to states with larger investments and less allocated to the states with smaller investments.
• Other desired payout distributions across the states can be generated by allocating the amount invested among the constituent states in different ways so as achieve a trader's desired payout distribution.
• a trader may select, for example, both the magnitude of the payouts and how those payouts are to be distributed should each state occur and let the DBAR exchange's multi-state allocation methods determine (1) the size of the amount invested in each particular constituent state; (2) the states in which investments will be made, and (3) how much of the total amount to be invested will be invested in each of the states so determined. Other examples below demonstrate how such selections may be implemented.
• a previous multi-state investment is reallocated to its constituent states periodically as the amounts invested in each state (and therefore returns) change during the trading period.
• a final reallocation is made of all the multi-state investments.
• a suspense account is used to record and reallocate multi-state investments during the course of trading and at the end of the trading period.
• Table 3.1.1-2 shows how the multi-state investments in the amount of $100,000 each could be allocated according to a preferred embodiment to the individual states over each range in order to achieve a payout for each multi-state range which is identical regardless of which state occurs w'thin each range.
• the multi-state investments are allocated in proportion to the previously invested amount in each state, and the multi-state investments marginally lower returns over (0,83] and (86.5, ⁇ ], but marginally increase returns over the range (83, 86.5], as expected.
• the payout for the constituent state [86.5,87] would receive a payout of $399.80 if the stock price fill in that range after the fulfillment of all of the predetermined termination criteria.
• each constituent state over the range [86.5, ⁇ ] would receive a payout of $399.80, no matter which of those states occurs.
• Groups of DBAR contingent claims can be structured using the system and methods of the present invention to provide market participants with a fuller, more precise view of the price for risks associated with a particular equity.
• Example 3.1.2 Multiple Multi-State Investments If numerous multi-state investments are made for a group of DBAR contingent claims, then in a preferred embodiment an iterative procedure can be employed to allocate all of the multi-state investments to their respective constituent states.
• the goal would be to allocate each multi-state investment in response to changes in amounts invested during the trading period, and to make a final allocation at the end of the trading period so that each multi-state investment generates the payouts desired by the respective trader.
• the process of allocating multi-state investments can be iterative, since allocations depend upon the amounts traded across the distribution of states at any point in time. As a consequence, in preferred embodiments, a given distribution of invested amounts will result in a certain allocation of a multi-state investment.
• each multi-state allocation is re-performed so that, after a number of iterations through all of the pending multi-state investments, both the amounts invested and their allocations among constituent states in the multi-state investments no longer change with each successive iteration and a convergence is achieved.
• convergence when convergence is achieved, further iteration and reallocation among the multi-state investments do not change any multi-state allocation, and the entire distribution of amounts invested across the states remains stable and is said to be in equilibrium.
• Computer code as illustrated in Table 1 above or related code readily apparent to one of skill in the art, can be used to implement this iterative procedure.
• a simple example demonstrates a preferred embodiment of an iterative procedure that may be employed.
• a preferred embodiment of the following assumptions are made: (i) there are four defined states for the group of DBAR contingent claims; (ii) prior to the allocation of any multi-state investments, $100 has been invested in each state so that the unit return for each of the four states is 3; (iii) each desires that each constituent state in a multi-state investment provides the same payout regardless of which constituent state actually occurs; and (iv) that the following other multi-state investments have been made:
• trade number 1001 in the first row is a multi-state investment of $100 to be allocated among constituent states 1 and 2
• trade number 1002 in the second row is another multi-state investment in the amount of $50 to be allocated among constituent states 1, 3, and 4; etc.
• each row shows the allocation among the constituent states of the multi- state investment entered into the corresponding row of Table 3.1.2-1, the first row of Table 3.1.2-2 that investment number 1001 in the amount of $100 has been allocated $73.8396 to state 1 and the remainder to state 2.
• the multi-state allocations identified above result in payouts to traders which are desired by the traders —that is, in this example the desired payouts are the same regardless of which state occurs among the constituent states of a given multi-state investment.
• the unit returns for each state are:
• Consideration of Investment 1022 in this example illustrates the uniformity of payouts for each state in which an investment is made (i.e., states 1, 3 and 4).
• Example 3.1.3 Alternate Price Distributions Assumptions regarding the likely distribution of traded amounts for a group of DBAR contingent claims may be used, for example, to compute returns for each defined state per unit of amount invested at the beginning of a trading period ("opening retums"). For various reasons, the amount actually invested in each defined state may not reflect the assumptions used to calculate the opening returns. For instance, investors may speculate that the empirical distribution of retums over the time horizon may differ from the no- arbitrage assumptions typically used in option pricing. Instead of a lognormal distribution, more investors might make investments expecting retums to be significantly positive rather than negative (perhaps expecting favorable news). In Example 3.1.1, for instance, if traders invested more in states above $85 for the price of MSFT common stock, the retums to states below $85 could therefore be significantly higher than returns to states above $85.
• Table 3.1.3-1 The type of complex distribution illustrated in Table 3.1.3-1 is prevalent in the traditional markets. Derivatives traders, actuaries, risk managers and other traditional market participants typically use sophisticated mathematical and analytical tools in order to estimate the statistical nature of future distributions of risky market outcomes. These tools often rely on data sets (e.g., historical time series, options data) that may be incomplete or unreliable.
• An advantage of the systems and methods of the present invention is that such analyses from historical data need not be complicated, and the full outcome distribution for a group of DBAR contingent claims based on any given event is readily available to all traders and other interested parties nearly instantaneously after each investment.
• Example 3.1.4 States Defined For Return Uniformity It is also possible in preferred embodiments of the present invention to define states for a group of DBAR contingent claims with irregular or unevenly distributed intervals, for example, to make the traded amount across the states more liquid or uniform. States can be constructed from a likely estimate of the final distribution of invested amounts in order to make the likely invested amounts, and hence the returns for each state, as uniform as possible across the distribution of states. The following table illustrates the freedom, using the event and trading period from Example 3.1.1, to define states so as to promote equalization of the amount likely to be invested in each state.
• Example 3.1.5 Government Bond -- Uniformly Constructed States The event, defined states, predetermined termination criteria and other relevant data for an illustrative group of DBAR contingent claims based on a U.S. Treasury Note are set forth below:
• Example 3.1.5 and Table 3.1.5-1 illustrate how readily the methods and systems of the present invention may be adapted to sources of risk, whether from stocks, bonds, or insurance claims.
• Table 3.1.5-1 also illustrates a distribution of defined states which is irregularly spaced ⁇ in this case finer toward the center of the distribution and coarser at the ends ⁇ in order to increase the amount invested in the extreme states.
• One of the advantages of the system and methods of the present invention is the ability to construct groups of DBAR contingent claims based on multiple events and their inter-relationships. For example, many index fund money managers often have a fundamental view as to whether indices of high quality fixed income securities will outperform major equity indices. Such opinions normally are contained within a manager's model for allocating funds under management between the major asset classes such as fixed income securities, equities, and cash.
• This Example 3.1.6 illustrates the use of a preferred embodiment of the systems and methods of the present invention to hedge the real-world event that one asset class will outperform another.
• the illustrative distribution of investments and calculated opening returns for the group of contingent claims used in this example are based on the assumption that the levels of the relevant asset-class indices are jointly lognormally distributed with an assumed correlation.
• traders are able to express their views on the co-movements of the underlying events as captured by the statistical correlation between the events.
• the assumption of a joint lognormal distribution means that the two underlying events are distributed as follows:
• Table 3.1.6 shows the illustrative distribution of state returns over the defined states for the joint outcomes based on this information, with the defined states as indicated .
• each cell contains the unit returns to the joint state reflected by the row and column entries.
• the unit return to investments in the state encompassing the joint occurrence of the JPMGBI closing on expiration at 249 and the SP500 closing at 1380 is 88. Since the correlation between two indices in this example is assumed to be 0.5, the probability both indices will change in the same direction is greater that the probability that both indices will change in opposite directions.
• the returns illustrated in Table 3.1.6-1 could be calculated as opening indicative retums at the start of each trading period based on an estimate of what the closing retums for the trading period are likely to be. These indicative or opening returns can serve as an "anchor point" for commencement of trading in a group of DBAR contingent claims. Of course, actual trading and trader expectations may induce substantial departures from these indicative values.
• Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on multiple underlying events or variables and their inter-relationships. Market participants often have views about the joint outcome of two underlying events or assets. Asset allocation managers, for example, are concerned with the relative performance of bonds versus equities.
• Joint Performance Demand-based markets or auctions can be structured to trade
• DBAR contingent claims including, for example, digital options, based on the joint performance or observation of two different variables.
• digital options traded in a demand-based market or auction can be based on an underlying event defined as the joint observation of non-farm payrolls and the unemployment rate.
• Example 3.1.7: Corporate Bond Credit Risk Groups of DBAR contingent claims can also be constructed on credit events, such as the event that one of the major credit rating agencies (e.g., Standard and Poor's, Moodys) changes the rating for some or all of a corporation's outstanding securities.
• Indicative returns at the outset of trading for a group of DBAR contingent claims oriented to a credit event can readily be constructed from publicly available data from the rating agencies themselves.
• Table 3.1.7-1 contains indicative returns for an assumed group of DBAR contingent claims based on the event that a corporation's Standard and Poor's credit rating for a given security will change over a certain period of time.
• states are defined using the Standard and Poor's credit categories, ranging from AAA to D (default).
• the indicative returns are calculated using historical data on the frequency of the occurrence of these defined states.
• a transaction fee of 1% is charged against the aggregate amount invested in the group of DBAR contingent claims, which is assumed to be $100 million.
• Example 3.1.7-1 the historical probabilities over the mutually exclusive and collectively exhaustive states sum to unity.
• the transaction fee affects the probability implied for each state from the unit return for that state. Actual trading is expected almost always to alter illustrative indicative retums based on historical empirical data.
• This Example 3.1.7 indicates how efficiently groups of DBAR contingent claims can be constructed for all traders or firms exposed to particular credit risk in order to hedge that risk. For example, in this Example, if a trader has significant exposure to the A- rated bond issue described above, the trader could want to hedge the event corresponding to a downgrade by Standard and Poor's.
• this trader may be particularly concerned about a downgrade corresponding to an issuer default or "D" rating.
• the empirical probabilities suggest a payout of approximately $1,237 for each dollar invested in that state. If this trader has $100,000,000 of the corporate issue in his portfolio and a recovery of ratio of 0.3 can be expected in the event of default, then, in order to hedge $70,000,000 of default risk, the trader might invest in the state encompassing a "D" outcome. To hedge the entire amount of the default risk in this example, the amount of the investment in this state should be $70,000,000/$ 1,237 or $56,589.
• Demand-based markets or auctions can be structured to offer a wide variety of products related to common measures of credit quality, including Moody's and S&P ratings, bankruptcy statistics, and recovery rates.
• DBAR contingent claims can be based on an underlying event defined as the credit quality of Ford corporate debt as defined by the Standard & Poor's rating agency.
• Example 3.1.8 Economic Statistics As financial markets have become more sophisticated, statistical information that measures economic activity has assumed increasing importance as a factor in the investment decisions of market participants. Such economic activity measurements may include, for example, the following U.S. federal government and U.S. and foreign private agency statistics:
• Demand-based markets or auctions for economic products provide market participants with a market price for the risk that a particular measure of economic activity will vary from expectations and a tool to properly hedge the risk.
• the market participants can trade in a market or an auction where the event of economic significance is an underlying measure of economic activity (e.g., the VIX index as calculated by the CBOE) or a measured parameter related to the underlying event (e.g., an implied volatility or standard deviation of the VIX index).
• the event of economic significance is an underlying measure of economic activity (e.g., the VIX index as calculated by the CBOE) or a measured parameter related to the underlying event (e.g., an implied volatility or standard deviation of the VIX index).
• traders often hedge inflation risk by trading in bond futures or, where they exist, inflation-protected floating rate bonds.
• a group of DBAR contingent claims can readily be constructed to allow traders to express expectations about the distribution of uncertain economic statistics measuring, for example, the rate of inflation or other relevant variables. The following information describes such
• states can be defined and indicative returns can be constructed from, for example, consensus estimates among economists for this index. These estimates can be expressed in absolute values or, as illustrated, in Table 3.1.8-1 in percentage changes from the last observation as follows:
• Demand-based markets or auctions can be structured to offer a wide variety of products related to commonly observed indices and statistics related to economic activity and released or published by governments, and by domestic, foreign and international government or private companies, institutions, agencies or other entities. These may include a large number of statistics that measure the performance of the economy, such as employment, national income, inventories, consumer spending, etc., in addition to measures of real property and other economic activity.
• An additional example follows: Private Economic Indices & Statistics:
• Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on economic statistics released or published by private sources.
• DBAR contingent claims can be based on an underlying event defined as the NAPM Index published by the National Association of Purchasing Managers.
• DBAR contingent claims including, for example, digital options, can be based on an underlying event defined as the level of the Riverside House Price Index at year-end, 2001.
• demand-based products on economic statistics will provide the following new opportunities for trading and risk management:
• Example 3.1.9 Corporate Events
• Corporate actions and announcements are further examples of events of economic significance which are usually unhedgable or uninsurable in traditional markets but which can be effectively structured into groups of DBAR contingent claims according to the present invention.
• a more aggressive strategy would involve selling or underweighting Microsoft stock, while purchasing a st ⁇ ng of digital options on higher than expected EPS growth In this case, the trader expects a multiple contraction to occur over the short to medium term, as the valuation becomes unsustainable.
• a trader with a $5 million notional exposure to Microsoft can buy a st ⁇ ng of digital call options, as follows-
• payouts displayed immediately above are net of premium investment.
• Premiums invested are based on the trader's assessment of likely stock p ⁇ ce (and p ⁇ ce multiple) reaction to a possible earnings surpnse. Similar trades in digital options on eamings would be made in successive quarters, resulting in a st ⁇ ng of options on higher than expected eamings growth, to protect against an upward shift in the earnings expectation curve, as shown in FIG. 21.
• a trader with a view on a range of earnings expectations for the quarter can profit from a spread strategy over the distribution.
• demand-based trading for DBAR contingent claims, including, for example, digital options, based on corporate eamings.
• the examples shown here are intended to be representative, not definitive.
• demand-based trading products can be based on corporate accounting measures, including a wide variety of generally accepted accounting information from corporate balance sheets, income statements, and other measures of cash flow, such as earnings before interest, taxes, depreciation, and amortization (EBITDA).
• EBITDA earnings before interest, taxes, depreciation, and amortization
• Demand-based markets or auctions for DBAR contingent claims can be based on a measure or parameter related to AOL EBITDA, such as the EBITDA figure reported by AOL that is used to provide a measure of operating earnings.
• AOL EBITDA the EBITDA figure reported by AOL that is used to provide a measure of operating earnings.
• the underlying event for these claims is the quarterly or annual EBITDA figure for AOL as calculated and released to the public by the reporting company.
• an equity investment manager might decide to underweight a high-multiple stock against a benchmark, and replace it with a series of DBAR digital options corresponding to a projected profile for earnings growth.
• the manager can compare the cost of this strategy with the risk of owning the underlying security, based on the company's PE ratio or some other metric chosen by the fund manager.
• an investor who expects a multiple expansion for a given stock would purchase demand-based trading digital put options on earnings, retaining the stock for a multiple expansion while protecting against a shortfall in reported earnings.
• DBAR contingent claims including, for example, digital options, based on earnings are not designed to hedge stock prices, they can provide a cost-effective means to mitigate the risk of equity ownership over longer term horizons. For example, periodically, three-month stock options that are slightly out-of-the-money can command premiums of 10% or more. The ability to insure against possible earnings or revenue shortfalls one quarter or more in the future via purchases of DBAR digital options may represent an attractive alternative to conventional hedge strategies for equity price risks.
• Example 3.1.10 Real Assets Another advantage of the methods and systems of the present invention is the ability to structure liquid claims on illiquid underlying assets such a real estate. As previously discussed, traditional derivatives markets customarily use a liquid underlying market in order to function properly. With a group of DBAR contingent claims all that is usually required is a real-world, observable event of economic significance. For example, the creation of contingent claims tied to real assets has been attempted at some financial institutions over the last several years. These efforts have not been credited with an appreciable impact, apparently because of the primary liquidity constraints inherent in the underlying real assets.
• a group of DBAR contingent claims according to the present invention can be constructed based on an observable event related to real estate.
• the relevant information for an illustrative group of such claims is as follows: Real Asset Index: Colliers ABR Manhattan Office Rent Rates
• Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on computer memory components.
• DBAR contingent claims can be based on an underlying event defined as the 64Mb (8x8) PC 133 DRAM memory chip prices and on the rolling 90-day average of Dynamic Random Access Memory DRAM prices as reported each Friday by ICIS-LOR, a commodity price monitoring group based in London.
• Example 3.1.11 Energy Supply Chain
• a group of DBAR contingent claims can also be constructed using the methods and systems of the present invention to provide hedging vehicles on non-tradable quantities of great economic significance within the supply chain of a given industry.
• An example of such an application is the number of oil rigs currently deployed in domestic U.S. oil production. The rig count tends to be a slowly adjusting quantity that is sensitive to energy prices.
• appropriately structured groups of DBAR contingent claims based on rig counts could enable suppliers, producers and drillers to hedge exposure to sudden changes in energy prices and could provide a valuable risk-sharing device.
• a group of DBAR contingent claims depending on the rig count could be constructed according to the present invention using the following information (e.g., data source, termination criteria, etc).
• DBAR contingent claims can be based on an underlying event defined as the Baker Hughes Rig Count observed on a semi-annual basis.
• Demand-based markets or auctions can be structured to offer a wide variety of products related to power and emissions, including electricity prices, loads, degree-days, water supply, and pollution credits.
• electricity prices, loads, degree-days, water supply, and pollution credits include electricity prices, loads, degree-days, water supply, and pollution credits.
• DBAR contingent claims including, for example, digital options, based on the price of electricity at various points on the electricity grid.
• DBAR contingent claims can be based on an underlying event defined as the weekly average price of electricity in kilowatt-hours at the New York Independent System
• Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on the actual load (power demand) experienced for a particular power pool, allowing participants to trade volume, in addition to price.
• DBAR contingent claims can be based on an underlying event defined as the weekly total load demand experienced by Pennsylvania-New Jersey-Maryland Interconnect (PJM Western Hub).
• DBAR contingent claims can be based on an underlying event defined as the cumulative precipitation observed at weather stations maintained by the National Weather
• DBAR contingent claims can be structured to trade DBAR contingent claims, including, for example, digital options, based on emission allowances for various pollutants.
• DBAR contingent claims can be based on an underlying event defined as price of Environmental Protection Agency (EPA) sulfur dioxide allowances at the annual market or auction administered by the Chicago Board of Trade.
• EPA Environmental Protection Agency
• Real estate mortgages comprise an extremely large fixed income asset class with hundreds of billions in market capitalization. Market participants generally understand that these mortgage-backed securities are subject to interest rate risk and the risk that borrowers may exercise their options to refinance their mortgages or otherwise "prepay" their existing mortgage loans. The owner of a mortgage security, therefore, bears the risk of being "called” out of its position when mortgage interest rate levels decline. Market participants expend considerable time and resources assembling econometric models and synthesizing various data populations in order to generate prepayment projections. To the extent that economic forecasts are inaccurate, inefficiencies and severe misallocation of resources can result. Unfortunately, traditional derivatives markets fail to provide market participants with a direct mechanism to protect themselves against a homeowner's exercise of its prepayment option. Demand-based markets or auctions for mortgage prepayment products, however, provide market participants with a concrete price for prepayment risk.
• Groups of DBAR contingent claims can be structured according to the present invention, for example, based on the following information: Asset Index: FNMA Conventional 30 year One-Month
• PSA Prepayment Speed
• products on mortgage prepayments may provide the following exemplary new opportunities for trading and risk management:
• Asset-specific applications In the simplest form, the owner of a prepayable mortgage-backed security carries, by definition, a series of short option positions embedded in the asset, whereas a DBAR contingent claim, including, for example, a digital option, based on mortgage prepayments would constitute a long option position.
• a security owner would have the opportunity to compare the digital option's expected return with the prospective loss of principal, correlate the offsetting options, and invest accordingly. While this tactic would not eliminate reinvestment risks, per se, it would generate incremental investment retums that would reduce the security owner's embedded liabilities with respect to short option positions.
• Prepayment puts plus discount MBS Discount mortgage-backed securities tend to enjoy two-fold benefits as interest rates decline in the form of positive price changes and increases in prepayment speeds. Converse penalties apply in events of increases in interest rates, where a discount MBS suffers from adverse price change, and a decline in prepayment income.
• a discount MBS owner could offset diminished prepayment income by investing in DBAR contingent claims, such as, for example, digital put options, or digital put option spreads on prepayments.
• An analogous strategy would apply to principal-only mortgage-backed securities.
• Prepayment calls plus premium MBS An expectation of interest rate declines that accelerate prepayment activity for premium mortgage-backed securities would motivate a premium bond-holder to purchase DBAR contingent claims, such as, for example, digital call options, based on mortgage prepayments to offset losses attributable to unwelcome paydowns. The analogue would also apply to interest-only mortgage-backed securities.
• Convexity additions An investment in a DBAR contingent claim, such as, for example, a digital option, based on mortgage prepayments should effectively add convexity to an interest rate sensitive investment. According to this reasoning, dollar-weighted purchases of a demand-based market or auction on mortgage prepayments would tend to offset the negative convexity exhibited by mortgage-backed securities. It is likely that expert participants in the mortgage marketplace will analyze and test, and ultimately harvest, the fruitful opportunities for combinations of DBAR contingent claims, including, for example, digital options, based on mortgage prepayments with mortgage-backed securities and derivatives.
• Groups of DBAR contingent claims can be structured using the system and methods of the present invention to provide insurance and reinsurance facilities for property and casualty, life, health and other traditional lines of insurance.
• the following information provides information to structure a group of DBAR contingent claims related to large property losses from hurricane damage: Event: PCS Eastern Excess $5 billion Index
• PCS Property Claim Services
• Last Announcement Date 7/1/99 Last Index Value: No events
• the frequency of claims and the distributions of the severity of losses are assumed and convolutions are performed in order to post indicative returns over the distribution of defined states. This can be done, for example, using compound frequency-severity models, such as the Poisson-Pareto model, familiar to those of skill in the art, which predict, with greater probability than a normal distribution, when losses will be extreme.
• market activity is expected to alter the posted indicative returns, which serve as informative levels at the commencement of trading.
• Demand-based markets or auctions can be structured to offer a wide variety of products related to insurance industry loss warranties and other insurable risks, including property and non-property catastrophe, mortality rates, mass torts, etc.
• An additional example follows:
• Property Catastrophe Demand-based markets or auctions can be based on the outcome of natural catastrophes, including earthquake, fire, atmospheric peril, and flooding, etc. Underlying events can be based on hazard parameters. For example, DBAR contingent claims can be based on an underlying event defined as the cumulative losses sustained in California as the result of earthquake damage in the year 2002, as calculated by the Property Claims Service (PCS).
• PCS Property Claims Service
• a demand-based trading catastrophe risk product such as, for example, a DBAR digital option, allows participants to buy or sell a precise notional quantity of desired risk, at any point along a catastrophe risk probability curve, with a limit price for the risk.
• a series of loss triggers can be created for catastrophic events that offer greater flexibility and customization for insurance transactions, in addition to indicative pricing for all trigger levels.
• Segments of risk coverage can be traded with ease and precision. Participants in demand-based trading catastrophe risk products gain the ability to adjust risk protection or exposure to a desired level. For example, a reinsurance company may wish to purchase protection at the tail of a distribution, for unlikely but extremely catastrophic losses, while writing insurance in other parts of the distribution where returns may appear attractive.
• (2) Credit quality Claims-paying ability of an insurer or reinsurer represents an important concern for many market participants. Participants in a demand-based market or auction do not depend on the credit quality of an individual insurance or reinsurance company. A demand-based market or auction is by nature self-funding, meaning that catastrophic losses in other product or geographic areas will not impair the ability of a demand-based trading catastrophe risk product to make capital distributions.
• Example 3.1.14 Conditional Events
• advantage of the systems and methods of the present invention is the ability to construct groups of DBAR contingent claims related to events of economic significance for which there is great interest in insurance and hedging, but which are not readily hedged or insured in traditional capital and insurance markets.
• Another example of such an event is one that occurs only when some related event has previously occurred. For pu ⁇ oses of illustration, these two events may be denoted A and B.
• q denotes the probability of a state
• q represents the conditional probability of state A given the prior occurrence of state and B
• q(A n B) represents the occurrence of both states A and B.
• a group of DBAR contingent claims may be constructed to combine elements of "key person" insurance and the performance of the stock price of the company managed by the key person.
• Many firms are managed by people whom capital markets perceive as indispensable or particularly important, such as Warren Buffett of Berkshire Hathaway.
• the holders of Berkshire Hathaway stock have no ready way of insuring against the sudden change in management of Berkshire, either due to a co ⁇ orate action such as a takeover or to the death or disability of Warren Buffett.
• a group of conditional DBAR contingent claims can be constructed according to the present invention where the defined states reflect the stock price of Berkshire Hathaway conditional on Warren Buffet's leaving the firm's management.
• Other conditional DBAR contingent claims that could attract significant amounts for investment can be constructed using the methods and systems of the present invention, as apparent to one of skill in the art.
• the systems and methods of the present invention can also be adapted by a financial intermediary or issuer for the issuance of securities such as bonds, common or preferred stock, or other types of financial instruments.
• securities such as bonds, common or preferred stock, or other types of financial instruments.
• the process of creating new opportunities for hedging underlying events through the creation of new securities is known as "securitization,” and is also discussed in an embodiment presented in Section
• securitization include the mortgage and asset-backed securities markets, in which portfolios of financial risk are aggregated and then recombined into new sources of financial risk.
• the systems and methods of the present invention can be used within the securitization process by creating securities, or portfolios of securities, whose risk, in whole or part, is tied to an associated or embedded group of
• DBAR contingent claims In a preferred embodiment, a group of DBAR contingent claims is associated with a security much like options are currently associated with bonds in order to create callable and putable bonds in the traditional markets.
• This example illustrates how a group of DBAR contingent claims according to the present invention can be tied to the issuance of a security in order to share risk associated with an identified future event among the security holders.
• the security is a fixed income bond with an embedded group of DBAR contingent claims whose value depends on the possible values for hurricane losses over some time period for some geographic region.
• DBAR Event Total Losses on a Saffir-Simpson Category 4
• Hurricane Geographic Property Claims Services Eastern North America
• the underwriter Goldman Sachs issues the bond, and holders of the issued bond put bond principal at risk over the entire distribution of amounts of Category 4 losses for the event. Ranges of possible losses comprise the defined states for the embedded group of DBAR contingent claims.
• the underwriter is responsible for updating the returns to investments in the various states, monitoring credit risk, and clearing and settling, and validating the amount of the losses.
• Goldman is "put" or collects the bond principal at risk from the unsuccessful investments and allocates these amounts to the successful investments.
• the mechanism in this illustration thus includes:
• Example 3.1.16 Exotic Derivatives
• the securities and derivatives communities frequently use the term "exotic derivatives" to refer to derivatives whose values are linked to a security, asset, financial product or source of financial risk in a more complicated fashion than traditional derivatives such as futures, call options, and convertible bonds.
• Examples of exotic derivatives include American options, Asian options, barrier options, Bermudan options, chooser and compound options, binary or digital options, lookback options, automatic and flexible caps and floors, and shout options.
• barrier options are rights to purchase an underlying financial product, such as a quantity of foreign currency, for a specified rate or price, but only if, for example, the underlying exchange rate crosses or does not cross one or more defined rates or "barriers.” For example, a dollar call/yen put on the dollar/yen exchange rate, expiring in three months with strike price 110 and "knock-out" barrier of 105, entitles the holder to purchase a quantity of dollars at 110 yen per dollar, but only if the exchange rate did not fall below 105 at any point during the three month duration of the option.
• Another example of a commonly traded exotic derivative, an Asian option depends on the average value of the underlying security over some time period.
• path-dependent derivatives such as barrier and Asian options
• path-dependent derivatives such as barrier and Asian options
• One of the advantages of the systems and methods of the present invention is the ability to construct groups of DBAR contingent claims with exotic features that are more manageable and transparent than traditional exotic derivatives. For example, a trader might be interested in the earliest time the yen/dollar exchange rate crosses 95 over the next three months. A traditional barrier option, or portfolio of such exotic options, might suffice to approximate the source of risk of interest to this trader. A group of DBAR contingent claims, in contrast, can be constructed to isolate this risk and present relatively transparent opportunities for hedging. A risk to be isolated is the distribution of possible outcomes for what barrier derivatives traders term the "first passage time," or, in this example, the first time that the yen/dollar exchange rate crosses 95 over the next three months.
• demand- based markets or auctions can be used to create and trade digital options (as desc ⁇ bed in Sections 6 and 7) on calculated underlying events (including the events desc ⁇ bed in this
• Path Dependent Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, on an underlying event that is the subject of a calculation. For example, digital options traded in a demand-based market or auction could be based on an underlying event defined as the average price of yen/dollar exchange rate for the last quarter of 2001.
• Example 3.1.17 Hedging Markets for Real Goods, Commodities and Services
• This characterization indicates that the choice to invest now or to defer an investment in goods or services or a plant, for example, in the face of changing uncertainty and information, frequently entails risks similar to those encountered by traders who have invested in options which provide the opportunity to buy or sell an underlying asset in the capital markets.
• Groups of DBAR contingent claims according to the present invention can be used by firms within a given industry to better analyze capital budgeting decisions, including those involving real options. For example, a group of DBAR contingent claims can be established which provides hedging opportunities over the distribution of future semiconductor prices. Such a group of claims would allow producers of semiconductors to better hedge their capital budgeting decisions and provide information as to the market's expectation of future prices over the entire distribution of possible price outcomes. This information about the market's expectation of future prices could then also be used in the real options context in order to better evaluate capital budgeting decisions. Similarly, computer manufacturers could use such groups of DBAR contingent claims to hedge against adverse semiconductor price changes.
• Groups of DBAR contingent claims according to the present invention can also be used to hedge arbitrary sources of risk due to price discovery processes. For example, firms involved in competitive bidding for goods or services, whether by sealed bid or open bid markets or auctions, can hedge their investments and other capital expended in preparing the bid by investing in states of a group of DBAR contingent claims comprising ranges of mutually exclusive and collectively exhaustive market or auction bids.
• the group of DBAR contingent claim serves as a kind of "meta-auction," and allows those who will be participating in the market or auction to invest in the distribution of possible market or auction outcomes, rather than simply waiting for the single outcome representing the market or auction result.
• Market or auction participants could thus hedge themselves against adverse market or auction developments and outcomes, and, importantly, have access to the entire probability distribution of bids (at least at one point in time) before submitting a bid into the real market or auction.
• a group of DBAR claims could be used to provide market data over the entire distribution of possible bids.
• Preferred embodiments of the present invention thus can help avoid the so-called Winner's Curse phenomenon known to economists, whereby market or auction participants fail rationally to take account of the information on the likely bids of their market or auction competitors.
• Demand-based markets or auctions can be structured to offer a wide variety of products related to commodities such as fuels, chemicals, base metals, precious metals, agricultural products, etc.
• products related to commodities such as fuels, chemicals, base metals, precious metals, agricultural products, etc.
• the following examples provide a further representative sampling:
• Fuels Demand-based markets or auctions can be based on measures related to various fuel sources.
• DBAR contingent claims including, e.g., digital options, can be based on an underlying event defined as the price of natural gas in Btu's delivered to the Henry Hub, Louisiana.
• Chemicals Demand-based markets or auctions can be based on measures related to a variety of other chemicals.
• DBAR contingent claims including, e.g., digital options, can be based on an underlying event defined as the price of polyethylene.
• Base Metals Demand-based markets or auctions can be based on measures related to various precious metals.
• DBAR contingent claims including, e.g., digital options
• Precious Metals Demand-based markets or auctions can be based on measures related to various precious metals.
• DBAR contingent claims including, e.g., digital options, can be based on an underlying event defined as the price per troy ounce of Platinum delivered to an approved storage facility.
• Agricultural Products Demand-based markets or auctions can be based on measures related to various agricultural products.
• DBAR contingent claims, including, e.g., digital options can be based on an underlying event defined as the price per bushel of #2 yellow co delivered at the Chicago Switching District.
• Another feature of the systems and methods of the present invention is the relative ease with which traders can hedge risky exposures.
• a group of DBAR contingent claims has two states (state 1 and state 2, or si
• the hedge ratio, ⁇ 2 just computed for a simple two state example can be adapted to a group of DBAR contingent claims which is defined over more than two states.
• the existing investments in states to be hedged can be distinguished from the states on which a future hedge investment is to be made.
• the latter states can be called the "complement" states, since they comprise all the states that can occur other than those in which investment by a trader has already been made, i.e., they are complementary to the invested states.
• a multi-state hedge in a preferred embodiment includes two steps: (1) determining the amount of the hedge investment in the complement states, and (2) given the amount so determined, allocating the amount among the complement states.
• the second step involves allocating the hedge investment among the complement states, which can be done by allocating et c among the complement states in proportion to the existing amounts already invested in each of those states.
• An example of a four-state group of DBAR contingent claims according to the present invention illustrates this two-step hedging process.
• the following assumptions are made: (i) there are four states, numbered 1 through 4, respectively; (ii) $50, $80, $70 and $40 is invested in each state, (iii) a trader has previously placed a multi-state investment in the amount of $10 ( H as defined above) for states 1 and 2; and (iv) the allocation of this multi-state investment in states 1 and 2 is $3.8462 and $6.15385, respectively.
• the amounts invested in each state, excluding the trader's invested amounts are therefore $46.1538, $73.84615, $70, and $40 for states 1 through 4, respectively.
• the amount invested in the states to be hedged i.e., states 1 and 2, exclusive of the multi-state investment of $10, is the quantity T H as defined above.
• the first step in a preferred embodiment of the two-step hedging process is to compute the amount of the hedge investment to be made in the complement states.
• the second step in this process is to allocate this amount between the two complement states, i.e., states 3 and 4.
• the trader now has the following amounts invested in states 1 through 4: ($3.8462, $6.15385, $5.8333, $3.3333); the total amount invested in each of the four states is $50, $80, $75.83333, and $43.3333); and the returns for each of the four states, based on the total amount invested in each of the four states, would be, respectively, (3.98333, 2.1146, 2.2857, and 4.75).
• Calculations for the other states yield the same results, so that the trader in this example would be fully hedged irrespective of which state occurs.
• a DBAR contingent claim exchange can be responsible for reallocating multi-state trades via a suspense account, for example, so the trader can assign the duty of reallocating the multi-state investment to the exchange.
• the trader can also assign to an exchange the responsibility of determining the amount of the hedge investment in the complement states especially as returns change as a result of trading. The calculation and allocation of this amount can be done by the exchange in a similar fashion to the way the exchange reallocates multi-state trades to constituent states as investment amounts change.
• Example 3.1.19 Quasi-Continuous Trading Preferred embodiments of the systems and methods of the present invention include a trading period during which returns adjust among defined states for a group of
• returns are allocated to the occurrence of a state based on the final distribution of amounts invested over all the states at the end of the trading period.
• a trader will not know his returns to a given state with certainty until the end of a given trading period.
• the changes in returns or "price discovery" which occur during the trading period prior to "locking-in” the final retums may provide useful information as to trader expectations regarding finalized outcomes, even though they are only indications as to what the final retums are going to be.
• a trader may not be able to realize prtjfits or losses during the trading period.
• the hedging illustration of Example 3.1.18 provides an example of risk reduction but not of locking-in or realizing profit and loss.
• a quasi-continuous market for trading in a group of DBAR contingent claims may be created.
• a plurality of recurring trading periods may provide traders with nearly continuous opportunities to realize profit and loss.
• the end of one trading period is immediately followed by the opening of a new trading period, and the final invested amount and state returns for a prior trading period are "locked in" as that period ends, and are allocated accordingly when the outcome of the relevant event is later known.
• An example illustrates how this feature of the present invention may be implemented.
• the example illustrates the hedging of a European digital call option on the yen/dollar exchange rate (a traditional market option) over a two day period during which the underlying exchange rate changes by one yen per dollar.
• two trading periods are assumed for the group of DBAR contingent claims
• Payout of Option Pays 100 million USD if exchange rate equals or exceeds strike price at maturity or expiration
• Table 3.1.19-1 shows how the digital call option struck at 120 could, as an example, change in value with an underlying change in the yen/dollar exchange rate.
• the second column shows that the option is worth 28.333% or $28,333 million on a $100 million notional on 8/12/99 when the underlying exchange rate is 115.55.
• the third column shows that the value of the option, which pays $100 million should dollar yen equal or exceed 120 at the expiration date, increases to 29.8137% or $29.8137 million per $100 million when the underlying exchange rate has increased by 1 yen to 116.55.
• the illustrative trader in this example has therefore been able to lock-in or realize the profit no matter which state finally occurs.
• This profit is identical to the profit realized in the traditional digital option, illustrating that systems and methods of the present invention can be used to provide at least daily if not more frequent realization of profits and losses, or that risks can be hedged in virtually real time.
• r t closing returns a state in which an investment was originally made at time t
• ⁇ t amount originally invested in the state at time t r c
• + ⁇ closing retums at time t+1 to state or states other than the state in which the original investment was made (i.e., the so-called complement states which are all states other than the state or states originally traded which are to be hedged)
• ⁇ the amount of the hedge investment
• Example 3.1.20 Value Units For Investments and Payouts
• the units of investments and payouts used in embodiments of the present invention can be any unit of economic value recognized by investors, including, for example, currencies, commodities, number of shares, quantities of indices, amounts of swap transactions, or amounts of real estate.
• the invested amounts and payouts need not be in the same units and can comprise a group or combination of such units, for example 25% gold, 25% barrels of oil, and 50% Japanese Yen.
• the previous examples in this specification have generally used U.S. dollars as the value units for investments and payouts.
• This Example 3.1.20 illustrates a group of DBAR contingent claims for a common stock in which the invested units and payouts are defined in quantities of shares.
• Example 3.1.1 the terms and conditions of Example 3.1.1 are generally used for the group of contingent claims on MSFT common stock, except for pu ⁇ oses of brevity, only three states are presented in this Example 3.1.20: (0,83], (83, 88], and (88, ⁇ ]- Also in this Example 3.1.20, invested amounts are in numbers of shares for each state and the exchange makes the conversion for the trader at the market price prevailing at the time of the investment.
• payouts are made according to a canonical DRF in which a trader receives a quantity of shares equal to the number of shares invested in states that did not occur, in proportion to the ratio of number of shares the trader has invested in the state that did occur, divided by the total number of shares invested in that state
• An indicative dist ⁇ bution of trader demand in units of number of shares is shown below, assuming that the total traded amount is 100,000 shares:
• An important feature of investing in value units other than units of currency is that the magnitude of the observed outcome may well be relevant, as well as the state that occurs based on that outcome. For example, if the investments in this example were made in dollars, the trader who has a dollar invested in state (88, ⁇ j would not care, at least in theory, whether the final p ⁇ ce of MSFT at the close of the observation pe ⁇ od were 89 or 500.
• a group of DBAR contingent claims using value units of commodity having a p ⁇ ce can therefore possess additional features compared to groups of DBAR contingent claims that offer fixed payouts for a state, regardless of the magnitude of the outcome within that state
• These features may prove useful in constructing groups of DBAR contingent claims which are able to readily provide ⁇ sk and return profiles similar to those provided by traditional de ⁇ vatives.
• the group of DBAR contingent claims described in this example could be of great interest to traders who transact in traditional derivatives known as "asset-or-nothing digital options" and "supershares options.”
• An advantage of the systems and methods of the present invention is that, in preferred embodiments, traders can generate an arbitrary distribution of payouts across the distribution of defined states for a group of DBAR contingent claims.
• the ability to generate a customized payout distribution may be important to traders, since they may desire to replicate contingent claims payouts that are commonly found in traditional markets, such as those corresponding to long positions in stocks, short positions in bonds, short options positions in foreign exchange, and long option straddle positions, to cite just a few examples.
• preferred embodiments of the present invention may enable replicated distributions of payouts which can only be generated with difficulty and expense in traditional markets, such as the distribution of payouts for a long position in a stock that is subject to being "stopped out” by having a market-maker sell the stock when it reaches a certain price below the market price.
• Such stop-loss orders are notoriously difficult to execute in traditional markets, and traders are frequently not guaranteed that the execution will occur exactly at the pre-specified price.
• the generation and replication of arbitrary payout distributions across a given distribution of states for a group of DBAR contingent claims may be achieved through the use of multi-state investments.
• traders before making an investment, traders can specify a desired payout for each state or some of the states in a given distribution of states. These payouts form a distribution of desired payouts across the distribution of states for the group of DBAR contingent claims.
• the distribution of desired payouts may be stored by an exchange, which may also calculate, given an existing distribution of investments across the distribution of states, (1) the total amount required to be invested to achieve the desired payout distribution; (2) the states into which the investment is to allocated; and (3) how much is to be invested in each state so that the desired payout distribution can be achieved.
• this multi-state investment is entered into a suspense account maintained by the exchange, which reallocates the investment among the states as the amounts invested change across the distribution of states.
• a final allocation is made at the end of the trading period when returns are finalized.
• the discussion in this specification of multi-state investments has included examples in which it has been assumed that an illustrative trader desires a payout which is the same no matter which state occurs among the constituent states of a multi-state investment.
• the amount invested by the trader in the multi-state investment can be allocated to the constituent state in proportion to the amounts that have otherwise been invested in the respective constituent states.
• these investments are reallocated using the same procedure throughout the trading period as the relative proportion of amounts invested in the constituent states changes.
• a trader may make a multi-state investment in which the multi-state allocation is not intended to generate the same payout irrespective of which state among the constituent state occurs. Rather, in such embodiments, the multi-state investment may be intended to generate a payout distribution which matches some other desired payout distribution of the trader across the distribution of states, such as, for example, for certain digital strips, as discussed in Section 6. Thus, the systems and methods of the present invention do not require amounts invested in multi-state investments to be allocated in proportion of the amounts otherwise invested in the constituent states of the multi-statement investment.
• amounts to be invested to produce an arbitrary distribution payouts can approximately be found by multiplying (a) the inverse of a diagonal matrix with the unit payouts for each state on the diagonal (where the unit payouts are determined from the amounts invested at any given time in the trading period) and (b) a vector containing the trader's desired payouts.
• the equation above shows that the amounts to be invested in order to produce a desired payout distribution are a function of the desired payout distribution itself (Pi, * ) and the amounts otherwise invested across the distribution of states (which are used to form the matrix ⁇ , which contains the payouts per unit along its diagonals and zeroes along the off-diagonals).
• the allocation of the amounts to be invested in each state will change if either the desired payouts change or if the amounts otherwise invested across the distribution change.
• a suspense account is used to reallocate the invested amounts, A;,*, in response to these changes, as described previously.
• a final allocation is made using the amounts otherwise invested across the distribution of states. The final allocation can typically be performed using the iterative quadratic solution techniques embodied in the computer code listing in Table 1.
• Example 3.1.21 illustrates a methodology for generating an arbitrary payout distribution, using the event, termination criteria, the defined states, trading period and other relevant information, as appropriate, from Example 3.1.1, and assuming that the desired multi-state investment is small in relation to the total amount of investments already made.
• Example 3.1.1 illustrative investments are shown across the distribution of states representing possible closing prices for MSFT stock on the expiration date of 8/19/99. In that example, the distribution of investment is illustrated for 8/18/99, one day prior to expiration, and the price of MSFT on this date is given as 85.
• an investment in a state receives the same return regardless of the actual outcome within the state. It is therefore assumed for pu ⁇ oses of this Example 3.1.21 that a trader would accept an appropriate replication of the traditional profit and loss from a traditional position, subject to only "discretization" error. For pu ⁇ oses of this Example 3.1.21, and in preferred embodiments, it is assumed that the profit and loss corresponding to an actual outcome within a state is determined with reference to the price which falls exactly in between the upper and lower bounds of the state as measured in units of probability, i.e., the "state average.” For this Example 3.1.21, the following desired payouts can be calculated for each of the states the amounts to be invested in each state and the resulting investment amounts to achieve those payouts:
• the far right column of Table 3.1.21-1 is the result of the matrix computation described above.
• the payouts used to construct the matrix ⁇ for this Example 3.1.21 are one plus the returns shown in Example 3.1.1 for each state.
• the systems and methods of the present invention may be used to achieve almost any arbitrary payout or return profile, e.g., a long position, a short position, an option "straddle", etc., while maintaining limited liability and the other benefits of the invention described in this specification.
• an iterative procedure is used to allocate all of the multi-state investments to their respective constituent states.
• Computer code as previously described and apparent to one of skill in the art, can be implemented to allocate each multi-state investment among the constituent states depending upon the distribution of amounts otherwise invested and the trader's desired payout distribution.
• NDFs non-deliverable forwards
• Groups of DBAR contingent claims can be structured using the system and methods of the present invention to support an active options market in emerging market currencies.
• products on emerging market currencies will provide the following new opportunities for trading and risk management:
• An investment bank can use demand-based trading emerging market currency products to overcome existing credit barriers.
• Groups of DBAR contingent claims can be structured using the system and methods of the present invention to develop an explicit mechanism by which market participants can express views regarding central bank target rates.
• demand- based markets or auctions can be based on central bank policy parameters such as the Federal Reserve Target Fed Funds Rate, the Bank of Japan Official Discount Rate, or the Bank of England Base Rate.
• the underlying event may be defined as the Federal Reserve Target Fed Funds Rate as of June 1, 2002. Because demand-based trading products settle using the target rate of interest, maturity and credit mismatches no longer pose market barriers.
• products on central bank target rates may provide the following new advantages for trading and risk management:
• Example 3.1.24 Weather In recent years, market participants have expressed increasing interest in a market for derivative instruments related to weather as a means to insure against adverse weather outcomes. Despite greater recognition of the role of weather in economic activity, the market for weather derivatives has been relatively slow to develop. Market-makers in traditional over-the-counter markets often lack the means to redistribute their risk because of limited liquidity and lack of an underlying instrument. The market for weather derivatives is further hampered by poor price discovery.
• a group of DBAR contingent claims can be constructed using the methods and systems of the present invention to provide market participants with a market price for the probability that a particular weather metric will be above or below a given level. For example, participants in a demand-based market or auction on cooling degree days
• CDDs heating degree days
• HDDs heating degree days
• the event observation could be specified as taking place at a preset location such as the Weather Bureau Army Navy Observation Station #14732.
• participants in a demand-based market or auction on wind-speed in Chicago may be able to see at a glance the market consensus price that cumulative wind-speeds will exceed certain levels.
• Example 3.1.25 Financial Instruments Demand-based markets or auctions can be structured to offer a wide variety of products on commonly offered financial instruments or structured financial products related to fixed income securities, equities, foreign exchange, interest rates, and indices, and any derivatives thereof.
• the possible outcomes can include changes which are positive, negative or equal to zero when there is no change, and amounts of each positive and negative change.
• DBAR contingent claims can be structured to trade DBAR contingent claims, including, for example, digital options, based on prices for equity securities listed on recognized exchanges throughout the world.
• DBAR contingent claims can be based on an underlying event defined as the closing price each week of Juniper Networks.
• the underlying event can also be defined using an alternative measure, such as the volume weighted average price during any day.
• DBAR contingent claims can be structured to trade DBAR contingent claims, including, for example, digital options, based on a variety of fixed income securities such as government T-bills, T-notes, and T-bonds, commercial paper, CD's, zero coupon bonds, co ⁇ orate, and municipal bonds, and mortgage-backed securities.
• DBAR contingent claims can be based on an underlying event defined as the closing price each week of Qwest Capital Funding IV* % notes, due February of 2011.
• the underlying event can also be defined using an alternative measure, such as the volume weighted average price during any day.
• DBAR contingent claims on government and municipal obligations can be traded in a similar way.
• Hybrid Security prices Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on hybrid securities that contain both fixed-income and equity features, such as convertible bond prices.
• DBAR contingent claims can be based on an underlying event defined as the closing price each week of Amazon.com 4% % convertible bonds due February 2009. The underlying event can also be defined using an alternative measure, such as the volume weighted average price during any day.
• Interest Rates Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on interest rate measures such as LIBOR and other money market rates, an index of
• AAA co ⁇ orate bond yields or any of the fixed income securities listed above.
• DBAR contingent claims can be based on an underlying event defined as the fixing price each v/eek of 3-month LIBOR rates.
• the underlying event could be defined as an average of an interest rate over a fixed length of time, such as a week or month.
• Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on foreign exchange rates.
• DBAR contingent claims can be based an underlying event defined as the exchange rate of the Korean Won on any day.
• Price & Return Indices Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on a broad variety of financial instrument price indices, including those for equities
• DBAR contingent claims can be based on an underlying event defined as the closing price each quarter of the S&P Technology index.
• the underlying event can also be defined using an alternative measure, such as the volume weighted average price during any day.
• other index measurements can be used such as return instead of price.
• Swaps Demand-based markets or auctions can be structured to trade DBAR contingent claims, including, for example, digital options, based on interest rate swaps and other swap based transactions.
• digital options traded in a demand-based market or auction are based on an underlying event defined as the 10 year swap rate at which a fixed 10 year yield is received against paying a floating 3 month LIBOR rate. The rate may be determined using a common fixing convention.
• derivatives on any security or other financial product or instrument may be used as the underlying instrument for an event of economic significance in a demand- based market or auction.
• such derivatives can include futures, forwards, swaps, floating rate notes and other structured financial products.
• securities (as well as other financial products or instruments) and derivatives thereof can be converted into equivalent DBAR contingent claims (for example, as in the embodiment discussed in Section 10) and traded as a demand-enabled product alongside DBAR contingent claims in the same demand-based market or auction.
• DBAR Portfolios It may be desirable to combine a number of groups of DBAR contingent claims based on different events into a single portfolio.
• the payouts to the amounts invested in this fashion can therefore be a function of a relative comparison of all the outcome states in the respective groups of DBAR contingent claims to each other. Such a comparison may be based upon the amount invested in each outcome state in the distribution for each group of contingent claims as well as other qualities, parameters or characteristics of the outcome state (e.g., the magnitude of change for each security underlying the respective groups of contingent claims). In this way, more complex and varied payout and return profiles can be achieved using the systems and methods of the present invention.
• DBARP Demand reallocation function
• a DRF is employed in which returns for each contingent claim in the portfolio are determined by (i) the actual magnitude of change for each underlying financial product and (ii) how much has been invested in each state in the distribution.
• a large amount invested in a financial product, such as a common stock, on the long side will depress the returns to defined states on the long side of a corresponding group of DBAR contingent claims.
• one advantage to a DBAR portfolio is that it is not prone to speculative bubbles. More specifically, in preferred embodiments a massive influx of long side trading, for example, will increase the returns to short side states, thereby increasing returns and attracting investment in those states. The following notation is used to explain further preferred embodiments of
• DBARP ⁇
• ⁇ is the actual magnitude of change for financial product i W
• i L is the amount of successful investments in financial product i L
• i f is the system transaction fee
• ⁇ , ⁇ p is the payout per value unit invested in financial product i for a successful investment r p , is the return per unit invested in financial product i for a successful investment
• the payout principle of a preferred embodiment of a DBARP is to return to a successful investment a portion of aggregate losses scaled by the normalized return for the successful investment, and to return nothing to unsuccessful investments.
• a large actual retum on a relatively lightly traded financial product will benefit from being allocated a high proportion of the unsuccessful investments.
• states can be defined so that traders can invest for IBM and MSFT to either depreciate or appreciate over the period. It is also assumed that the distribution of amounts invested in the various states is the following at the close of trading for the current trading period:
• the retums in this example and in preferred embodiments are a function not only of the amounts invested in each group of DBAR contingent claims, but also the relative magnitude of the changes in p ⁇ ces for the underlying financial products or in the values of the underlying events of economic performance.
• the MSFT traders receive higher retums since MSFT significantly outperformed IBM In other words, the MSFT longs were "more correct" than the IBM shorts.
• the IBM retums in this strig ⁇ o are 1.5 times the retums to the MFST investments, since less was invested in the IBM group of DBAR contingent claims than in the MSFT group.
• the payouts in this example depend upon both the magnitude of change in the underlying stocks as well as the correlations between such changes. A statistical estimate of these expected changes and correlations can be made in order to compute expected returns and payouts during trading and at the close of each trading period. While making such an investment may be somewhat more complicated that in a DBAR range derivative, as discussed above, it is still readily apparent to one of skill in the art from this specification or from practice of the invention.
• the preceding example of a DBARP has been illustrated with events corresponding to closing prices of underlying securities. DBARPs of the present invention are not so limited and may be applied to any events of economic significance, e.g., interest rates, economic statistics, commercial real estate rentals, etc.
• other types of DRFs for use with DBARPs are apparent to one of ordinary skill in the art, based on this specification or practice of the present invention.
• Another advantage of the groups of DBAR contingent claims according to the present invention is the ability to provide transparent risk calculations to traders, market risk managers, and other interested parties. Such risks can include market risk and credit risk, which are discussed below. 4.1 Market Risk
• Market risk calculations are typically performed so that traders have information regarding the probability distribution of profits and losses applicable to their portfolio of active trades. For all trades associated with a group of DBAR contingent claims, a trader might want to know, for example, the dollar loss associated with the bottom fifth percentile of profit and loss. The bottom fifth percentile corresponds to a loss amount which the trader knows, with a 95% statistical confidence, would not be exceeded. For the pu ⁇ bses of this specification, the loss amount associated with a given statistical confidence (e.g., 95%, 99%) for an individual investment is denoted the capital-at-risk
• CAR computed not only for an individual investment but also for a plurality of investments related to for the same event or for multiple events.
• VAR Value-at-Risk
• MCS Monte Carlo Simulation
• HS Historical Simulation
• VAR is a method that commonly relies upon calculations of the standard deviations and correlations of p ⁇ ce changes for a group of trades These standard deviations and correlations are typically computed from histo ⁇ cal data The standard deviation data are typically used to compute the CAR for each trade individually
• a trader has made a traditional purchase of a stock, say $100 of IBM; ( ⁇ ) using previously computed standard deviation data, it is determined that the annual standard deviation for IBM is 30%; (in) as is commonly the case, the p ⁇ ce changes for IBM have a normal dist ⁇ bution; and (iv) the percentile of loss to be used is the bottom fifth percentile.
• the bottom fifth percentile of loss corresponds to approximately 1.645 standard deviations, so the CAR in this example — that is, loss for the IBM position that would not be exceeded with 95% statistical confidence — is 30%*1.645*$100, or $49.35.
• C is the correlation mat ⁇ x of the underlying events
• w is the vector containing the CAR for each active position in the portfolio
• w ⁇ is the transpose of W.
• steps implement the VAR methodology for a group of DBAR contingent claims of the present invention.
• the steps are first listed, and details of each step are then provided.
• the steps are as follows: (1) beginning with a distribution of defined states for a group of DBAR contingent claims, computing the standard deviation of returns in value units (e.g., dollars) for each investment in a given state;
• step (3) adjusting the number resulting from the computation in step (2) for each investment so that it corresponds to the desired percentile of loss
• step (3) (4) arranging the numbers resulting from step (3) for each distinct DBAR contingent claim in the portfolio into a vector, w, having dimension equal to the number of distinct DBAR contingent claims;
• VAR methodology of steps (l)-(6) above can be applied to an arbitrary group of DBAR contingent claims as follows. For pu ⁇ oses of illustrating this methodology, it is assumed that all investments are made in DBAR range derivatives using a canonical DRF as previously described. Similar analyses apply to other forms of DRFs.
• step (1) the standard deviation of returns per unit of amount invested for each state i for each group of DBAR contingent claim is computed as follows:
• ⁇ is the standard deviation of returns per unit of amount invested in each state i
• T is the total amount invested in state i
• T is the sum of all amounts invested across the distribution of states
• qi is the implied probability of the occurrence of state i derived from T and T J
• r is the retum per unit of investment in state i.
• this standard deviation is a function of the amount invested in each state and total amount invested across the distribution of states, and is also equal to the square root of the unit return for the state. If ⁇ , is the amount invested in state i, otj* ⁇ j is the standard deviation in units of the amount invested (e.g., dollars) for each state i.
• Step (2) computes the standard deviation for all investments in a group of DBAR contingent claims. This step (2) begins by calculating the correlation between each pair of states for every possible pair within the same distribution of states for a group of DBAR contingent claims. For a canonical DRF, these correlations may be computed as follows:
• step (2) the correlation coefficients pi. j are put into a matrix C s (the subscript s indicating correlation among states for the same event) which contains a number of rows and columns equal to the number of defined states for the group of
• DBAR contingent claims The correlation matrix contains l's along the diagonal, is symmetric, and the element at the i-th row and j-th column of the matrix is equal to py.
• a n xl vector U is constructed having a dimension equal to the number of states n, in the group of DBAR contingent claims, with each element of U being equal to a,*Oj.
• Step (3) involves adjusting the previously computed standard deviation, k , for every group of DBAR contingent claims in a portfolio by an amount corresponding to a desired or acceptable percentile of loss.
• k standard deviation
• a normal distribution is used for illustrative pu ⁇ oses, and other types of distributions (e.g., the
• Student T distribution can be used to compute the number of standard deviations corresponding to the any percentile of interest. As discussed above, the maximum amount that can be lost in preferred embodiments of canonical DRF implementation of a group of DBAR contingent claims is the amount invested.
• the standard deviations w are adjusted to reflect the constraint that the most that can be lost is the smaller of (a) the total amount invested and (b) the percentile loss of interest associated with the CAR calculation for the group of
• this updates the standard deviation for each event by substituting for it a CAR value that reflects a multiple of the standard deviation corresponding to an extreme loss percentile (e.g., bottom fifth) or the total invested amount, whichever is smaller.
• a CAR value that reflects a multiple of the standard deviation corresponding to an extreme loss percentile (e.g., bottom fifth) or the total invested amount, whichever is smaller.
• Step (5) involves the development of a symmetric correlation matrix, C e , which has a number of rows and columns equal to the number of groups of DBAR contingent claims, y. in which the trader has one or more investments.
• Correlation matrix C e can be estimated from historical data or may be available more directly, such as the correlation matrix among foreign exchange rates, interest rates, equity indices, commodities, and other financial products available from JP Morgan's RiskMetrics database. Other sources of the correlation information for matrix C e are known to those of skill in the art.
• the entry at the i-th row and j-th column of the matrix contains the correlation between the i-th and j-th events which define the i-th and j-th DBAR contingent claim for all such possible pairs among the m active groups of DBAR contingent claims in the portfolio.
• Step (6) the CAR for the entire portfolio of m groups of DBAR contingent claims is found by performing the following matrix computation, using each w k from step
• This CAR value for the portfolio of groups of DBAR contingent claims is an amount of loss that will not be exceeded with the associated statistical confidence used in Steps (1)- (6) above (e.g., in this illustration, 95%).
• the relevant underlying event upon which the states are defined is the respective closing price of each stock one month forward;
• the posted returns for IBM and GM respectively for the three respective states are, in U.S.
• Steps (l)-(6) are used to implement VAR in order to compute CAR for this example.
• the standard deviations of state returns per unit of amount invested in each state for the IBM and GM groups of contingent claims are, respectively, (2, .8165, 2) and (1.5274, 1.225, 1.5274).
• the amount invested in each state in the respective group of contingent claims, oi; is multiplied by the previously calculated standard deviation of state returns per investment, ⁇ increment so that the standard deviation of returns per state in dollars for each claim equals, for the IBM group: (2, 2.4495, 4) and, for the GM group, (0,1.225, 0).
• the left matrix is the correlation between each pair of state retums for the IBM group of contingent claims and the right matrix is the corresponding matrix for the GM group of contingent claims.
• the standard deviation of returns per state in dollars, OjOi, for each investment in this example can be arranged in a vector with dimension equal to three (i.e., the number of states):
• Step (2) a matrix calculation can be performed to compute the total standard deviation for all investments in each of the two groups of contingent claims, respectively:
• Step (4) in the VAR process described above the quantities Wi and w 2 are placed into a vector which has a dimension of two, equal to the number of groups of DBAR contingent claims in the illustrative trader's portfolio:
• a correlation matrix C e with two rows and two columns is either estimated from historical data or obtained from some other source (e.g., RiskMetrics), as known to one of skill in the art. Consistent with the assumption for this illustration that the estimated correlation between the price changes of IBM and GM is 0.5, the correlation matrix for the underlying events is as follows: 1 «;
• Step (6) a matrix multiplication is performed by pre- and post- multiplying C e by the transpose of w and by w, and taking the square root of the resulting product:
• MCS Monte Carlo Simulation
• Step (1) of the MCS methodology involves estimating the statistical distribution for the events underlying the DBAR contingent claims using conventional econometric techniques, such as GARCH. If the portfolio being analyzed has more than one group of DBAR contingent claim, then the distribution estimated will be what is commonly known as a multivariate statistical distribution which describes the statistical relationship between and among the events in the portfolio. For example, if the events are underlying closing prices for stocks and stock price changes have a normal distribution, then the estimated statistical distribution would be a multivariate normal distribution containing parameters relevant for the expected price change for each stock, its standard deviation, and correlations between every pair of stocks in the portfolio. Multivariate statistical distribution is typically estimated from historical time series data on the underlying events (e.g., history of prices for stocks) using conventional econometric techniques.
• GARCH econometric
• Step (2) of the MCS methodology involves using the estimated statistical distribution of Step (1) in order to simulate the representative scenarios.
• Such simulations can be performed using simulation methods contained in such reference works as
• the resulting profits and losses can be arranged into ascending order so that, for example, percentiles corresponding to any given profit and loss number can be computed.
• a bottom fifth percentile for example, would correspond to a loss for which the trader could be 95% confident would not be exceeded, provided that enough scenarios have been generated to provide an adequate representative sample.
• This number could be used as the CAR value computed using MCS for a group of DBAR contingent claims.
• statistics such as average profit or loss, standard deviation, skewness, kurtosis and other similar quantities can be computed from the generated profit and loss distribution, as known by one of skill in the art.
• HS Historical Simulation
• Step (1) involves obtaining, for each of the underlying events corresponding to each group of DBAR contingent claims, a historical time series of outcomes for the events. For example, if the events are stock closing prices, time series of closing prices for each stock can be obtained from a historical database such as those available from Bloomberg, Reuters, or Datastream or other data sources known to someone of skill in the art.
• Step (2) involves using each observation in the historical data from Step (1) to compute payouts using the DRF for each group of DBAR contingent claims in the portfolio. From the payouts for each group for each historical observation, a portfolio profit and loss can be computed. This results in a distribution of profits and losses corresponding to the historical scenarios, i.e., the profit and loss that would have been obtained had the trader held the portfolio throughout the period covered by the historical data sample.
• Step (3) involves arranging the values for profit and loss from the distribution of profit and loss computed in Step (2) in ascending order.
• a profit and loss can therefore be computed corresponding to any percentile in the distribution so arranged, so that, for example, a CAR value corresponding to a statistical confidence of 95% can be computed by reference to the bottom fifth percentile.
• a trader may make investments in a group of DBAR contingent claims using a margin loan.
• an investor may make an investment with a profit and loss scenario comparable to a sale of a digital put or call option and thus have some loss if the option expires "in the money," as discussed in Section 6, below.
• credit risk may be measured by estimating the amount of possible loss that other traders in the group of contingent claims could suffer owing to the inability of a given trader to repay a margin loan or otherwise cover a loss exposure. For example, a trader may have invested $1 in a given state for a group of DBAR contingent claims with $.50 of margin.
• the DRF collects $1 from the trader (ignoring interest) which would require repayment of the margin loan.
• the traders with successful trades may potentially not be able to receive the full amounts owing them under the DRF, and may therefore receive payouts lower than those indicated by the finalized returns for a given trading period for the group of contingent claims.
• the risk of such possible losses due to credit risk may be insured, with the cost of such insurance either borne by the exchange or passed on to the traders.
• One advantage of the system and method of the present invention is that, in preferred embodiments, the amount of credit risk associated with a group of contingent claims can readily be calculated. In preferred embodiments, the calculation of credit risk for a portfolio of groups of
• DBAR contingent claims involves computing a credit-capital-at-risk (“CCAR") figure in a manner analogous to the computation of CAR for market risk, as described above.
• the computation of CCAR involves the use of data related to the amount of margin used by each trader for each investment in each state for each group of contingent claims in the portfolio, data related to the probability of each trader defaulting on the margin loan (which can typically be obtained from data made available by credit rating agencies, such as Standard and Poors, and data related to the correlation of changes in credit ratings or default probabilities for every pair of traders (which can be obtained, for example, from JP Morgan's CreditMetrics database).
• CCAR computations can be made with varying levels of accuracy and reliability.
• VAR methodology for example, can be adapted to the computation of CCAR for a group of DBAR contingent claims, although it is also possible to use MCS and HS related techniques for such computations.
• MCS and HS related techniques for such computations.
• the steps that can be used in a preferred embodiment to compute CCAR using VAR- based, MCS-based, and HS-based methods are described below.
• Step (i) of the VAR-based CCAR methodology involves obtaining, for each trader in a group of DBAR contingent claims, the amount of margin used to make each trade or the amount of potential loss exposure from trades with profit and loss scenarios comparable to sales of options in conventional markets.
• Step (ii) involves obtaining data related to the probability of default for each trader who has invested in the groups of DBAR contingent claims. Default probabilities can be obtained from credit rating agencies, from the JP Morgan CreditMetrics database, or from other sources as known to one of skill in the art. In addition to default probabilities, data related to the amount recoverable upon default can be obtained. For example, an AA-rated trader with $1 in margin loans may be able to repay $.80 dollars in the event of default.
• Step (iii) involves scaling the standard deviation of returns in units of the invested amounts. This scaling step is described in step (1) of the VAR methodology described above for estimating market risk.
• the standard deviation of each return, determined according to Step (1) of the VAR methodology previously described, is scaled by (a) the percentage of margin [or loss exposure] for each investment; (b) the probability of default for the trader; and (c) the percentage not recoverable in the event of default.
• Step (iv) of this VAR-based CCAR methodology involves taking from step (iii) the scaled values for each state for each investment and performing the matrix calculation described in Step (2) above for the VAR methodology for estimating market risk, as described above.
• the standard deviations of returns in units of invested amounts which have been scaled as described in Step (iii) of this CCAR methodology are weighted according to the correlation between each possible pair of states (matrix C s , as described above).
• the resulting number is a credit-adjusted standard deviation of returns in units of the invested amounts for each trader for each investment on the portfolio of groups of DBAR contingent claims.
• the standard deviations of returns that have been scaled in this fashion are arranged into a vector whose dimension equals the number of traders.
• Step (v) of this VAR-based CCAR methodology involves performing a matrix computation, similar to that performed in Step (5) of the VAR methodology for CAR described above.
• the vector of credit-scaled standard deviations of retums from step (iv) are used to pre- and post-multiply a correlation matrix with rows and columns equal to the number of traders, with l's along the diagonal, and with the entry at row i and column j containing the statistical correlation of changes in credit ratings described above.
• the square root of the resulting matrix multiplication is an approximation of the standard deviation of losses, due to default, lor all the traders in a group of DBAR contingent claims. This value can be scaled by a number of standard deviations corresponding to a statistical confidence of the credit-related loss not to be exceeded, as discussed above.
• any given trader may be omitted from a CCAR calculation.
• the result is the CCAR facing the given trader due to the credit risk posed by other traders who have invested in a group of DBAR contingent claims.
• This computation can be made for all groups of DBAR contingent claims in which a trader has a position, and the resulting number can be weighted by the correlation matrix for the underlying events, C e . as described in Step (5) for the VAR-based CAR calculation.
• the result corresponds to the risk of loss posed by the possible defaults of other traders across all the states of all the groups of DBAR contingent claims in a trader's portfolio.
• MCS Simulation
• CCAR for a portfolio of DBAR contingent claims of the present invention involves two steps, as described below.
• Step (i) of the MCS methodology is to estimate a statistical distribution of the events of interest.
• the events of interest may be both the primary events underlying the groups of DBAR contingent claims, including events that may be fitted to multivariate statistical distributions to compute CAR as described above, as well as the events related to the default of the other investors in the groups of DBAR contingent claims.
• the multivariate statistical distribution to be estimated relates to the market events (e.g., stock price changes, changes in interest rates) underlying the groups of DBAR contingent claims being analyzed as well as the event that the investors in those groups of DBAR contingent claims, grouped by credit rating or classification will be unable to repay margin loans for losing investments.
• a multivariate statistical distribution to be estimated might assume that changes in the market events and credit ratings or classifications are jointly normally distributed. Estimating such a distribution would thus entail estimating, for example, the mean changes in the underlying market events (e.g., expected changes in interest rates until the expiration date), the mean changes in credit ratings expected until expiration, the standard deviation for each market event and credit rating change, and a correlation matrix containing all of the pairwise correlations between every pair of events, including market and credit event pairs.
• a preferred embodiment of MCS methodology as it applies to CCAR estimation for groups of DBAR contingent claims of the present invention typically requires some estimation as to the statistical correlation between market events (e.g., the change in the price of a stock issue) and credit events (e.g., whether an investor rated A- by Standard and Poors is more likely to default or be downgraded if the price of a stock issue goes down rather than up).
• market events e.g., the change in the price of a stock issue
• credit events e.g., whether an investor rated A- by Standard and Poors is more likely to default or be downgraded if the price of a stock issue goes down rather than up.
• a preferred approach to estimating correlation between events is to use a source of data with regard to credit-related events that does not typically suffer from a lack of statistical frequency.
• Two methods can be used in this preferred approach.
• data can be obtained that provide greater statistical confidence with regard to credit-related events.
• expected default frequency data can be purchased from such companies as KMV Co ⁇ oration. These data supply probabilities of default for various parties that can be updated as frequently as daily.
• more frequently observed default probabilities can be estimated from market interest rates.
• data providers such as Bloomberg and Reuters typically provide information on the additional yield investors require for investments in bonds of varying credit ratings, e.g., AAA, AA, A, A-.
• Other methods are readily available to one skilled in the art to provide estimates regarding default probabilities for various entities. Such estimates can be made as frequently as daily so that it is possible to have greater statistical confidence in the parameters typically needed for MCS, such as the correlation between changes in default probabilities and changes in stock prices, interest rates, and exchange rates.
• Step (ii) of a MCS technique involves the use of the multivariate statistical distributions estimated in Step (i) above in order to simulate the representative scenarios.
• simulations can be performed using methods and software readily available and known to those of skill in the art.
• the simulated default rate can be multiplied by the amount of losses an investor faces based upon the simulated market changes and the margin, if any, the investor has used to make losing investments.
• the product represents an estimated loss rate due to investor defaults. Many such scenarios can be generated so that a resulting distribution of credit-related expected losses can be obtained.
• the average value of the distribution is the mean loss.
• the lowest value of the top fifth percentile of the distribution would correspond to a loss for which a given trader could be 95% confident would not be exceeded, provided that enough scenarios have been generated to provide a statistically meaningful sample.
• the selected value in the distribution corresponding to a desired or adequate confidence level, is used as the CCAR for the groups of DBAR contingent claims being analyzed.
• HS Histo ⁇ cal Simulation
• Step (I) involves obtaining the same data for the market-related events as desc ⁇ bed above in the context of CAR.
• histo ⁇ cal time se ⁇ es data are also used for credit-related events such as downgrades and defaults.
• methods desc ⁇ bed above can be used to obtain more frequently observed data related to credit events.
• frequently-observed data on expected default probabilities can be obtained from KMV Co ⁇ oration.
• Other means for obtaining such data are known to those of skill in the art.
• Step (n) involves using each observation in the histo ⁇ cal data from the previous step (l) to compute payouts using the DRF for each group of DBAR contingent claims being analyzed.
• the amount of margin to be repaid for the losing trades, or the loss exposure for investments with profit and loss strig ⁇ os comparable to digital option "sales,” can then be multiplied by the expected default probability to use HS to estimate CCAR, so that an expected loss number can be obtained for each investor for each group of contingent claims.
• These losses can be summed across the investment by each trader so that, for each histo ⁇ cal observation data point, an expected loss amount due to default can be att ⁇ ubbed to each trader
• the loss amounts can also be summed across all the investors so that a total expected loss amount can be obtained for all of the investors for each histo ⁇ cal data point.
• Step (in) involves arranging, in ascending order, the values of loss amounts summed across the investors for each data point from the previous step (n).
• An expected loss amount due to credit-related events can therefore be computed corresponding to any percentile in the distribution so arranged.
• a CCAR value corresponding to a 95% statistical confidence level can be computed by reference to 95 th percentile of the loss distribution.
• a large trader who takes the market's fundamental mid-market valuation of 6.79% as correct or fair might want to trade a swap for a large amount, such as 750 million pounds.
• the large amount of the transaction could reduce the likely offered rate to 6.70%, which is a full 7 basis points lower than the average offer (which is probably applicable to offers of no more than 100 million pounds) and 9 basis points away from the fair mid-market value.
• the difference in value between a trader's position at the fair or mid-market value and the value at which the trade can actually be completed, i.e. either the bid or offer, is usually called the liquidity charge.
• the relationship between price (or returns) and quantity invested (i.e., demanded) is determined mathematically by a DRF.
• the implied probability q, for each state i increases, at a decreasing rate, with the amount invested in that state:
• T is the total amount invested across all the states of the group of DBAR contingent claims and T, is the amount invested in the state i.
• T is the total amount invested across all the states of the group of DBAR contingent claims and T, is the amount invested in the state i.
• a set of bid and offer curves is available as a function of the amount invested.
• the first of the expressions immediately above shows that small percentage changes in the amount invested in state i have a decreasing percentage effect on the implied probability for state i, as state i becomes more likely (i.e., as q, increases to 1).
• the second expression immediately above shows that a percentage change in the amount invested in a state j other than state i will decrease the implied probability for state i in proportion to the implied probability for the other state j.
• Implied “Bid” q, - (1 ⁇ 9
• Implied "Offer” q, +q, * ( -I)* ⁇ 7;
• the implied "bid” demand response function shows the effect on the implied state probability of an investment made to hedge an investment of size ⁇ Tj.
• the size of the hedge investment in the complement states is proportional to the ratio of investments in the complement states to the amount of investments in the state or states to be hedged, excluding the investment to be hedged (i.e., the third term in the denominator).
• the implied "offer" demand response function above shows the effect on the implied state probability from an incremental investment of size ⁇ T, in a particular defined state. In preferred embodiments of systems and methods of the present invention, only the finalized returns for a given trading period are applicable for computing payouts for a group of DBAR contingent claims.
• a group of DBAR contingent claims imposes no permanent liquidity charge, as the traditional markets typically do. Accordingly, in preferred embodiments, traders can readily calculate the effect on returns from investments in the DBAR contingent claims, and unless these calculated effects are permanent, they will not affect closing returns and can, therefore, be ignored in appropriate circumstances. In other words, investing in a preferred embodiment of a group of DBAR contingent claims does not impose a permanent liquidity charge on traders for exiting and entering the market, as the traditional markets typically do.
• Liquidity effects may be permanent from investments in a group of DBAR contingent claims if a trader is attempting to make a relatively very large investment near the end of a trading period, such that the market may not have sufficient time to adjust back to fair value.
• a trader can readily calculate the effects on returns to a investment which the trader thinks might be permanent (e.g., at the end of the trading period), due to the effect on the market from a large investment amount.
• T t+ ⁇ is the total amount invested in period t+1
• T c t+ ⁇ is the amount invested in the complement state in period t+1.
• the expression for H is the quadratic solution which generates a desired payout, as described above but using the present notation. For example, if $1 billion is the total amount, T, invested in trading period 2, then, according to the above expressions, the hedge trade investment assuming a permanent effect on returns is $70,435 million compared to $70.18755 million in Example 3.1.19.
• the amount of profit and loss locked-in due to the new hedge is $1,232 million, compared to $1.48077 in Example 3.1.19.
• the difference represents the liquidity effect, which even in the example where the invested notional is 10% of the total amount invested, is quite reasonable in a market for groups of DBAR contingent claims. There is no ready way to estimate or calculate such liquidity effects in traditional markets.
• the DBAR methods and systems of the present invention may be used to implement financial products known as digital options and to facilitate an exchange in such products.
• a digital option (sometimes also known as a binary option) is a derivative security which pays a fixed amount should specified conditions be met (such as the price of a stock exceeding a given level or "strike” price) at the expiration date. If the specified conditions are met, a digital option is often characterized as finishing "in the money.”
• a digital call option for example, would pay a fixed amount of currency, say one dollar, should the value of the underlying security, index, or variable upon which the option is based expire at or above the strike price of the call option.
• a digital put option would pay a fixed amount of currency should the value of the underlying security, index or variable be at or below the strike price of the put option.
• a spread of either digital call or put options would pay a fixed amount should the underlying value expire at or between the strike prices.
• a strip of digital options would pay out fixed ratios should the underlying expire between two sets of strike prices.
• the strike prices for the respective options are marked using familiar options notation where the subscript "c” indicates a call, the subscript “p” indicates a put, the subscript “s” indicates “spread,” and the superscripts "1" and "u” indicate lower and upper strikes, respectively.
• a digital call option at a strike price for the underlying stock at 50 would pay the same amount if, at the fulfillment of all of the termination criteria, the underlying stock price was 51, 60, 75 or any other value at or above 50.
• digital options represent the academic foundations of options theory, since traditional equity options could in theory be replicated from a portfolio of digital spread options whose strike prices are set to provide vanishingly small spreads.
• the methods and systems of the present invention can be used to create a derivatives market for digital options spreads.
• each investment in a state of a mutually exclusive and collectively exhaustive set of states of a group of DBAR contingent claims can be considered to correspond to either a digital call spread or a digital put spread. Since digital spreads can readily and accurately be used to replicate digital options, and since digital options are known, traded and processed in the existing markets, DBAR methods can therefore be represented effectively as a market for digital options — that is, a DBAR digital options market.
• DBAR DOE DBAR digital options exchange
• the illustrative interface of Table 6.1.1 contains hypothetical market information on DBAR digital options on Microsoft stock ("MSFT”) for a given expiration date. For example, an investor who desires a payout if MSFT stock closes higher than 50 at the expiration or observation date will need to "pay the offer" of $.4408 per dollar of payout. Such an offer is “indicative” (abbreviated "IND") since the underlying DBAR distribution — that is, the implied probability that a state or set of states will occur — may change during the trading period.
• IND the bid/offer spreads presented in Table 6.1.1 are presented in the following manner.
• the "offer" side in the market reflects the implied probability that underlying value of the stock (in this example
• the "bid” side in the market is the "price” at which a claim can be “sold” including the transaction fee.
• the term “sold” reflects the use of the systems and methods of the present invention to implement investment profit and loss scenarios comparable to "sales” of digital options, discussed in detail below.
• the amount in each "offer” cell is greater than the amount in the corresponding "bid” cell.
• the bid/offer quotations for these digital option representations of DBAR contingent claims are presented as percentages of (or implied probabilities for) a one dollar indicative payout.
• Table 6.1.1 The illustrative quotations in Table 6.1.1 can be derived as follows. First the payout for a given investment is computed assuming a 10 basis point transaction fee.
• This payout is equal to the sum of all investments less 10 basis points, divided by the sum of the investments over the range of states corresponding to the digital option. Taking the inverse of this quantity gives the offer side of the market in "price" terms. Performing the same calculation but this time adding 10 basis points to the total investment gives the bid side of the market.
• transaction fees are assessed as a percentage of payouts, rather than as a function of invested amounts.
• the offer (bid) side of the market for a given digital option could be, for example, (a) the amount invested over the range of states comprising the digital option , (b) plus (minus) the fee (e.g., 10 basis points) multiplied by the total invested for all of the defined states, (c) divided by the total invested for all of the defined states.
• An advantage of computing fees based upon the payout is that the bid/offer spreads as a percentage of "price” would be different depending upon the strike price of the underlying, with strikes that are less likely to be "in the money” having a higher percentage fee.
• this can be accomplished by allocating an investment, using the multistate methods previously disclosed, in such a manner that the same payout is received from the investment should the option expire "in-the-money", e.g., above the strike price of the underlying for a call option and below the strike price of the underlying for a put.
• the multistate methods used to allocate the investment need not be made apparent to traders.
• the DBAR methods and systems of the present invention could effectively operate "behind the scenes" to improve the quality of the market without materially changing interfaces and trading screens commonly used by traders. This may be illustrated by considering the DBAR construction of the MSFT Digital
• the notation (x, y] is used to indicate a single state part of a set of mutually exclusive and collectively exhaustive states which excludes x and includes y on the interval.
• a convention is adopted for puts, calls, and spreads which is consistent with the internal representation of the states. For example, a put and a call both struck at 50 cannot both be paid out if the underlying asset, index or variable expires exactly at 50.
• the following convention could be adopted: calls exclude the strike price, puts include the strike price, and spreads exclude the lower and include the upper strike price. This convention, for example, would be consistent with internal states that are exclusive on the lower boundary and inclusive on the upper boundary.
• Another preferred convention would have calls including the strike price and puts excluding the strike price, so that the representation of the states would be inclusive on the lower boundary and exclusive on the upper.
• related conventions exist in traditional markets. For example, consider the situation of a traditional foreign exchange options dealer who sells an "at the money” digital and an “at the money” put, with strike price of 100. Each is equally likely to expire "in the money,” so for every $1.00 in payout, the dealer should collect $.50. If the dealer has sold a $1.00 digital call and put, and has therefore collected a total of $1.00 in premium, then if the underlying expires exactly at 100, a discontinuous payout of $2.00 is owed. Hence, in a preferred embodiment of the present invention, conventions such as those described above or similar methods may be adopted to avoid such discontinuities.)
• a digital call or put may be constructed with DBAR methods of th". present invention by using the multistate allocation algorithms previously disclosed.
• the construction of a digital option involves allocating the amount to be invested across the constituent states over which the digital option is "in-the- money" (e.g., above the strike for a call, below the strike for a put) in a manner such that the same payout is obtained regardless of which state occurs among the "in the money" constituent states. This is accomplished by allocating the amount invested in the digital option in proportion to the then-existing investments over the range of constituent states for which the option is "in the money.” For example, for an additional $1,000,000 investment a digital call struck at 50 from the investments illustrated in Table 6.2.1, the construction of the trade using multistate allocation methods is:
• the distribution of investments across the states comprising the digital option may change, and may therefore require that the multistate investments be reallocated so that, for each digital option, the payout is the same for any of its constituent "in the money" states, regardless of which of these constituent states occurs after the fulfillment of all of the termination criteria, and is zero for any of the other states.
• the group of investments or contract is said to be in equilibrium. A further detailed description of the allocation methods which can be used to achieve this equilibrium is provided in connection with the description of FIGs. 13-14. 6.3 Digital Option Spreads
• a digital option spread trade may be offered to investors which simultaneously execute a buy and a "sell" (in the synthetic or replicated sense of the term, as described below) of a digital call or put option.
• An investment in such a spread would have the same payout should the underlying outcome expire at any value between the lower and upper strike prices in the spread.
• the spread covers one state, then the investment is comparable to an investment in a DBAR contingent claim for that one state.
• the spread covers more than one constituent state, in a preferred embodiment the investment is allocated using the multistate investment method previously described so that, regardless of which state occurs among the states included in the spread trade, the investor receives the same payout.
• Traders in the derivatives markets commonly trade related groups of futures or options contracts in desired ratios in order to accomplish some desired pu ⁇ ose. For example, it is not uncommon for traders of LIBOR based interest rate futures on the Chicago Mercantile Exchange ("CME") to execute simultaneously a group of futures with different expiration dates covering a number of years. Such a group, which is commonly termed a "strip,” is typically traded to hedge another position which can be effectively approximated with a strip whose constituent contracts are executed in target relative ratios. For example, a strip of LIBOR-based interest rate futures may be used to approximate the risk inherent of an interest rate swap of the same maturity as the latest contract expiration date in the strip.
• CME Chicago Mercantile Exchange
• the DBAR methods of the present invention can be used to allow traders to construct strips of digital options and digital option spreads whose relative payout ratios, should each option expire in the money, are equal to the ratios specified by the trader.
• a trader may desire to invest in a strip consisting of the 50, 60, 70, and 80 digital call options on MSFT, as illustrated in Table 6.1.1.
• the trader may desire that the payout ratios, should each option expire in the money, be in the following relative ratio: 1:2:3:4.
• the underlying price of MSFT at the expiration date (when the event outcome is observed) be equal to 65, both the 50 and 60 strike digital options are in the money.
• a multistate allocation algorithm can be used dynamically to reallocate the trader's investments across the states over which these options are in the money (50 and above, and 60 and above, respectively) in such a way as to generate final payouts which conform to the indicated ratio of 1:2.
• the multistate allocation steps may be performed each time new investments are added during the trading period, and a final multistate allocation may be performed after the trading period has expired.
• the act of selling a digital option, spread, or strip means that the investor (in the case of a sale, a seller) receives the cost of the option, or premium, if the option expires worthless or out of the money. Thus, if the option expires out of the money, the investor/seller's profit is the premium. Should the option expire in the money, however, the investor/seller incurs a net liability equal to the digital option payout less the premium received. In this situation, the investor/seller's net loss is the payout less the premium received for selling the option, or the notional payout less the premium. Selling an option, which is equivalent in many respects to the activity of selling insurance, is potentially quite risky, given the large contingent liabilities potentially involved. Nonetheless, option selling is commonplace in conventional, non-DBAR markets.
• an advantage of the digital options representation of the DBAR methods of the present invention is the presentation of an interface which displays bids and offers and therefore, by design, allows users to make investments in sets of DBAR contingent claims whose P&L scenarios are comparable to those from traditional "sales” as well as purchases of digital calls, puts, spreads, and strips.
• "selling" entails the ability to achieve a profit and loss profile which is analogous to that achieved by sellers of digital options instruments in non-DBAR markets, i.e., achieving a profit equal to the premium should the digital option expire out of the money, and suffering a net loss equal to the digital option payout (or the notional) less the premium received should the digital option expire in the money.
• the mechanics of "selling” involves converting such "sell” orders to complementary buy orders.
• a sale of the MSFT digital put options with strike price equal to 50 would be converted, in a preferred DBAR DOE embodiment, to a complementary purchase of the 50 strike digital call options.
• a detailed explanation of the conversion process of a "sale" to a complementary buy order is provided in connection with the description of FIG. 15.
• the complementary conversion of DBAR DOE "sales" to buys is facilitated by inte ⁇ reting the amount to be "sold” in a manner which is somewhat different from the amount to be bought for a DBAR DOE buy order.
• the amount in an order to be "sold” when a trader specifies an amount in an order to be "sold," the amount is inte ⁇ reted as the total amount of loss that the trader will suffer should the digital option, spread, or strip sold expire in the money. As indicated above, the total amount lost or net loss is equal to the notional payout less the premium from the sale. For example, if the trader "sells" $1,000,000 of the MSFT digital put struck at 50, if the price of MSFT at expiration is 50 or below, then the trader will lose $1,000,000.
• the order amount specified in a DBAR DOE "sell" order is inte ⁇ reted as the net amount lost should the option, strip, or spread sold expire in the money.
• the amount would be inte ⁇ reted and termed a "notional” or “notional amount” less the premium received, since the actual amount lost should the option expire in the money is the payout, or notional, less the premium received.
• the amount of a buy order in a preferred DBAR DOE embodiment, is inte ⁇ reted as the amount to be invested over the range of defined states which will generate the payout shape or profile expected by the trader. The amount to be invested is therefore equivalent to the option "premium" in conventional options markets.

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