MXPA99002620A - Method and apparatus for automated opening of options exchange - Google Patents

Abstract

A computer-based system for determining a set of opening prices for a number of series of options traded on an options exchange and for allocating public order imbalances at the opening of trading. Market makers input a current position, a desired target position and market maker orders (104) for options series from market maker terminals. An order entry system receives public orders (102) for options series. A controller (2) determines a set of implied volatilities (prices) for each options series that will maximize a weighted volume of trades across all options series at the opening. Contra orders than can be matched at the opening price are then executed. If there is a residual imbalance of non-executed public orders, the residual imbalance of non-executed public orders is assigned to individual ones of the plurality of market makers so as to minimize a cumulative measure of deviation between the desired target position and the current position of each market maker. The system is applicable to an options exchange, this term including any facility operating an over-the-counter market in options.

Description

METHOD AND APPARATUS FOR AUTOMATIC OPENING OF CHANGE OF OPTIONS Field of the Invention The present invention is directed to a method and apparatus for automatically opening or reopening a change of options, and more particularly, to a method and apparatus for opening all series of options substantially simultaneously when opens or reopens the commercial deal in a change of options and for the optimization of the distribution of the unfavorable balances of the public order for the creators of the market.

Copyright Notice A portion of the description of this patent document contains material that is subject to copyright protection. The owner of the copyright does not oppose the facsimile reproduction by any of the patent document or the patent description, as it appears in the archives or patent records of the Patent and Trademark Office. , but reserves in other respects all rights of any kind of copyright.

Background of the Invention There are currently five changes of equity options in the United States of America, and about fifty changes traded in options across the world. The options are traded in a number of financial instruments, such as, for example, stocks, currencies, treasury instruments, interest rates, market indexes, commodities and the like. When a change of options opens the trade every morning, or reopens the trade after a trade interruption in the preceding instrument on the day of the commercial deal, the change leads to an opening "rotation" procedure to determine the opening price for each option. The opening rotation can take upwards of 45 minutes, during which the price of the preceding instrument can change dramatically. Currently, the opening rotation consumes a significant portion of the day of commercial dealings. Additionally, the current methods that use the changes of options to distribute the unfavorable balances in the public orders for the creators of the market in the opening, usually result in undesirable and inefficient distributions. To better explain the problems associated with opening and reopening commercial deals in an options market, an explanation of the options is appropriate. For purposes of clarity, this patent will discuss the equity options marketed by the United States of America. However, it will be appreciated that the description herein also applies to (a) options and other financial instruments that are traded in the United States of America and non-US changes, and (b) options of all types that are traded in the United States. changes n Americans. An equity option is a securities contract which gives the owner the right, but not the obligation, to buy or sell a particular stock (called the preceding stock) at a specific price (called the bargain price) on or before of a given date. Typically, there are two basic types of options, namely, Sale options and Purchase options. An American-style equity purchase option gives its owner the right to buy 100 shares of the preceding stock at the bargain price on or before a given date. An American-style equity sale option gives the owner the right to sell 100 shares of the preceding stock at the bargain price on or before a given date. (In the United States of America, an option contract normally equals 100 shares). For American ethyl options, the owner of the option can exercise the contract at any time before expiration. For European stylistic options, the option can not be exercised until the last day of commercial dealings before expiration. Equity options are generally traded in US options changes at any time and there is a pricing mechanism for the preceding instrument, for example, approximately during the normal hours of operation of the changes of values of the United States of North America. The maturity for an option contract is typically on the Saturday after the third Friday of the month of expiration for the particular contract. In this way, the third Friday of the month is the last day of business deal for all equity options that expire that month.If the option owner does not exercise the option before maturity, then the option after the option expires and does not entitle the owner and does not place any obligation on the undersigned (the undersigned is the person who assumes, for a purchase option, the obligation to sell an action, or for a sale option, the obligation to buy an action Suppose that the PQR Corp. is a publicly traded stock, which also has options that were publicly traded in. A typical option for this action could be a Buy option October 70 PQR, a purchase option October 70 PQR, is a contract that gives the owner of the contract the right to buy 100 shares of the commercial capital of the PQR Corp. at $ 70 per share, until the third Saturday in October, if the buyer decides to exercise that right Generally, there are four months of maturity available for each equity option. In addition, there are usually three or more bargain prices available for each month of maturity of each equity option. In this way, for a single action, there will probably be at least 24 and quite possibly many more options marketed for a particular precedent. (It is not unusual to have 60 different options available for a single action). For example, for the PQR Corp. the following series of options can be traded in a change of options: Sale Option PQR January 70 PQR Sale Option April 70 PQR Sale Option July 70 PQR Sale Option January 75 Option of PQR Sale April 75 PQR Sale Option July 75 PQR Sale Option January 80 PQR Sale Option April 80 PQR Sale Option July 80 There would also be a similar number of series of purchase options. In this way, it will be apparent that for each preceding action, there could be dozens of sets of options, each of which would be valued differently. Therefore, for each preceding action, there are many series of options that must be evaluated when trading in an opening or reopening option change. Frequently the option brokers use the following terms. A "type" of option is either Vent or Purchase. A "class" option consists of option contracts that have the same title. A "series" of options consists of option contracts of the same class that have the same bargain value and expiration month. For example, the Purchase PQR October 60 options constitute a series. A premium is the price a buyer of the option pays for the right to buy or sell the preceding title. Usually the premium is quoted for an option contract on a per share basis, for example, the option to buy PQR October 60 $ 5 1/4 - in this example, the premium is $ 1/4, so the cost of the option contract would be $ 525 One option could be "inside-the-money," "in-the-money," or "outside-the-money." A Purchase option is within the money if the price of the preceding action is higher than the bargain price, that is, the owner of the Buy option has the right to buy the stock at a price that is less than the price that The owner would have to pay to buy the shares in the open market. A Vent option is within-the-money if the price of the preceding share is below the bargain price. An option is in-money when it has a bargain price that is roughly equal to the actual market price of the preceding stock. A Buy option is out-of-the-money if the price of the preceding stock is below the bargain price. A Sale option is out-of-the-money if the price of the preceding stock is above the bargain price. The intrinsic value of an option contract is the inside-of-the-money portion of the option premium. The time value of an option contract is the part of a total premium of the option that exceeds its intrinsic value - it is the amount that the buyer is willing to pay for an option, on its intrinsic value, in the hope that its value will increase before expiration due to a favorable change in the price of the preceding one. In this way, the premium for an out-of-money option, consists entirely of the value of time. In accordance with the above, the premium for an option contract (the total price of the option) is its intrinsic value plus its time value. Under unusual market conditions, it might happen that the market premium for a deep-inside-the-money option is actually lower than its intrinsic value. This condition could be the result of an inadequate liquidity in the previous title, which induces the creators of the options market to buy these contracts only at discount prices with respect to their theoretical values. (This phenomenon has no harmful impact on the utility of the present invention). There are five factors that can be quantified that influence an option price. These factors are: * the price of the preceding title * the bargain price of the option * the time for expiration * the volatility of the preceding title * the current "risk free" interest rate. By using these five factors as an input to a theoretical option valuation model, such as, for example, the Black-Scholes model or the Cox-Ross-Rubenstein model, one can determine the theoretical value of the option. Negotiators of the option use the theoretical option value as an appraisal guide. Additionally, given the real market value of an option, one can use a theoretical valuation model of the option to derive the implied volatility from the preceding one. There are other non-quantifiable factors that influence the price of an option, such as: * the calculations of the market participants of future volatility * the calculations of the future performance of the present share * the supply and demand of the option and of the precedent * the depth of the market for the option. The theoretical valuation models of the option produce values that reflect a sensitivity of options to changes in one of the five quantifiable factors. Greek names are assigned to these sensitivities, such as delta, gama, theta, ro and vega. The delta is a measure of the rate of change in a theoretical value of the option for a change of one unit in the price of the preceding title. In this way, the delta is the theoretical amount by which the price of the option can be expected to change for a small change in the price of the preceding one. As such, it provides a local measure of the equivalent position risk of a position of the option with respect to a position in the preceding title. You can express delta as a percentage, for example, 63 percent (or simply "63" with the percentage symbol involved). Each option contract has its own theoretical singular delta that determine the five quantifiable factors that were described above. The range is a measure of the rate of change in an option delta for a change of one unit in the price of the preceding title. The range expresses how much the option delta should theoretically change for a $ 1 change in the price of the preceding one. The range is the largest when the option is in-the-money. As the price of the preceding stock moves away from the bargain price of the option (in any direction), the range of this option will decrease. The range provides a local measure of the exchange rate of l delta, with respect to the price of the preceding one. The theta is a measure of the rate of change in the theoretical value of the option for a change of one unit in time to the expiration date of the option. The veg (also known as kappa), is a measure of the rate of change in a theoretical value of the option for a one-unit change in the volatility of the preceding security. The ro is a measure of the rate of change in a theoretical value of the option for a change of one unit in the free interest rate d risk. The delta and the range are the main measures used by those who trade in options. For example, if a trader has a portfolio that has a large absolute value of delta and a large absolute value of range, the trader would have a large position that is very sensitive to movements in the price of the preceding one, and therefore, trader would have a high risk exposure. Volatility is a measure of the price fluctuation of the stock. Mathematically, the volatility and the annualized standard deviation of the daily price changes of an action. The volatility involved is the volatility that would cause the theoretical value of the premium of an option to coincide with the market value of the premium, given the fixed values of the four remaining quantifiable factors. It will be appreciated that trading in options is a complex matter, particularly in light of the number of different option contracts that are listed in a change of options, their correlations, and their relation to the preceding action. Each series will have premiums, deltas, different supply / demand characteristics. The increase in the complexity of the situation is that you can also trade options on stock indices, such as the S &P500 index. The United States of America options markets are typically conducted using an "open-cry" trade method, whereby the rivals of the floor, representing public orders, and the creators of the market who trade for their own accounts. , they make positions and offers in the trading floor. Typically, commercial dealings are made in a stock exchange - or a specific place on the trading floor of a change assigned for the trading of a specific option class. U market creator is a member of change in the floor of commerce that buys and sells options for its own account that has the responsibility of making positions and offers to maintain a fair and orderly market. A floor broker is a trader in a change floor, who executes orders of commerce for the public. At the opening (or reopening) of a change of options, the change leads to an opening rotation procedure to determine the opening price for each option. It will be appreciated that in an opening or reopening, there is a disproportionate number of public buyers and sellers that is represented in each series at any particular opening price. There are many series to open; Currently, the opening price of each one is determined in the rotation. For each series, taking into account the supply and demand of public order, the creators of the market indicate their bid and offer prices, which converge towards an agreed opening price for that series. All commercial deals of public order that can be "matched at that price, and generally there will be, at this stage, an unfavorable balance of unmatched orders." The opening for all series in a class of options can take upwards 45 minutes, during which the preceding instrument can dramatically change, resulting in price discrepancies throughout the series.When multiple series of options are opened in a common precedent, variations in the positions and offers of the order Throughout the series, they will also produce discrepancies in the opening prices with respect to the theoretical prices that would correspond to a single implied volatility across all series, for example, a large unfavorable balance of purchase orders in a series. particular, it can cause it to open up to a significantly higher volatility involved than that of another series. The creators of the market must rectify the unfavorable balances between the positions and public offers at the opening. Also, as stated above, changes in the price of the preceding title during the time it takes to cycle through the opening may result in additional significant discrepancies in the opening prices through the series. For example, if the preceding action or the price of the index is falling rapidly, a late opening call that had been in-the-money at the beginning of the opening rotation could be opened effectively, at a lower price than the call of earlier opening that would have opened in-the-money. In some changes, once a series is opened, it can not be traded until the end of the opening rotation. Because it takes time to perform the opening rotation, regular trade in a particular series can be delayed for a significant period of time. In this way, in summary, the present opening method that uses the option changes, takes an undue amount of time and results in inconsistencies in the appraisal between the related series. There are additional problems related to current opening methods that use changes in options, such as ", for example, the mechanism by which residual unfavorable balance is distributed in public orders to market makers. A group has an obligation to satisfy the residual unfavorable balance in public orders at the opening price.The current method to meet this objective is a rounded-Robin transfer of the residual contracts to each market maker. For example, a market maker who is short delta may wish to be a buyer of options contracts and another market maker who is long may wish to increase his long position. to the opening with its real position and its desired objective position after the opening ura No attempt is made to comply with these wishes in the distribution of residual balances of public order. Since each market maker has unique wishes, the actual rounded distribution of the residual balance in public orders might not improve and could possibly worsen the actual position of each market maker with respect to their desired position. In accordance with the above, an opening method is needed to trade in a change of options that facilitates the simultaneous opening of an options market and that takes into account the supply and demand of public order and the consistency of the valuation between different series. More desirably, an opening method is needed that simultaneously determines an opening price for all series, where the opening price reached is a reasonable compromise between (a), which has the price of consistent opening across all series with respect to the volatility involved; and (b) having an opening price that accommodates variations in the supply and demand of public order. In addition, there is a need for a method of distributing unfavorable residual balances of public order among the creators of the market at the opening, which optimizes the position of each market maker with respect to their desired position.

SUMMARY OF THE INVENTION The present invention is a method and system implemented by computer that provides an automatic simultaneous opening of commercial deal in a change of. options The present invention allows flexibility in the degree to which the unfavorable balances of supply and demand of public order through a series, imposes variations in the implied volatilities of the opening, while at the same time providing the optimal allocation of the creators of the market to compensate residual unfavorable balances. As used herein, the term "opening" also includes "reopening." In accordance with the foregoing, the present invention can be used to reopen commercial treatment in a change of options after it interrupts trade during the day of commercial dealings. The present invention can also be used to facilitate commercial dealings when a customer requires a purchase market in one or more option series, that is, a purchase request. The present invention determines the opening prices for each series of options, so that all option series can be opened simultaneously at the option change. The present invention allows all option series to be opened simultaneously at a price that: I. It corresponds reasonably well with a single value of volatility involved (or in the most general case, a limited set of implied volatilities corresponding to a volatility bias involved previously determined, against the bargain price ratio); II. Optimizes volume (or heavy volume measurements) across all series; and III. It makes it easier for the creators of the options market to balance the variations in the supply and demand of public orders in each series at prices that provide an incentive for the creators of the market. The first characteristic (I) eliminates the total inconsistencies in the volatility involved in the opening, while still allowing some amplitude for variations in market demand. The second characteristic (II) fulfills the general purpose of a change of options, that is, to maximize mutual satisfaction among all participants to the greatest possible degree. The third characteristic (III) provides an improvement over the current methods for that of the creators of the market to the positions that are required in the opening. Each market maker comes to the opening with his own real position (as delta and range specify), and his own actual objective position after opening (as delta and range specify). The desired objective position can be dependent on the absolute and relative values of the volatilities involved that are determined at the opening. These real and objective positions impact the preferences of the market maker on the participation in the rectification of unfavorable balances in public orders between the different series. In this way, in accordance with the principles of the present invention, the public orders can be optimized through all the creators of the market. The present invention proceeds in two stages. In the first step, the present invention determines a reasonably consistent set of volatilities involved that will maximize a heavy volume of commercial deals across all series in the opening. At the end of the first stage, there will generally be a residual unfavorable balance in public orders in each series that is not matched between buyers and sellers. These residual unfavorable balances between public orders require that they be compensated by assigning contrapositions to the creators of the market. In accordance with the foregoing, in the second step, the present invention allocates the residual public orders to the creators of the market, in order to minimize a cumulative measure of deviation between the desired target positions after opening and the actual positions of each market manufacturer at the conclusion of the first stage. In the representative embodiment of the present invention, the first stage can be formulated as an optimization problem. At one extreme, there is the optimal implied volatility that can be determined so that there is absolute consistency in the volatility involved across all the series. At the other extreme, there is the optimal volatility of each individual series that can be determined to satisfy the supply and demand of the market. The present invention calculates a set of volatilities involved in the opening that establishes a reasonable compromise between these extremes. From these values of implied volatility, the corresponding price is determined for each series of options. The present invention also facilitates a change (or other entity) to determine the point of compromise between these two positions. Alternatively, this commitment point in the opening can be conducted by market by means of a number of previously determined variables and / or may be required to fall within specified limits. It will be appreciated that, with the appropriate hardware and computer software, the volatilities of the opening and the price for all series can be determined substantially simultaneously. The opening prices and the corresponding volatilities, once determined by the present invention, for the creators of the market can be released. (and, if it is seen to be desirable, to other interested parties), to be able to help the market makers to determine their desired objective position after opening. In the representative embodiment of the present invention, the second stage can be considered as a subsequent optimization problem that minimizes a cumulative measure of the deviation between the desired objective after opening and the actual positions of the creators of the market, subject to the pressure that all unfavorable balances of public order must be compensated through the series. This second optimization problem can be solved according to the present invention, as a quadratic integer programming problem with the linear equality pressures. In the second stage, each market maker provides its real delta and range positions as input, before the opening and its desired delta and range positions after opening. (If necessary, other measures, such as theta, ro and vega, can also be included as target variables). The public orders are distributed to the creators of the market, in accordance with the solution of this second optimization problem. The first and second stages are independent and either can be implemented without the other. For example, a change of options may only implement the first stage to determine the opening price for each option, but make the decision to distribute the unfavorable balances of the public order, using the present Robin-Robin allocation of residual contracts to each creator of the market. Alternatively, a change of options may implement only the second stage, using the present opening rotation procedure, to determine. the opening price for each option. but using the present invention to distribute residual unfavorable balances of public order to the creators of the market. By extension, the present invention can also be used to effect commercial deals in market structures of purchase conducted periodically or by event (the latter should not be confused with the types of purchase option). It will also be appreciated that the principles of the present invention can be used to open commercial deals in any market where there are multiple instruments that derive their value each from a preceding instrument. For example, 1-a present invention could be adapted to be used in the opening of commercial deals in a future trading market. The present invention could also be adapted for use in the bond market (with the interest rates taking the place of the volatilities involved). Therefore, as used herein, the term "option" includes, where appropriate, forward transactions, bonds and instruments that derive their value from a preceding instrument or parameter.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a block diagram of the total system of the present invention. Figure 2 summarizes the inputs and outputs of the present invention. Figures 3A and 3B show the values that relate to example one. Figures 4A and 4B show a diagram of the optimal and rounded-Robin allocation errors for example one. Figures 5A and 5B show the values that are related to example two. Figures 6A and 6B show a diagram of the optimal and rounded-Robin allocation errors for example two.

Detailed Description Referring now to the drawings, and initially to Figure 1, there is illustrated a block diagram of a general design in accordance with a representative embodiment of the present invention. A central controller 2 controls the opening and dispensing process of the present invention. Coupled to controller 2, there are a number of market makers 4-10 terminals that can be used to provide information towards, and receiving the information from the controller 2. Also coupled to the controller 2, there is one or more input / output devices 12 that the change can use to provide information to, control the operation of, and receive the information from the controller 2. It can give input to the information about. public commands to controller 2 from an order entry system 14. Order entry system 14 may comprise regular option entry terminals or, for example, order entry terminals as described in the PCT Application PCT Number / US96 / 07265, filed on April 26, 1996, entitled "Crossing Network Utilizing Satisfaction Density Profile With Price Discovery Features", which is expressly incorporated herein by reference in its entirety. In the terminals of creators of the 4-10 market, the creators of the market can enter their orders, their real position, that is, their position at the end of the first stage, and their desired objective position, that is, the position in which They want to be after the opening. You can enter the actual position and the desired target position in the form of deltas and ranges. In the first stage, controller 2 determines a set of implied volatilities that will maximize a heavy volume of public clearing orders across all option series. After determining the set of volatilities involved, the controller 2, in the second stage, using the actual position of the desired objective position of each of the creators of the market, assigns any of the residual public orders to the individual market makers, to minimize a cumulative measure of deviation between the desired objective position and the actual position of each market maker after it. For changes with large volumes, controller 2 is preferably a computer that can perform calculations at speeds of multiple gigaflops, such as, for example with the present technology, an IBM SP2 computer. A storage device 3 is coupled to the controller 2. The storage device 3 can comprise a database for storing the information that is received from the creators of the market and for storing the results of the processing by the controller 2. It can be received the information that is received from the creators of the market, in the form of files, and stored as such in the device, storage 3. Typically, each creator of the market in the change, will have access to a terminal market maker, such as one of 4-10. Market maker terminals 4-10 can be personal computers or workstations or high-energy manual wireless input terminals. The market creator terminals 4-10 can communicate with "the controller 2. For example, the market creator terminals can be coupled to the controller 2 over a local area network (LAN), a Wide Area Network (WAN), through wireless communication protocols or through the Internet Each terminal creator of the market includes one or more input / output devices that allow the entry of orders and current and positions It is possible to visually display the output, such as the volatilities and public orders of the opening that is assigned to the creators of the market In accordance with the present invention, the controller 2 solves two optimization problems. it may consider the operation of the present invention in two stages, each including a different optimization problem, Figure 2 summarizes the inputs and outputs of each stage of the present invention. In step one, the public orders (102) are introduced to the controller 2 by the order entry system 14 and the orders of the market maker (104) are introduced to the controller 2 through the market creator terminals (4-10). ). The output of the first stage is a set of prices (implied volatilities) for each series (106). All commercial deals that may occur at that price are executed, and there will generally be, at this stage, a residual unfavorable balance of unmatched orders. In step two, the creator of the market introduces, through the terminals of the market maker (4-10), its real position and its desired position (108). This introduction to the present invention can be in the form of two sets of deltas and ranges of each market maker. (Alternatively, each market maker can enter this information as the desired change in delta and range). If the present invention did not perform step one, the residual public commands (110) must also be introduced to controller 2, for example, by the order 14 entry system. The output of the second stage is the assignment of public orders to the creators of the market (112).

Optimization of the First Stage The first stage is to determine a reasonably consistent set of volatilities involved (which will, in general, incorporate a bias in the volatility involved against the bargain price), which will maximize the heavy volume of mutual satisfan of the orders public compensation through all the series in the opening. By "reasonably consistent", it is meant that some variation in the implied volatility between the individual series is acceptable, to accommodate the unfavorable balance in public orders (ie, a higher implied volatility to buy unfavorable balances and lower implied volatility). to sell unfavorable balances). At one extreme, the present invention could allow each series to open independently, using a single price purchase option that is based exclusively on supply and demand in each series, without taking into account 'any inconsistency of the volatility involved. . PCT Application Number PCT / US96 / 07265, filed on April 26, 1996, entitled "Crossing Network Utilizing Satisfan Density Profile With Price Discovery Features", describes a method that facilitates each series to be opened independently using an option of a single price. Using this method, controller 2 would determine an opening price to maximize the heavy volume of mutual satisfan that is based on public supply and demand, that is, it determines which volatilities involved will maximize the heavy volume in each series individually. Alternatively, if this method is not used, an opening price could be determined which maximizes the volume of commercial dealings. By allowing each series to be opened individually, using a single-price purchase option based exclusively on supply and demand in each series, it would allow the creators of the market to offset the unfavorable balances of public order to the more favorable prices for them (ie, buy low, sell high), but could result in large discrepancies of volatility involved through the series and / or the lowest volume traded. At the other extreme, the present invention could insist on the absolute consistency of a single volatility involved (or a set of volatilities involved satisfying a prescribed bias in volatility against the bargain price), without taking into account any corresponding unfavorable balance in public orders between the individual series, but it could require that the creators of the market compensate the unfavorable large balances of purchase and sale at the most favorable prices for them. Ideally, the present invention facilitates control of the opening point between these extremes, in order to provide a compromise between these conflig desires. To this end, suppose that a prescribed implied volatility bias ratio is known, so that for any given implied volatility that corresponds to a particular bargain price, the "appropriate" implied volatilities of all other bargain prices can be calculated. . This allows for expected expected open volatilities across the series, against which to measure the induced deviations of public order. Let s be a vector representing one of these consistent sets of volatilities involved. At the other extreme, let s be the vector of volatility involved that maximizes the respee heavy volumes that were marketed in each series individually. Let me let i be such a parameter, that 0 =? I < : l. For the series d option i ', the present invention defines the implied volatility of the aperture as a funn of s that is: s ± = (1 -? I) s ± -x-? ± s ± (1) which has the effect of allowing the volatilide involved in the opening to vary from one end to maximize the heavy volume traded in each individual series, to the other extreme to force the consistency of the implied volatility through the series, since the parameter? It varies from 0 to 1. This parameter can be set uniformly across all series (for example, by changing options), or it can be addressed by market through a number of ible variables in the opening. For example, sup qu μ y? they are the mean and standard deviation, respectively, of the elements of the vector s _. Then one could specify? by the formula where tanh (x) is the function of the hyperbolic tangent. Since the? ._ in this equation will tend towards zero, as well as s_? deviates significantly from μ, this has the effect in equation (1) of "pushing" the implied volatility of the opening in the series of options i towards s_ ± 'when the last variable is an absentee among the set of volatilities involved in the individual series. (The parameter 'a' in equation (2) controls the speed at which? ._ varies between 0 and 1, as a function of the remaining portion of the argument). The final step is to determine the value (s) (coordinated) of s_¿. in equation (1) for which the corresponding values of dx maximize the total heavy volume traded on all option series. For these particular volatility values, the corresponding price is determined for each series, and the two closest trade deals are identified above and below this price. If there is a corresponding residual unfavorable balance of buyers for both price increases between the public orders, the controller 2 adjusts as the opening price the higher of the two, and vice versa in the case of an unfavorable balance of the seller in both prices . If the unfavorable balance changes from buyers to sellers between the two price increases, controller 2 selects as the opening price which yields the highest heavy volume of mutual satisfaction in that series. (In the pathological case where there were no purchase (sale) orders in any series that could be used to establish an opening price, the present invention could select the respective prices just below (above) the minimum involved volatility ( maximum) through all the series that correspond to a unit satisfaction value among all the limit orders for sale (purchase)). Another method to choose the?. ^ Has the objective of maximizing the net profit potential of the creators of the market in the process of compensating the unfavorable balances of the public order, perhaps within some limits in the permissible deviation from a consistent set of volatilities involved. Controller 2 determines each set of consistent implied volatilities over the range of possible opening volatilities involved. For each _s_j in this set, controller 2 determines the side (purchase or sale) of the unfavorable balance of the corresponding public order in the series. For an unfavorable purchase balance, the controller 2 is modified upwards in the price increases from the price pj corresponding to ü and in each price P + calculates the product of the unfavorable balance of the remaining purchase minus the price of the deviation ( Pj +? "Pj) 1 which represents the net potential gain available to the market makers by selling at the price Pj + K and unwinding the short position at the price Pj. The analogous procedure for unfavorable sales balances is followed, modifying downwards in the price In each series, controller 2 finds the price for which this net profit potential is maximized, perhaps allowing a specified limit of change in the maximum deviation from Pj. opening prices as the whole of the previous procedure that maximizes the heavy volume marketed through all the series, after which the values d ^ are calculated. or correspond to these prices. * • Once the values of _5-¡_ are determined by one of the above procedures, they are replaced within the arguments s in equations (3) to (10) below. In 'exchange options, these opening volatilities can be compensated for market makers (or other interested persons), before proceeding to the optimization of the second stage of the assignments of the market maker for the unfavorable balances of the public order. This would give the creators of the market more information on which to determine their delta and range objectives as detailed below.

Optimization of the Second Stage After the previous step, there will generally be a residual unfavorable balance in public orders in each series that is not equated between buyers and sellers. In accordance with the rules of change, these residual unfavorable balances between public orders must be compensated by assigning the contrapositions to the creators of the market. The problem of assigning the market maker to opening can be formulated as an optimization problem that minimizes a cumulative measure of the deviation between the desired objective after opening and the actual positions of the market makers, subject to the pressures that all unfavorable balances of public order must be compensated through the series. To this end, the following variables are defined: N number of option series in the appropriate title (combined purchase and sale options) K number of market makers in option class (s) unfavorable balance size (in the number of contracts) in public orders for series i to implied volatility s (positive integer for more buyers, negative integer for more sellers) X-. (s) delta position of the market maker j ° before opening to the implied volatility s Xj (s) desired delta entry of the market maker after opening to the implied volatility (s) market maker's range position j before opening to the volatility involved s and-, < * > desired position of the market maker's range after opening to the volatility involved (s) delta value of the series i "to the volatilid involved s Ti (s) range value of the series i * to the volatilid involved s For the series i *, suppose that the creator d market j ° changes its position through the contracts mj in opening allocation (positive if you are buying, negative is selling) The resulting change in this position of is given by: d ± j = 100mi: f • A ± (s ±), (3) and its corresponding change in its range position is through:? ij = 100mi: / • TL (s), (4) The net change in the delta position of the market creation j ° over all the series is then ? dl. = £ l00.t ?? (dI),? - l and the corresponding change in the range position of the market maker j ° on all the series is (6) S Y, = S? = l 100% -r. (5-) We leave that - ?. (d.) = XJ Y I OOm -? (s) '. 7); =! be the "error" between the desired delta position of market creation j, after the opening and its real position where you must change its positions by m j in each of the respective series. Similarly, let's let er, (d > i oo / i ,. -r / a.) (3) is the "error" between the desired range position of market creation j °, after opening and its actual position where it should change its positions per m in each of the respective series Assuming that there are creators of the market K, the market maker's assignment problem, is found the values of mij- (i = l, ..., N; j ' = l, ..., K), which minimizes the errors of the square-sum deviation of all the creators of the market subject to pressures which reflect the requirement that the creators of the market compensate in an exact way the unfavorable balances of the public order in each series. The present invention can be directly increased to extend the target variables (9) to include the other Greek parameters associated with the options (e.g., theta, ro, vega) and also to extend (10) to include the specified inequality pressures of the creator of the market on the commitment of capital. In accordance with the present invention, the second optimization problem is a quadratic integer programming problem with linear equalization pressures. In order to rewrite equations (7) - (10) in matrix annotation, we define ? = [?, (s,) ío)] t (13) ? = [y, "& ,; - X; - > ÍZ] ~ (16, D = [D, (d,) D. (o] t Equations (7) and (8) can be written in annotation of the matrix as e? = C-100 (? 7?) 7"(18) er =? -100 (Tr-W) r (19) The optimization problem then comes to you from (9) and (10), to find ' min (Cr- 100? r_) (C - 100 r?) + (Cr- \ 0QTtM) (? - ÍOO? / T); 20) subject to pressure Ml? - D, (21) where l? denotes a vector of dimensional column of K, whose elements are all unit. The union of the pressure equation (21) to the objective function (20) using a vector Lagrange multiplier, and then the adjustment of the partial derivatives of this expression with respect to M¿ (the rows M) and of? to zero, results in the following equation for the optimum M: -200? (C-100 r?) - 20? r ^ (-100? ^ r- ?? l? = 0, k = \? ' , .2) M \ K * D = 0 (23) by previously multiplying (22) with the vector lkr and using (23), results in ? .24) Substituting this expression into (22), yields the following matrix equation for M: XtM = Ytt (25: where -Y = ?? G + GTG,: 26: -? oo? tr) i, (27) Note that both Xt and Yt are rank arrays whose columns are linear combinations of the vectors? r. In this way Xt and the augmented matrix [Xt -. Yt] have same rank (= 2) and therefore, there is a solution of (25) This solution can be expressed in the form M = M + V, (2a) where M is a rank 2 matrix whose columns s linear combinations of the vectors? and T and V is a matr whose columns are orthogonal to? and r. In this way, you can write M as where A is a 2 + K matrix that represents the coeficient of the linear combinations of? and r included in the columns of M. From (26) and (29), we have 3- where the term inside the brackets above represents the column. 'j * of an NxK matrix. Using 825), and the equalization coefficients of? and T between (27) and (30) obtenem where In this way, from (29) and (32), we can write -W = [? _r] _? - lz 34 From (23) and (28), we have (M + V) lk = -D (35) showing in this way, after some algebra, that M. = CD, (36) where C is a matrix 2 of NxN range that is given by c = - (? r? 2? 7- (; nrr? - ??? | 2rr - (? rr)? rj) 37) \ B \ Therefore, from (35) and (36), We have the following pressure equation for V: Vlx-dtxQD. (38) where IN is the dimensional identity matrix of N, together with the implicit pressures orthogonally in the definition of V:? Rí '= 0, rrF = 0' - (39) The determination of the minimum standard solution V, e equivalent to finding the solution for the optimization problem rastromin (V V), (40) v subject to the pressures in (38) and (39). Again, when using the Lagrange multipliers technique, we have the following set of equations satisfied by the optimal result: ? tV = 0, GG = O. Since the last two equations require that the columns of V be orthogonal to both? As for F, the term in the first equation that includes?, must cancel in an exact way the two terms that include μ and? , and this way we have 2. "^? 'l [. = 0 (42, where?' is orthogonal to? and r.) Subsequent multiplication by lk and the use of the second equation, produces Thus V- - l (I ^ ODl [(44) Consequently, the combination of (28), (34) and (44) results in an optimal closed-form solution for the assignments of the compensation contracts for each market share, with the objective of rectifying the unfavorable balances in the orders public: From (18), (19) and (43) in which the optimal errors are given by £ ,. = --_ (46, I OOGG) K Note the following implications of these expressions: A) the optimal errors are identical for the market maker, since the error vector is a constan by the unit vector; and B) the magnitude of the optimal error that is added to all the creators of the market, represents the sum of all the changes of delta (range) that the creators of the market desire and the sum of all the changes of the (range) that dictate the unfavorable balances of the public order through the option series. In this way, it is possible (although unlikely) that the error could be reduced to cer if the desire of the creator of the aggregate market were to compensate in an exact way the unfavorable balance of the delta (range) aggregate in public orders. In general, this optimal solution will not result in integer values of the elements of the matrix M, and therefore optimization is completed by finding the nearest whole point in the dimensional space of NK that lies in the subspace defined by the equation (21), which results in the minimum square error as mediant (twenty) . Rather than using exhaustive or exotic research approaches to this relatively insubstantial problem, controller 2 could find an approximately optimal whole-point solution by considering the nature of the pressure equations (21) which require that ? X -D.Xo,),, _1JV? that is, the row sum of row i of matrix M must equal the integer value -Di (if_). A simple procedure can be obtained that will produce an almost optimal solution by rounding up or down the elements of the row j * of the matrix M to its integer values m near, and then make adjustments of more or less __:? or rounding the elements of the row as necessary to remain in accordance with (44). For example, if row sum of row i * after rounding, is Di (if) + r, then for r == l, controller 2 identifies the row elements r with the small fractional parts m that were rounded , and round them down. For r = -1, controller 2 performs the reverse procedure by rounding up the elements of the row r with the larger fractional parts that were rounded down This will ensure that, at most, a change of ± 1 c will be assigned to optimal number contracts in a given series any market maker.

Example To illustrate the relative performance of the optimal allocation with respect to the Robin rounding allocation of unfavorable public order balances for market makers, we consider the following examples. We suppose that there are ten series of options, with 30 creators of the market Suppose that the values of?, R and D in the ten series are given by the vectors: Suppose further that in the diagrams of Figures 3 and 3B, the values? Y ? of the 30 market makers. In Figures 4A and 4B are the errors of the optimal Robin-rounded assignment shown for? Y ? , respectively. The error of the average square root (rms) po creator of the market in _ ", is 721 for the optimal a-signation and 4,529 for the rounded-Robin assignment. The corresponding average square root error for the creator of the market in ?, is 135 and 544, respectively As a second example, let?, r and D in the series of options 10, give them the vectors: Suppose further that in the diagrams of Figures 5 and 5B, the values f and? of the 30 market makers, respectively. In Figures 6A and 6B the errors of the optimal assignment and rounded-Robin for? Y ? , respectively. The error of the average square root per market maker in f, is 74 for the optimal allocation. The error of the corresponding average square root by creator of the market in? , is 158 and 527, respectively. These examples demonstrate the substantial improvement in the objective errors of the market maker of the average square root using the optimal allocation method of the present invention compared to the rounded-Robin allocation method of the prior art. The controller 2 of the representative embodiment of the present invention can be implemented using a logic circuit or a computer memory comprising encoded instructions that can be read by computer, such as a computer program. The functionality of the logic circuit or the memory of the computer is described in detail later. In general, the present invention has practical application as it facilitates the opening of the options market essentially instantaneously and efficiently distributes the residual public orders to the creators of the market. It should be appreciated that the solution proposed by the present invention could not be achieved manually by a human. In accordance with the present invention, entries can be received from many terminals of the market maker (which can be located in a multitude of different locations), and this input is transmitted and stored electronically at a central location for processing. No human could in any way perform the communications, calculations and optimizations that are required to concurrently determine the volatilities involved for each of the many series of options and the efficient allocation of residual public orders.

Claims (36)

1. CLAIMS 1. A computer-based system to open the trading deal in options, comprising: a plurality of input devices to receive from each of a plurality of market makers a real position, a desired objective position and the creator's orders of the market for the series of options; an order entry system to receive public orders for the series of options; and a controller, coupled to the plurality of input devices and the order entry system, the controller comprising: (a) means for determining a set of prices for each set of options that will maximize a heavy volume of business deals to through all the series of options at the opening, (b) means to execute all the orders that may occur in a set of prices, (c) means to determine a residual unfavorable balance of public orders not executed, and (d) means , using the real position and the desired objective position of each one of the plurality of the creators of the market, to assign the residual unfavorable balance of the public orders not executed to individual subjects of the plurality of creators of the market, in order to minimize a Cumulative measure of deviation between the desired objective position and the actual position of each market maker.
2. 2. The system according to claim 1, wherein the set of prices comprises a set of volatilities involved.
3. 3. The system according to claim 1, wherein the set of prices for each series of options is determined simultaneously.
4. The system according to claim 1, characterized in that it also comprises a plurality of output devices, coupled to the controller, to output the set of prices to the plurality of creators of the market.
5. The system according to claim 1, wherein the means for determining the price set further comprises means for determining a set of opening volatilities for each series, which is a reasonable compromise, in accordance with a previously determined parameter, between the consistency in the appraisal through each series and the demand for public order through each series.
6. 6. The system according to claim 5, wherein the parameter is established by a change of options.
7. 7. The system according to claim 5, wherein the parameter is determined in the opening flight.
8. The system according to claim 1, wherein the actual position of each of the plurality of market makers is entered as a delta measure and a gamma measure.
9. The system according to claim 1, wherein the desired objective position of each of the plurality of market makers is entered as a delta measure and a gamma measure.
10. 10. A computer-based system "for determining a set of opening prices for a plurality of options series, comprising: a plurality of input devices to receive from each of the plurality of market makers for the series of options an order entry system to receive public orders for the series of options, and a controller, coupled to the plurality of input devices and the order entry system, using the orders of the creators of the market and public orders for determine a set of prices for each series of options, which will maximize a heavy volume of commercial deals through all the series of options in the opening
11. 11. The system according to claim 10, wherein the controller also comprises means for execute all public orders and orders from the creators of the market that could occur in the given set of prices.
12. 12. The system in accordance with the claim 10, where the set of prices for each set of options is determined simultaneously.
13. 13. The system in accordance with the claim 10, characterized in that it also comprises a plurality of output devices, coupled to the controller, to output the set of prices towards the plurality of creators of the market.
14. The system according to claim 10, wherein the means for determining the price set further comprises means for determining a set of opening volatilities for each series which is a reasonable compromise, in accordance with a previously determined parameter, between the consistency in the appraisal through each series in the demand for public order through each series.
15. 15. The system according to claim 14, wherein the parameter is set by a change of options.
16. 16. The system according to claim 10, wherein the parameter is determined on the flight at the opening.
17. 17. A computer-based system for distributing the unfavorable balances of public order to the opening of commercial treatment in options, which comprises: a memory that stores a plurality of orders for options that represent a residual unfavorable balance of public orders in each series of options that do not match an opening price that corresponds to that series of options; a plurality of input devices to receive from each of the plurality of creators of the market, a real position and a desired objective position; and a controller, coupled to the memory and the plurality of input devices, using the actual position and the desired objective position of each of the plurality of market makers, to allocate each public order to the residual unfavorable balance of the public orders to individual subjects of the plurality of creators of the market, in order to minimize a cumulative measure of deviation between the desired objective position and the actual position of each market maker.
18. 18. The system in accordance with the claim 17, where the real position of each one of the plurality of creators of the market is introduced as a delta measure and a gamma measure.
19. 19. The system according to claim 17, wherein the desired objective position of each of the plurality of market creators is entered as a delta measure and a gamma measure.
20. 20. A method implemented by computer to open trading deals in options through a plurality of market makers, comprising: receiving from each of the plurality of market makers a real position, a desired objective position and the orders of the market maker for the series of options; receive public orders for the series of options; and determine a set of prices for each set of options to maximize a heavy volume of commercial deals through all the series of options at the opening; Execute all orders that may occur in the set of prices determined in the previous step; if there is a residual unfavorable balance of the public orders not executed, assign the residual unfavorable balance of the public orders not executed to individual subjects of the plurality of market makers, in order to minimize a cumulative measure of deviation between the desired objective position and the real position of each creator of the market.
21. 21. The method according to claim 20, wherein the set of prices comprises a set of volatilities involved.
22. 22. The method according to claim 20, wherein the set of prices for each set of options is determined simultaneously.
23. 23. The method according to claim 20, characterized in that it also comprises the step of outputting the determined set of prices.
24. 24. The method according to claim 20, where the step to determine the set of prices also includes the step of determining a set of volatilities for each series, which is a reasonable compromise, in accordance with a commitment parameter, between the consistency in the appraisal through each series and the demand for public order through each series.
25. The method according to claim 24, characterized in that it also comprises the step of setting the commitment parameter in advance, by means of a change of options.
26. 26. The method of compliance with the claim 24, characterized in that it also comprises the step of determining the parameter of the commitment to flight, to the opening.
27. 27. The method according to claim 20, wherein the step to receive from each of the plurality of the creators of the market a real position, also comprises the reception from each of the plurality of the creators of the market, of a delta measure and a range measure that correspond to the actual position.
28. 28. The method according to claim 20, wherein the step to receive from each of the plurality of creators of the market a desired objective position, also comprises the reception from each of the plurality of the creators of the market, of a delta measure and a gamma measure corresponding to the desired objective position.
29. 29. A method implemented by computer to determine a set of opening prices for a plurality of series of. commercialized options, which includes: receiving orders for series of options from a plurality of market makers; receive public orders for the series of options; and determine a set of prices for home series of options, where the set of prices maximizes a heavy volume of commercial deals through all the series of options at the opening.
30. 30. The method according to claim 29, characterized in that it also comprises the step of executing all possible public orders and the orders of the creators of the market to the determined set of prices. .
31. 31. The method in accordance with the claim 29, where the step to determine a set of prices for each set of options also includes the step of simultaneously determining a set of prices for each set of options.
32. 32. The method according to claim 29, wherein the step for determining a set of prices for each set of options further comprises the steps of: providing a parameter; and determine a set of open volatilities for each series, which is a reasonable compromise, in accordance with the parameter, between the consistency in the appraisal through each series and the demand for public order through each series.
33. 33. A method implemented by computer to distribute the unfavorable balance of the public order to the opening of commercial deals in options, which comprises: providing a plurality of orders for the options that represent an unfavorable balance of public orders in each series of options that they do not equate an opening price that corresponds to that series of options; receive from each of a plurality of market makers, a real position and a desired objective position; and automatically assign each public order in the residual unfavorable balance of public orders to individual subjects of the plurality of creators of the market, in order to minimize a cumulative measure of deviation between the desired objective position and the actual position of each creator of the market. market.
34. 34. The method according to claim 33, wherein the step to receive from each of the plurality of the creators of the market a real position, also comprises the reception from each of the plurality of the creators of the market, of a delta measure and a range measure that correspond to the actual position.
35. 35. The method according to claim 33, wherein the step to receive from each of the plurality of creators of the market a desired objective position, also comprises the reception from each of the plurality of the creators of the market, a delta measure and a gamma measure corresponding to the desired objective position.
36. 36. A method implemented by computer to open commercial deals in options comprising: receiving from each of the plurality of market makers a real position, a desired objective position and the orders of the market maker for the series of options; receive public orders for the series of options; and concurrently determine a set of opening prices for each series of options; execute all possible public orders and orders from the market maker to the set of prices determined in the previous step; if there is a residual unfavorable balance of the public orders not executed, to optimally assign the residual unfavorable balance of public orders not executed to individual subjects of the plurality of market makers, taking into account the desired objective position and the actual position of every creator of the market.