JP2016510923A - Method and system for creating public debt volatility index and derivative product trading based thereon - Google Patents

Abstract

A computer system for calculating a bond volatility index includes a memory configured to store at least one program and at least one processor communicatively coupled to the memory, wherein at least one program is at least one processor. When executed by the at least one processor, the data regarding the option of the bond derivative is received, the data regarding the option of the bond derivative is used to calculate the bond volatility index, and the data regarding the bond volatility index is transmitted. [Selection] Figure 1

Description

Related Applications This application was filed on March 15, 2013, claiming priority from US Provisional Application No. 61 / 650,150, filed May 22, 2012 and now lapsed. US patent application Ser. No. 13 / 931,114, filed on Jun. 28, 2013 as a continuation-in-part of continuation of U.S. Ser. No. 13 / 842,197. Each of which is incorporated herein by reference in its entirety. All patents, patent applications and references cited anywhere in this specification are hereby incorporated by reference in their entirety.

TECHNICAL FIELD This description relates to the bond derivative investment market.

  A derivative is a financial instrument whose price depends at least in part on the price and / or characteristics of other security known as the underlying asset. Specific examples of the underlying asset include, but are not limited to, interest financial products (eg, bonds), commodities, securities, electronic trading funds, indices, and the like. Two exemplary well-known derivatives are options and futures contracts.

  Derivatives such as options and futures contracts can be traded over-the-counter and / or on other trading platforms such as organized exchanges (eg Chicago Board Options Exchange (CBOE)) For over-the-counter trading, individual trading parties can customize each trade to meet their individual needs, while for trading platforms or exchange traded derivatives, standardized derivatives Contract buy and sell orders are submitted to exchanges, which are collated and executed, and modern exchanges typically have a computer system dedicated to trading, thereby creating electronic communication networks such as the Internet. The order can be submitted electronically via Figure 1. It shows a specific example of the constant of the computer system.

  When the transaction is verified and executed, the details of the executed transaction are transmitted to a clearing corporation that mediates between the holders and the writers of the derivative contract. When exchange-traded derivatives are exercised, cash or underlying assets are delivered to securities settlement companies as necessary, and securities settlement companies distribute assets appropriately and as defined by the outcome of the transaction. To do.

  An option contract is not mandatory for a contract holder, depending on the option style (eg, US or European), but at a specific price before a certain date. The right to buy or sell Conversely, an option contract imposes an obligation on the contract seller to deliver the underlying asset at a specific price prior to a certain date, depending on the option style (eg, US or European). US options can be exercised at any time prior to expiration. European options can only be exercised when they expire, ie at a predetermined point in time.

  In general, there are two types of options: call and put. A call option gives the buyer the right to purchase the underlying asset at a specific price (ie, strike price) and imposes an obligation on the seller to deliver the underlying asset to the buyer at the strike price. A put option gives the buyer the right to sell the underlying asset at a specific price (ie, strike price) and imposes an obligation on the seller to purchase the underlying asset at the strike price.

  There are usually two types of settlement processing: spot settlement and cash settlement. In-kind settlement involves the transfer of funds from one party to the other in exchange for delivery of the underlying asset. In cash settlement, funds are transferred from one party to the other according to a calculation that incorporates data about the underlying asset.

  Futures contracts impose obligations on futures buyers to accept the underlying goods or assets on a future fixed date. Thus, the seller of futures contracts has an obligation to deliver goods or assets at a given price on a specified date. Futures are settled using physical or cash settlement. Both option contracts and futures contracts can be based on an abstract market index, such as an index, and are typically traded on an exchange. As used herein, the term “underlying tenor” means the maturity date of the underlying bond of the futures, and the options are not specified directly on the bond and the futures This is based on the futures option.

  A forward contract imposes obligations on forward buyers to accept the underlying goods or assets on a future fixed date. Accordingly, the forward contract seller is obliged to deliver the goods or assets at the given price on the specified date. Forwards are settled using physical or cash settlement. Any forward contract can be based on an abstract market index, such as an index, and is typically an OTC transaction. As used herein, the term “underlying bond tenor” means the maturity date of the underlying bond, and the option is not directly stated on the bond, This is based on the forward option.

  An index is a statistical overall index that indicates the performance of a market or market sector over various time periods, i.e., a numerical value that serves as a benchmark for performance. Specific examples of indices include the Dow Jones Industrial Average, the NASDAQ (National Association of Securities Dealers Automated Quotations: NASDAQ), the Standard & Poor's 500 (S & P 500: registered trademark), etc. . As noted above, index options are typically cash settled. For example, a buyer of an index call option receives the right to use cash settlement to purchase an amount of the index value multiplied by a multiplier such as $ 100, rather than the index itself. Thus, if the buyer of an index call option exercises the option, the option seller, if the option is in-the-money, the difference between the current value of the target index and the exercise price The amount multiplied by the multiplier must be paid to the holder.

  An example of an index on which derivatives are based is an index that measures the volatility of a market or market subsection. For example, CBOE has created and published the CBOE Market Volatility Index or VIX®, which is the primary measure of short-term volatility market forecasts represented by S & P 500 stock index option prices. In addition, CBOE offers exchange-type derivative products (both futures and options) using VIX as the underlying asset. The volatility index and derivative products based on it are widely accepted in the financial industry as an effective tool for hedging positions and as a device for expressing investment projections on the direction of volatility.

  A government bond is a debt instrument issued by a sovereign entity. Government bonds have various maturities and may be accompanied by periodic fixed or floating rate payments, ie coupons. Depending on the issuing government or bond period, public bonds are referred to by different names, for example, but not limited to, US Treasury bill, US Treasury note, US Treasury Treasury bond, German long-term government bond (German bund), German 5-year interest-bearing government bond (German bund), German 2-year interest-bearing government bond (German schatz), Japanese government bond (JGB), UK bond (UK) Gilt) etc.

  The inventors have several volatility indices, but bonds that are theoretically consistent with the prices available in the existing market for options on futures and forward bond bonds (GB) derivatives ( GB) We found that the market volatility measure has not been realized. In particular, there is no standardized benchmark that estimates the volatility in the public debt (GB) market over a given investment period and tenor of the underlying bond. Since there is no standardized benchmark that reflects the fair market value of the option-implied of expected public debt (GB) market volatility, traders, other market participants and / or asset managers Currently, by trading public debt (GB) futures and options, we hedge other financial positions, make market and / or take certain investment positions related to market volatility. However, the strategy of risk hedging by trading options on public debt (GB) futures does not necessarily produce an accurate profit / loss that depends on the price, that is, not the absolute price level that is established when the option expires, but ends from the start of trading. There is a tendency for the price movement path to affect profit and loss.

  Thus, some embodiments of the present invention provide techniques for calculating an effective volatility index associated with the public debt (GB) market. Further, some embodiments of the present invention provide techniques for instantiating derivative products and / or facilitating trading of derivative products based on such indices.

  In some embodiments, calculated using data on bond derivative-based options, such as futures and forwards (ie, options to enter into underlying bond derivative contracts and give the owner an unobligated right) Technology is provided to create and publish one or more volatility indices that have been created and to facilitate the electronic creation and trading of derivative instruments based on one or more indices related to volatility.

  Additional features and advantages of the invention will be set forth in the detailed description that follows, and in part will be obvious from the description, or may be obvious by practice of the disclosure. The objects and advantages of the invention will be realized and attained by the method particularly pointed out in the written description and claims hereof as well as the appended drawings.

  In order to achieve these and other advantages, and based on the objectives of the invention as embodied and comprehensively described herein, a computer system for calculating a bond volatility index provided by the present invention comprises at least one program. A memory configured to store and at least one processor communicatively coupled to the memory, and when the at least one program is executed by the at least one processor, the at least one processor is configured for the bond derivative. Data on options is received, data on options of bonds derivatives is used to calculate a bond volatility index, and data on bonds volatility index is transmitted.

  In some embodiments, the data on bond derivative options includes data on bond derivative option prices.

  In some embodiments, the data relating to the option price of the bond derivative includes data relating to the price of the bond futures option or the bond forward option.

  In other embodiments, the data relating to the option price of the bond derivative includes data relating to the price of the European option of the bond forward.

  In some embodiments, the data relating to the option price of the bond derivative includes data relating to the price of the non-European option of the bond forward.

  In some embodiments, if the data on the prices of bond derivative options includes data on the prices of non-European options on bond forwards, the data on prices of non-European options on bond forwards may be Convert to data about type option price.

  In some embodiments, the calculation of the bond volatility index includes evaluating an optional basket of bond derivatives that is required for pricing independent of a diversified swap contract model for bond derivatives.

ｔは、公債ボラティリティ指数が算出される時刻を示し、
Ｔは、公債デリバティブのオプションの期限を示し、
Ｔ_Ｄは、オプションの基礎となる公債デリバティブの満期を示し、Ｔ_Ｄ≧Ｔであり、
Ｔ_Ｎは、公債の期限を示し、
Ｚ＋１は、指数計算で使用されるオプションの総数を示し、
Ｋ_０は、Ｚ＋１個のオプションの最低行使価格（lowest strike）を示し、
Ｋ_ｉは、Ｚ＋１個のオプションのｉ番目に高い行使価格（i^th highest strike）を示し、
Ｋ_Ｚは、Ｚ＋１個のオプションの最高行使価格（highest strike）を示し、
ｉ≧１のとき、ΔＫ_ｉ＝１／２（Ｋ_ｉ＋１−Ｋ_ｉ−１）、及びΔＫ_０＝（Ｋ_１−Ｋ_０），ΔＫ_Ｚ＝（Ｋ_Ｚ−Ｋ_Ｚ−１）であり、
価格が時刻ｔにおいて観測可能である場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になるプットオプション及びコールオプションの基礎となる、公債デリバティブ契約の時刻ｔにおける価格であり、
価格が時刻ｔで観測可能でない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小になる行使価格（strike）であり、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがある場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）に等しく、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがない場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）であり、
Ｐ_ｔ（Ｔ）は、Ｔを満期とするデフォルトなし割引債の時刻ｔの価格であり、
Ｐｕｔ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるプットオプションの時刻ｔにおける価格であり、
Ｃａｌｌ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるコールオプションの時刻ｔにおける価格であり、
ＧＢ−ＶＩ（ｔ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブのＴで期限になるオプションに基づいて算出された公債ボラティリティ指数の時刻ｔにおける値である。 In some embodiments, the bond volatility index is calculated by the following equation at time t:

t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, underlying the put option and call option would limit at T _D , The price of bond derivative contract at time t,
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
GB-VI (t, T, T _D , T _N ) was calculated based on an option that expires at T of a bond derivative that expires at T _D , with the underlying bond maturing at T _N It is the value at time t of the public debt volatility index.

ｔは、公債ボラティリティ指数が算出される時刻を示し、
Ｔは、公債デリバティブのオプションの期限を示し、
Ｔ_Ｄは、オプションの基礎となる公債デリバティブの満期を示し、Ｔ_Ｄ≧Ｔであり、
Ｔ_Ｎは、公債の期限を示し、
Ｚ＋１は、指数計算で使用されるオプションの総数を示し、
Ｋ_０は、Ｚ＋１個のオプションの最低行使価格（lowest strike）を示し、
Ｋ_ｉは、Ｚ＋１個のオプションのｉ番目に高い（i^th highest strike）を示し、
Ｋ_Ｚは、Ｚ＋１個のオプションの最高行使価格（highest strike）を示し、
ｉ≧１のとき、ΔＫ_ｉ＝１／２（Ｋ_ｉ＋１−Ｋ_ｉ−１）、及びΔＫ_０＝（Ｋ_１−Ｋ_０），ΔＫ_Ｚ＝（Ｋ_Ｚ−Ｋ_Ｚ−１）であり、
価格が時刻ｔにおいて観測可能である場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になるプットオプション及びコールオプションの基礎となる、公債デリバティブ契約の時刻ｔにおける価格であり、
価格が時刻ｔで観測可能でない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小になる行使価格（strike）であり、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがある場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）に等しく、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがない場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）であり、
Ｐ_ｔ（Ｔ）は、Ｔを満期とするデフォルトなし割引債の時刻ｔの価格であり、
Ｐｕｔ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるプットオプションの時刻ｔにおける価格であり、
Ｃａｌｌ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるコールオプションの時刻ｔにおける価格であり、
ＧＢ−ＶＩ^ｂｐ（ｔ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブのＴで期限になるオプションに基づいて算出された公債ボラティリティ指数の時刻ｔにおける値である。 In some embodiments, the bond volatility index is calculated by the following equation at time t:

t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, underlying the put option and call option would limit at T _D , The price of bond derivative contract at time t,
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
GB-VI ^bp (t, T, T _D , T _N ) is calculated based on the option that expires at T of the bond derivative that expires at T _D , with the underlying bond maturing at T _N The value at the time t of the public bond volatility index.

であり、
ｔは、公債ボラティリティ指数が算出される時刻を示し、
Ｔは、公債デリバティブのオプションの期限を示し、
ｔ_ｊは、Ｔ以降で最初の利払いを示し
Ｔ_Ｄは、オプションの基礎となる公債デリバティブの満期を示し、Ｔ_Ｄ≧Ｔであり、
Ｔ_Ｎは、公債の期限を示し、
Ｚ＋１は、指数計算で使用されるオプションの総数を示し、
Ｋ_０は、Ｚ＋１個のオプションの最低行使価格（lowest strike）を示し、
Ｋ_ｉは、Ｚ＋１個のオプションのｉ番目に高い行使価格（i^th highest strike）を示し、
Ｋ_Ｚは、Ｚ＋１個のオプションの最高行使価格（highest strike）を示し、
ｉ≧１のとき、ΔＫ_ｉ＝１／２（Ｋ_ｉ＋１−Ｋ_ｉ−１）、及びΔＫ_０＝（Ｋ_１−Ｋ_０），ΔＫ_Ｚ＝（Ｋ_Ｚ−Ｋ_Ｚ−１）であり、
価格が時刻ｔにおいて観測可能である場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になるプットオプション及びコールオプションの基礎となる、公債デリバティブ契約の時刻ｔにおける価格であり、
価格が時刻ｔで観測可能でない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小になる行使価格（strike）であり、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがある場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）に等しく、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがない場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）であり、
Ｐ_ｔ（Ｔ）は、Ｔを満期とするデフォルトなし割引債の時刻ｔの価格であり、
Ｐｕｔ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるプットオプションの時刻ｔにおける価格であり、
Ｃａｌｌ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるコールオプションの時刻ｔにおける価格であり、
Ｎは、公債の利払いの総数であり、
Ｃ_ｉは、公債のＮ個の利子のうちのｉ番目の利子の額であり、
ｎは、公債の１年あたりの利払いの頻度であり、
ｙは、公債の利回りであり、
ｘは、公債の利回りであり、

In some embodiments, if there is no interest incurred at time T, then the bond volatility index is calculated by the following equation at time t:

And
t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
t _j is, T _D shows the first interest payment in the following T indicates the maturity of the public debt derivatives to be the option of the foundation, is a T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, underlying the put option and call option would limit at T _D , The price of bond derivative contract at time t,
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
N is the total number of interest payments on bonds,
C _i is the amount of the i-th interest out of N interest on the bond,
n is the frequency of interest payment per year for government bonds,
y is the bond yield,
x is the bond yield,

であり、
ｔは、公債ボラティリティ指数が算出される時刻を示し、
Ｔは、公債デリバティブのオプションの期限を示し、
Ｔ_Ｄは、オプションの基礎となる公債デリバティブの満期を示し、Ｔ_Ｄ≧Ｔであり、
Ｔ_Ｎは、公債の期限を示し、
Ｚ＋１は、指数計算で使用されるオプションの総数を示し、
Ｋ_０は、Ｚ＋１個のオプションの最低行使価格（lowest strike）を示し、
Ｋ_ｉは、Ｚ＋１個のオプションのｉ番目に高い行使価格（i^th highest strike）を示し、
Ｋ_Ｚは、Ｚ＋１個のオプションの最高行使価格（highest strike）を示し、
ｉ≧１のとき、ΔＫ_ｉ＝１／２（Ｋ_ｉ＋１−Ｋ_ｉ−１）、及びΔＫ_０＝（Ｋ_１−Ｋ_０），ΔＫ_Ｚ＝（Ｋ_Ｚ−Ｋ_Ｚ−１）であり、
価格が時刻ｔにおいて観測可能である場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になるプットオプション及びコールオプションの基礎となる、公債デリバティブ契約の時刻ｔにおける価格であり、
価格が時刻ｔで観測可能でない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小になる行使価格（strike）であり、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがある場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）に等しく、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがない場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）であり、
Ｐ_ｔ（Ｔ）は、Ｔを満期とするデフォルトなし割引債の時刻ｔの価格であり、
Ｐｕｔ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるプットオプションの時刻ｔにおける価格であり、
Ｃａｌｌ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるコールオプションの時刻ｔにおける価格であり、
Ｎは、公債の利払いの総数であり、
Ｃ_ｉは、公債のＮ個の利子のうちのｉ番目の利子の額であり、
ｎは、公債の１年あたりの利払いの頻度であり、
ｘは、公債の利回りであり、

In some embodiments, the bond volatility index is calculated by the following equation at time t:

And
t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, underlying the put option and call option would limit at T _D , The price of bond derivative contract at time t,
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
N is the total number of interest payments on bonds,
C _i is the amount of the i-th interest out of N interest on the bond,
n is the frequency of interest payment per year for government bonds,
x is the bond yield,

  In some embodiments, the at least one processor further creates a standardized exchange-type derivative product based on the bond volatility index and transmits data regarding the standardized exchange-type derivative product. To do.

  In some embodiments, the transmission of data relating to standardized exchange-type derivative products is the settlement price, bid price, offer price or trading of standardized exchange-type derivative products. Includes transmission of data regarding one or more of the prices.

  In another embodiment, in a non-volatile computer-readable medium having recorded computer-executable instructions for configuring a computer to perform a method for calculating a bond volatility index when executed on a computer, the method comprises: Receiving data relating to the option of the bond derivative, calculating the bond volatility index using the data relating to the option of the bond derivative, and transmitting data relating to the bond volatility index.

  In some embodiments of non-volatile computer readable media, the data on bond derivative options includes data on bond derivative option prices.

  In one embodiment of the non-volatile computer-readable medium, the data relating to the price of the bond derivative option includes data relating to the price of the bond future or bond forward option.

  In some embodiments of non-volatile computer readable media, the data relating to the option price of the bond derivative includes data relating to the price of the European option of the bond forward.

  In some embodiments of non-volatile computer readable media, the data relating to the option price of the bond derivative includes data relating to the price of the non-European option of the bond forward.

  In some embodiments of non-volatile computer readable media, if the data on the price of bond derivative options includes the price of non-European option prices on bond forwards, the price of non-European options on bond forwards Convert the data into data on the European option price for bond forwards.

  In some embodiments of non-volatile computer readable media, the calculation of bond volatility index evaluates an optional basket of bond derivatives that is required for pricing independent of a swap model for bond derivatives. including.

ｔは、公債ボラティリティ指数が算出される時刻を示し、
Ｔは、公債デリバティブのオプションの期限を示し、
Ｔ_Ｄは、オプションの基礎となる公債デリバティブの満期を示し、Ｔ_Ｄ≧Ｔであり、
Ｔ_Ｎは、公債の期限を示し、
Ｚ＋１は、指数計算で使用されるオプションの総数を示し、
Ｋ_０は、Ｚ＋１個のオプションの最低行使価格（lowest strike）を示し、
Ｋ_ｉは、Ｚ＋１個のオプションのｉ番目に高い行使価格（i^th highest strike）を示し、
Ｋ_Ｚは、Ｚ＋１個のオプションの最高行使価格（highest strike）を示し、
ｉ≧１のとき、ΔＫ_ｉ＝１／２（Ｋ_ｉ＋１−Ｋ_ｉ−１）、及びΔＫ_０＝（Ｋ_１−Ｋ_０），ΔＫ_Ｚ＝（Ｋ_Ｚ−Ｋ_Ｚ−１）であり、
価格が時刻ｔにおいて観測可能である場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になるプットオプション及びコールオプションの基礎となる、公債デリバティブ契約の時刻ｔにおける価格であり、
価格が時刻ｔで観測可能でない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小になる行使価格（strike）であり、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがある場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）に等しく、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがない場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）であり、
Ｐ_ｔ（Ｔ）は、Ｔを満期とするデフォルトなし割引債の時刻ｔの価格であり、
Ｐｕｔ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるプットオプションの時刻ｔにおける価格であり、
Ｃａｌｌ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるコールオプションの時刻ｔにおける価格であり、
ＧＢ−ＶＩ（ｔ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブのＴで期限になるオプションに基づいて算出された公債ボラティリティ指数の時刻ｔにおける値である。 In some embodiments of non-volatile computer readable media, the bond volatility index is calculated by the following equation at time t:

t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, underlying the put option and call option would limit at T _D , The price of bond derivative contract at time t,
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
GB-VI (t, T, T _D , T _N ) was calculated based on an option that expires at T of a bond derivative that expires at T _D , with the underlying bond maturing at T _N It is the value at time t of the public debt volatility index.

ｔは、公債ボラティリティ指数が算出される時刻を示し、
Ｔは、公債デリバティブのオプションの期限を示し、
Ｔ_Ｄは、オプションの基礎となる公債デリバティブの満期を示し、Ｔ_Ｄ≧Ｔであり、
Ｔ_Ｎは、公債の期限を示し、
Ｚ＋１は、指数計算で使用されるオプションの総数を示し、
Ｋ_０は、Ｚ＋１個のオプションの最低行使価格（lowest strike）を示し、
Ｋ_ｉは、Ｚ＋１個のオプションのｉ番目に高い行使価格（i^th highest strike）を示し、
Ｋ_Ｚは、Ｚ＋１個のオプションの最高行使価格（highest strike）を示し、
ｉ≧１のとき、ΔＫ_ｉ＝１／２（Ｋ_ｉ＋１−Ｋ_ｉ−１）、及びΔＫ_０＝（Ｋ_１−Ｋ_０），ΔＫ_Ｚ＝（Ｋ_Ｚ−Ｋ_Ｚ−１）であり、
価格が時刻ｔにおいて観測可能である場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になるプットオプション及びコールオプションの基礎となる、公債デリバティブ契約の時刻ｔにおける価格であり、
価格が時刻ｔで観測可能でない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小になる行使価格（strike）であり、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがある場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）に等しく、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがない場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）であり、
Ｐ_ｔ（Ｔ）は、Ｔを満期とするデフォルトなし割引債の時刻ｔの価格であり、
Ｐｕｔ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるプットオプションの時刻ｔにおける価格であり、
Ｃａｌｌ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるコールオプションの時刻ｔにおける価格であり、
ＧＢ−ＶＩ^ｂｐ（ｔ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブのＴで期限になるオプションに基づいて算出された公債ボラティリティ指数の時刻ｔにおける値である。 In some embodiments of non-volatile computer readable media, the bond volatility index is calculated by the following equation at time t:

t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, underlying the put option and call option would limit at T _D , The price of bond derivative contract at time t,
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
GB-VI ^bp (t, T, T _D , T _N ) is calculated based on the option that expires at T of the bond derivative that expires at T _D , with the underlying bond maturing at T _N The value at the time t of the public bond volatility index.

であり、
ｔは、公債ボラティリティ指数が算出される時刻を示し、
Ｔは、公債デリバティブのオプションの期限を示し、
ｔ_ｊは、Ｔ以降の最初の利払いを示し
Ｔ_Ｄは、オプションの基礎となる公債デリバティブの満期を示し、Ｔ_Ｄ≧Ｔであり、
Ｔ_Ｎは、公債の期限を示し、
Ｚ＋１は、指数計算で使用されるオプションの総数を示し、
Ｋ_０は、Ｚ＋１個のオプションの最低行使価格（lowest strike）を示し、
Ｋ_ｉは、Ｚ＋１個のオプションのｉ番目に高い行使価格（i^th highest strike）を示し、
Ｋ_Ｚは、Ｚ＋１個のオプションの最高行使価格（highest strike）を示し、
ｉ≧１のとき、ΔＫ_ｉ＝１／２（Ｋ_ｉ＋１−Ｋ_ｉ−１）、及びΔＫ_０＝（Ｋ_１−Ｋ_０），ΔＫ_Ｚ＝（Ｋ_Ｚ−Ｋ_Ｚ−１）であり、
価格が時刻ｔにおいて観測可能である場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になるプットオプション及びコールオプションの基礎となる、公債デリバティブ契約の時刻ｔにおける価格であり、
価格が時刻ｔで観測可能でない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小になる行使価格（strike）であり、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがある場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）に等しく、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがない場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）であり、
Ｐ_ｔ（Ｔ）は、Ｔを満期とするデフォルトなし割引債の時刻ｔの価格であり、
Ｐｕｔ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるプットオプションの時刻ｔにおける価格であり、
Ｃａｌｌ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるコールオプションの時刻ｔにおける価格であり、
Ｎは、公債の利払いの総数であり、
Ｃ_ｉは、公債のＮ個の利払いのうちのｉ番目の利子の額であり、
ｎは、公債の１年あたりの利払いの頻度であり、
ｙは、公債の利回りであり、
ｘは、公債の利回りであり、

In some embodiments of non-volatile computer readable media, if there is no interest incurred at time T, then the bond volatility index is calculated at time t by the following equation:

And
t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
t _j is, T _D shows the first interest payment after the T indicates the maturity of the public debt derivatives to be the option of the foundation, is a T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, underlying the put option and call option would limit at T _D , The price of bond derivative contract at time t,
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
N is the total number of interest payments on bonds,
C _i is the amount of the i-th interest of the N interest payments on public debt,
n is the frequency of interest payment per year for government bonds,
y is the bond yield,
x is the bond yield,

であり、
ｔは、公債ボラティリティ指数が算出される時刻を示し、
Ｔは、公債デリバティブのオプションの期限を示し、
Ｔ_Ｄは、オプションの基礎となる公債デリバティブの満期を示し、Ｔ_Ｄ≧Ｔであり、
Ｔ_Ｎは、公債の期限を示し、
Ｚ＋１は、指数計算で使用されるオプションの総数を示し、
Ｋ_０は、Ｚ＋１個のオプションの最低行使価格（lowest strike）を示し、
Ｋ_ｉは、Ｚ＋１個のオプションのｉ番目に高い行使価格（i^th highest strike）を示し、
Ｋ_Ｚは、Ｚ＋１個のオプションの最高行使価格（highest strike）を示し、
ｉ≧１のとき、ΔＫ_ｉ＝１／２（Ｋ_ｉ＋１−Ｋ_ｉ−１）、及びΔＫ_０＝（Ｋ_１−Ｋ_０），ΔＫ_Ｚ＝（Ｋ_Ｚ−Ｋ_Ｚ−１）であり、
価格が時刻ｔにおいて観測可能である場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になるプットオプション及びコールオプションの基礎となる、公債デリバティブ契約の時刻ｔにおける価格であり、
価格が時刻ｔで観測可能でない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小になる行使価格（strike）であり、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがある場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）に等しく、
Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）で行使されるオプションがない場合、Ｋ_＊は、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）であり、
Ｐ_ｔ（Ｔ）は、Ｔを満期とするデフォルトなし割引債の時刻ｔの価格であり、
Ｐｕｔ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるプットオプションの時刻ｔにおける価格であり、
Ｃａｌｌ_ｔ（Ｋ_ｉ，Ｔ，Ｔ_Ｄ，Ｔ_Ｎ）は、Ｔ_Ｎで満期になる基礎となる公債を有する、Ｔ_Ｄで期限になる公債デリバティブを基礎とする、Ｋ_ｉで行使され、Ｔで期限になるコールオプションの時刻ｔにおける価格であり、
Ｎは、公債の利払いの総数であり、
Ｃ_ｉは、公債のＮ個の利払いのうちｉ番目の利子の額であり、
ｎは、公債の１年あたりの利払いの頻度であり、
ｘは、公債の利回りであり、

In some embodiments of non-volatile computer readable media, the bond volatility index is calculated by the following equation at time t:

And
t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, underlying the put option and call option would limit at T _D , The price of bond derivative contract at time t,
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
N is the total number of interest payments on bonds,
C _i is the amount of the i-th interest of the N of interest payments on public debt,
n is the frequency of interest payment per year for government bonds,
x is the bond yield,

  In some embodiments of the non-volatile computer readable medium, the at least one processor further creates a standardized exchange-type derivative product based on the bond volatility index, and the standardized exchange-type Submit data on derivative products.

  In some embodiments of non-volatile computer readable media, transmission of data regarding a standardized exchange-type derivative instrument is a settlement price, a bid price, a selling price or a transaction price of the standardized exchange-type derivative instrument. Transmission of data relating to one or more of the above.

  The foregoing is a non-limiting summary of the invention, and some of these embodiments are defined by the claims.

It is a figure which shows the computerized transaction system of a financial exchange. It is a figure which shows the back end transaction system of a financial exchange. 6 is a flowchart of a method for calculating a basis point bond (GB) price volatility index. 3 is a flowchart of a method for calculating a percentage public bond (GB) price volatility index. FIG. 1 illustrates a general purpose computer system that can be modified by computer hardware or software to be custom designed and specialized to be suitable for use in a financial exchange computerized trading system. 6 is a flowchart of a method for calculating a basis point public debt (GB) yield volatility index. 6 is a flowchart of a method for calculating a period-corrected basis point public debt (GB) yield volatility index.

  Some embodiments of the present invention can be implemented on known or later developed financial transaction systems and / or other well-known financial systems. Financial transaction systems and other well known financial systems typically include client and server computers that include computer hardware (eg, computer processors, memory, storage, input / output devices, other well known components of a computer system, etc.) Electronic communication equipment such as electronic communication lines, routers, switches, electronic information storage systems such as network-connected storage and storage area networks) and computer software (ie, instructions that cause computer hardware to function in a particular manner) The combination achieves the desired system performance. The financial transaction system may be an open outcry system in a standing hall, a pure electronic system, or a combination of an open outcry system in a standing hall and a pure electronic system. .

  Figure 1 creates and publishes public debt (GB) futures option-based indices (such as public debt (GB) volatility index) and / or creates and lists derivative contracts based on public debt (GB) futures option indices 1 illustrates an electronic commerce system 100 that can be used to trade. It will be apparent to those skilled in the art that the system 100 described in detail below can be implemented using a combination of computer hardware and software as described in the previous paragraph. It is also clear that the method described below can be realized by the system described here.

  The system 100 includes components operated by an exchange and components operated by others who access and trade the exchange. Components shown in broken lines are components operated by an exchange. Components outside the dashed line are components that are operated by other than the exchange but are necessary for the operation of the transaction to be performed. The exchange component 122 of the trading system 100 includes an electronic trading platform 120, a membership interface 108, a matching engine 110, and a backend system 112. Clearing Corporation's system 114 and Member Firm's back-end system 116 are not operated by an exchange but are essential back-end systems for processing transactions and concluding contracts.

  Market Makers can directly access the trading platform 120 via a personal input device 104 connected to the member interface 108. A market maker can present the price of a derivative contract of the present invention, eg, a public debt (GB) volatility index derivative contract. However, the non-member customer 102 needs to access the exchange via a member company. The customer order is forwarded via the member company forwarding system 106. The member company forwarding system 106 sends the order to the exchange via the member interface 108. The member interface 108 manages all communication between the member company forwarding system 106 and the market maker's personal input device 104, determines whether the order can be processed by the trading platform, and processes the order. Determine the appropriate matching engine. Although only a single matching engine 110 is shown in the system 100, the trading platform 120 may include multiple matching engines. For efficient execution of trading, different exchange traded products may be assigned to different matching engines. When the member interface 102 receives an order from the member company forwarding system 106, the member interface 108 determines the appropriate matching engine 110 to process the order and sends the order to the appropriate matching engine. The matching engine 110 executes the transaction by pairing corresponding marketable buy / sell orders. Non-marketable orders are placed in an electronic order book.

  Once the order has been fulfilled, the matching engine 110 sends details of the fulfilled transaction to the exchange backend system 112, the securities settlement company system 114, and the member company backend system 116. The matching engine also updates the order book to reflect market changes based on fulfilled transactions. Due to market changes, orders that were not previously marketable may become marketable. In this case, the matching engine 110 fulfills such an order.

  The exchange backend system 112 performs many different functions. For example, the exchange backend system 112 issues contract definitions and listing data. The bond (GB) futures option index of the present invention, for example, the bond (GB) volatility index described below, and pricing information for derivative contracts related to the index of the present invention, is exchanged from the exchange back-end system to the market data vendor 118. It will be announced. Customers 102, market makers 104 and other users can access market data relating to the indices of the present invention and derivative contracts based on the indices of the present invention, for example, via a dedicated network, online services, and the like.

  The exchange back-end system also evaluates the underlying asset or asset on which the derivative contract of the present invention is based. At expiration, the back-end system 112 determines an appropriate payment amount and provides the final financial payment data to the securities payment company 114. The securities settlement company 114 functions as a bank of the exchange and performs a final mark-to-market on a member company margin account based on the position of the customer of the member company. . The final market value evaluation reflects the final settlement amount of the derivative contract of the present invention, and the securities settlement company makes withdrawals / withdraws to the account of the member company accordingly. These data are also sent to the member company's system 116, which may update the customer's account.

  FIG. 2 illustrates an exchange used to create and publish an index of the present invention, eg, a public debt (GB) volatility index, and / or to create, list and trade a derivative contract based on the index of the present invention. 1 illustrates an embodiment of a back-end system 112. The derivative contract of the present invention has a definition stored in module 202, which includes, for example, a trading platform such as a contract symbol, a definition of the underlying asset or asset associated with the derivative, a term of calculation period associated with the derivative, etc. Includes all relevant data for derivative contracts traded on 120. Pricing data storage and publication module 204 receives contract information from derivative contract definition module 202 and receives transaction data from matching engine 110. Pricing data storage and publication module 204 provides market data vendor 118 with market data regarding open bids and offers and recent transactions. The pricing data storage and publication module 204 also sends the transaction data to the securities settlement company 114, which, when each transaction date is closed, determines the current market price of the derivative contract of the present invention. Take account of the market value of member company accounts. The settlement calculation module 206 receives input from the derivative monitoring module 208. On the settlement date, the settlement calculation module 206 calculates the settlement amount based on the underlying asset or a value related to the asset, for example, the value of the public debt (GB) volatility index. The settlement calculation module 206 sends the settlement amount to the securities settlement company 114, and the securities settlement company 114 performs a final market price evaluation on the account of the member company and settles the derivative contract of the present invention.

  FIG. 5 illustrates an exemplary embodiment of a general-purpose computer system that can be used with one or more of the components shown in FIG. 1 or other trading systems configured to perform the methods described in further detail below. The system is shown at 500. Computer system 500 may include a set of instructions that cause computer system 500 to perform one or more of the methods or computer-based functions disclosed herein. The computer system 500 may operate as a stand-alone device or may be connected to other computer systems or peripheral devices using, for example, a network.

  In a networked deployment, the computer system may operate within the capacity of the server, may operate as a client user computer in a server-client user network environment, and may be a peer computer in a peer-to-peer (or distributed) network environment. It may operate as a system. The computer system 500 includes a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a mobile device, a palmtop computer, and a laptop computer. May be implemented as a variety of devices including top computers, desktop computers, network routers, switches or bridges, some other machine that executes a set of instructions (sequential or otherwise) that specify the operation of the machine, etc. Or may be incorporated into these devices. In particular embodiments, computer system 500 may be implemented using electronic devices that provide voice, video or data communications. Furthermore, although a single computer system 500 is illustrated herein, the term “system” may execute a set or sets of instructions, individually or in cooperation, to implement one or more computer functions. And any collection of systems or subsystems to be interpreted.

  As shown in FIG. 5, a computer system 500 may include a processor 502 that is a central processing unit (CPU), a graphics processing unit (GPU), or both. In addition, the computer system 500 can include a main memory 504 and a static memory 506 that can communicate with each other via a bus 508. Further, as shown in this figure, a computer system 500 includes a video display unit 510, such as a liquid crystal display (LCD), an organic light emitting diode (OLED), a flat panel display, and a solid state display. Alternatively, a cathode ray tube (CRT) can be included. Further, the computer system 500 can include an input device 512 such as a keyboard and a cursor control device 514 such as a mouse. The computer system 500 can also include a disk drive unit 516, a signal generation device 518 such as a speaker or remote controller, and a network interface device 520.

  In certain embodiments, as shown in FIG. 5, the disk drive unit 516 can include a computer-readable medium 522, which can store one or more sets of instructions 524, eg, software. Further, the instructions 524 can embody one or more of the methods or logic disclosed herein. In certain embodiments, the instructions 524 reside completely or at least partially in main memory 504, static memory 506, and / or processor 502 during execution by computer system 500. Main memory 504 and processor 502 may also include computer-readable media.

  In variations, dedicated hardware, such as application specific integrated circuits, programmable logic arrays, and other hardware devices may be constructed to implement one or more of the methods disclosed herein. Applications that can include the devices and systems of the various embodiments broadly encompass a variety of electronic and computer systems. One or more embodiments disclosed herein employ two or more specific interconnected hardware modules or devices with associated control and data signals that can communicate between and through the modules. Or as part of an application specific IC. The system thus encompasses implementations in software, firmware and hardware.

  In various embodiments herein, the methods disclosed herein may be implemented by a software program executable by a computer system. Further, non-limiting exemplary embodiments include implementations with distributed processing, component / object distributed processing, and parallel processing. Alternatively, a virtual computer system process may be constructed that performs one or more of the methods or functions disclosed herein.

  This specification includes computer-readable media that store instructions 524 or that receive and execute instructions 524 in response to propagated signals so that devices connected to network 526 can receive audio over network 526. Can communicate video or data. Further, the network interface device 520 may send or receive instructions 524 over the network 526.

  Although computer readable media is illustrated as a single medium, the term “computer readable medium” refers to a single medium or multiple media, eg, a centralized or distributed database, and / or one or more sets of Includes an associated cache and server for storing instructions. The term “computer-readable medium” also stores a set of instructions for execution by a processor or for causing a computer system to perform any one or more of the methods or operations disclosed herein, Any medium that encodes or conveys.

  In certain exemplary, non-limiting embodiments, the computer-readable medium can include a solid state memory, such as a memory card or other package that houses one or more non-volatile read-only memories. Further, the computer readable medium may be random access memory or other volatile memory or rewritable memory. In addition, computer-readable media can include magneto-optical media or optical media, such as disks or tapes, or other storage devices that capture information transmitted on a transmission medium. A digital file or other self-contained information archive or set of archives attached to an email can be considered a distribution medium equivalent to a tangible storage medium. Accordingly, the disclosure herein includes one or more computer-readable media or distribution media and other equivalent successor media that can store data or instructions.

  While this specification describes components and functions that can be implemented in particular embodiments with reference to specific standards and protocols commonly used by investment advisory companies, the present invention describes such It is not limited to standards and protocols. For example, standards for Internet and packet-switched network transmissions (eg, TCP / IP, UDP / IP, HTML, HTTP) represent specific examples at the current state of the art. Such standards are regularly replaced by faster or more efficient equivalent standards that have essentially the same functionality. Accordingly, replacement standards and protocols having the same or similar functions as those disclosed herein are considered equivalents thereof.

  In one embodiment, a system and method for calculating and publishing a public debt (GB) volatility index is provided. Public debt (GB) volatility indices (GB-VI) are shown in FIGS. 1, 2 and 5 and can be calculated and published using the system described in detail above. In general, GB-VI reflects the fair value of contracts to deliver the realized volatility of any tenor public debt (GB) futures, and public debt (GB) futures in any investment period. Reflects the expected volatility of the price. Also, in the index design framework, realized and expected futures and forward volatility are mathematically equivalent, so this index is used to deliver the actual volatility of public debt (GB) forwards. It can also be interpreted as the fair value of the contract and reflects the expected volatility of public bond (GB) forward prices within any investment period. In some embodiments of the present invention, GB-VI can be calculated for bonds (GB) in any country and currency in which bond futures (forwards) and bond futures (forwards) option markets exist. In some embodiments of the present invention, GB-VI is calculated based on market related data for public debt (GB) futures or forward options. For example, GB-VI is currently particularly suited to the Government Bond (GB) Futures (Forward) and Government Bond (GB) Futures (Forward) Options Market for government bonds issued by the United States, Germany, United Kingdom and other government agencies To do.

  In some embodiments of the present invention, the maturity and tenor on the “Volatility surface” (ie, the maturity of the option and the future or underlying bond tenor of the option). (Tenor)) for each combination of GB-VI, which is calculated for at-the-money and out-of-the-money of put options and call options for bond futures. This is done by consolidating prices (ie, option “skew”, “volatility skew”) into a single formula, which may be independent of any option pricing model. These GB-VIs are consistent with effective market practices that quote volatility in the interest rate market with respect to either basis point price volatility or percentage price volatility. (In this specification, unless otherwise noted, volatility means price volatility, not yield volatility.) Furthermore, GB-VI is a basis (not price volatility). You may quote in terms of point yield volatility, or you may quote in terms of modified duration-based basis yield yield volatility based on model-free conversion from price volatility to yield volatility. Furthermore, the GB-VI described herein can reflect the fair market price of contracts for futures trading of bonds (GB) volatility for each point on the volatility surface, ie, any maturity and underlying tenor.

ここで、ｔは、評価日であり、Ｔ_ｉ，ｉ∈［ｉ_ｔ，Ｎ］は、利払日であり、Ｔ_ｉは、Ｔ_０における発行の後の最初の利払日であり、
は、最初の利払日ｔであり、Ｔ_Ｎは、元金の返済と共に最後の利払いが行われる債券の満期であり、Ｃ_ｉ／Ｎは、Ｔ_ｉにおける利払いであり、Ｐ_ｔ（Ｔ_ｉ）は、Ｔ_ｉを満期とするデフォルトなし割引債の時刻ｔの価格であり、公債（ＧＢ）価格の不確実性の主な原因を表している。 Uncertainty associated with the public debt (GB) market is due to changes in the term structure of interest rates. Mathematically, the value B _t (T _N ) of a coupon-bearing government bond is expressed as follows:

Where t is the evaluation date, T _i , iε [i _t , N] is the interest payment date, T _i is the first interest payment date after issuance at T ₀ ,
Is the first interest payment date t, T _N is the maturity of the bond with the last interest payment along with the repayment of principal, C _i / N is the interest payment at T _i , and P _t (T _i ) is the price at time t of default without discount bonds with maturity of T _i, represents a major cause of public debt (GB) price of uncertainty.

In a public bond (GB) forward contract, one party agrees to deliver the public bond (GB) to the other party at a fixed price at a later date. The forward price F _t (T, T _N ) at time t for delivery of a bond that matures at T _N at T is expressed by the following equation.

Depending on the contract, the seller can select from a set of multiple “deliverable” bonds (GB), where the underlying bond B _t (T _N ) is a flat price of transaction or some scalar value. It can be interpreted as a tracked price of the “cheapest delivery” public debt (GB) quoted by a price adjusted based on a “conversion factor”.

ここで、Ｔ_Ｄは、Ｔで満期になるオプションの基礎となる公債先渡の満期を表し、Ｔ_Ｄ≧Ｔである。Ｋ_＊は、現在の先渡価格Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）である。時刻ｔにおいて先渡価格を観測できない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小となる行使価格（strike）である。 Here, the forward adjustment deals with the case where no option is exercised at the ATM forward price, and K _* is the first effective strike price below the current forward price F _t (T, T _N ) (strike ). If the forward price cannot be observed at time t, F _t (T, T _N ) is the strike price at which the difference between the put price and the call price is minimized. More generally, the following holds for any constant multiplier CM.

Here, T _D represents the maturity of the bond forward, which is the basis of the option that matures at T, and T _D ≧ T. K _* is the first valid strike price below the current forward price F _t (T _D , T _N ). If the forward price cannot be observed at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized.

A “government bond basis point variance swap agreement” is an agreement in which party A agrees to pay party B the following amount at time T at time t.

これは、ＢＰ ＧＢ分散スワップ合意の換算された公正価格である。
より一般化すれば、あらゆる一定の乗数ＣＭについて、以下が成り立つ。

ここで、Ｔ_Ｄは、Ｔで満期になるオプションの基礎となる公債先渡の満期を表し、Ｔ_Ｄ≧Ｔである。Ｋ_＊は、現在の先渡価格Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）を下回る最初の有効な行使価格（strike）である。時刻ｔにおいて先渡価格を観測できない場合、Ｆ_ｔ（Ｔ_Ｄ，Ｔ_Ｎ）は、プット価格とコール価格の間の差分が最小となる行使価格（strike）である。 In some embodiments, the “Basis Point Government Bond Price Volatility Index” is expressed as follows:

This is the translated fair value of the BP GB diversified swap agreement.
More generally, the following holds for any constant multiplier CM.

Here, T _D represents the maturity of the bond forward, which is the basis of the option that matures at T, and T _D ≧ T. K _* is the first valid strike price below the current forward price F _t (T _D , T _N ). If the forward price cannot be observed at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized.

ここで、ｄｃ（ｙｅａｒ）は、公債のために用いられる日数算出の取り決めに基づく１年の日数であり、ｄｃ（Ｔ−ｔ）は、公債のために用いられる日数計算の取り決めに基づくｔとＴの間の日数である。
そして、幾つかの実施形態では、「ベーシスポイント公債利回りボラティリティ指数」は、以下のように表すことができる。

ここで、Ｔ_Ｄは、Ｔで満期になるオプションの基礎となる公債先渡の満期を表し、Ｔ_Ｄ≧Ｔである。 Public debt (GB) market volatility is most commonly measured and traded by price volatility, but as a further formulation of public debt (GB) futures volatility, basis point yield volatility can also be assumed.
The expected bond price B _* (T _N ) is defined as follows:
GB-VI ^bP (t, T, T _N ) = B _* (T _N ) × GB-VI (t, T, T _N )
The corresponding profit / loss Y _B (T _N ) is defined as follows.

Here, dc (year) is the number of days in a year based on the number calculation convention used for public bonds, and dc (T−t) is t based on the number calculation convention used for public bonds. The number of days between T.
And in some embodiments, the “Basis Point Bond Yield Volatility Index” can be expressed as:

Here, T _D represents the maturity of the bond forward, which is the basis of the option that matures at T, and T _D ≧ T.

記号の意味は、先の段落で定義した通りである。 In some embodiments, the “Modified Duration-Based Basis Point Government Bond Yield Volatility Index” is defined as follows:

The meaning of the symbols is as defined in the previous paragraph.

ここで、以下が成り立つ。

PCT_GBVI, BP_GBVI, for BPY_GBVI and MDBPY_GBVI, optional maturity, for short T _{<T D} from the underlying bonds (GB) forwards, can be calculated adjustment period in consideration of the influence of the maturity of the difference. The four adjusted exponential equations are shown below.

Here, the following holds.

  In the mathematical expression and formula of the public debt volatility index described above, the price of the European option of the public debt (GB) forward is adopted. However, as long as the price of options with other exercise styles or options based on other public debt (GB) derivatives is not substantially different from the equivalent price of European options forwarded by public debt (GB), These options may be used directly in the expression. For example, “Flesaker, B. 1993,“ Testing the Heath-Jarrow-Morton / Ho-Lee Model of Interest Rate Contingent Claims Pricing ”Journal of Financial and Quantitative Analysis 28,” and “Bikbov, R. and M. Chernov, 2011 , "Yield Curve and Volatility: Lessons from Eurodollar Futures and Options" Journal of Financial Econometrics 9, the price of out-of-the-money American-style options for bond futures It can be concluded that it is not substantially different from the price of the European option for equivalent bond forwards.

  Several exchanges currently list US-style options for public debt (GB) futures. For cases where the price of a US option on a public bond (GB) future is substantially different from the price of a European option on a public bond (GB) forward, the inventors will correspond to the price of a US bond future option. Developed a method to convert European bond forward option price. This is because (1) a model of interest rate dynamics is selected, its parameters are estimated from historical data, and (2) the difference between the observed option price and the option price predicted by the model in (1) is This can be done by defining and calibrating the risk price to be minimal and using the risk price calibrated in (2) to calculate the European option for bond forwards predicted from the model.

In one exemplary approach, the price of a US option on a bond future can be converted to the price of a European option on a bond forward. This exemplary approach is performed as follows.

  Maturities differ in public bond (GB) forward and forward option markets that are traded in cycles based on standardized roll dates (eg, quarterly updates in March, June, September, and December) A combination of two or more forward options can be used to calculate an index by maturity corresponding to any maturity between the shortest maturity used and the longest maturity. The same approach can be used for public debt (GB) futures and futures options.

ここで、Ｉ_ｔ ^ＢＰは、ベーシスポイント公債価格ボラティリティ指数のサンドイッチ型組合せであり、Ｉ_ｔ ^ｐｅｒｃは、パーセンテージ公債価格ボラティリティ指数のサンドイッチ型組合せである。 For public debt (GB) forward and forward option transactions with maturity cycles, the first non-limiting example is the “sandwich combination”, which is the index of the most recent renewal date. The m month horizon volatility index is calculated as follows:

Here, I _t ^BP is a sandwich type combination of basis point bond price volatility index, and I _t ^perc is a sandwich type combination of percentage bond price volatility index.

  Also, in the case of government bond (GB) forward and forward option transactions with maturity cycles, a second non-limiting example is based on the skew index of a specific futures option contract with a shorter time to maturity. A volatility index may be calculated. For example, if the index is based on an option that expires in 3 months for a 10-year bond, the index on the first day reflects the expected volatility over the next 3 months, the next day starting from the next 3 months This process is repeated until the expiry date of the option naturally ends, reflecting an expected volatility over the subtracted period and an index of 3 months. The same approach can be used for public debt (GB) futures and futures options.

  FIG. 3 is a flowchart outlining a multi-step embodiment for calculating and publishing a basis point bond price volatility index in accordance with the present invention. In step 302, data is electronically received from an electronic data source. The received data includes data relating to public bond (GB) options. In step 304, the data is cleaned and normalized based on well-known techniques to generate bond (GB) option price data that is input into an exponential formula for all valid maturity / tenor / strike combinations. . In step 306, if the option price is not the price of the European bond futures option, this price may optionally be converted to the corresponding price of the European bond futures option. In step 308, for each combination of maturity and tenor, all valid strike prices are entered into the above-described equation BP_GBVI to calculate a basis point bond (GB) volatility index.

  FIG. 4 is a flowchart outlining a multi-step embodiment for calculating and announcing percentage bond price volatility based on the present invention. In step 402, data is electronically received from an electronic data source. The received data includes data relating to public bond (GB) options. In step 404, the data is cleaned and normalized based on well-known techniques to generate bond (GB) option price data that is input into an exponential formula for all valid maturity / tenor / strike combinations. . In step 406, if the option price is not the price of the European bond futures option, this price may optionally be converted to a corresponding price of the European bond futures option. In step 408, for all valid strike prices, the price of each combination of maturity and tenor is entered into the above formula PCT_GBVI to calculate the percent bond price volatility index.

  FIG. 6 is a flowchart outlining a multi-step embodiment for calculating and publishing a basis point bond yield volatility index in accordance with the present invention. In step 602, data is electronically received from an electronic data source. The received data includes data relating to public bond (GB) options. In step 604, the data is cleaned and normalized based on well-known techniques to generate public bond (GB) option price data that is input into an exponential formula for all valid maturity / tenor / strike combinations. . In step 606, if the option price is not the price of a European bond futures option, this price may optionally be converted to a corresponding price of a European bond futures option. In step 608, for all valid strike prices, the price of each combination of maturity and tenor is entered into the above-described equation BPY_GBVI to calculate the basis point bond yield volatility index.

  FIG. 7 is a flowchart outlining an embodiment of multiple steps for calculating and publishing a period-based basis point bond yield volatility index in accordance with the present invention. In step 702, data is electronically received from an electronic data source. The received data includes data relating to public bond (GB) options. In step 704, the data is cleaned and normalized based on well-known techniques to generate public bond (GB) option price data that is input to the exponential formula for all valid maturity / tenor / strike combinations. . In step 706, if the option price is not the price of a European bond futures option, this price may optionally be converted to a corresponding price of a European bond futures option. In step 708, for all valid strike prices (strikes), the price of each combination of maturity and tenor is entered into the above-described formula MDBPY_GBVI to calculate a period-based basis point bond yield volatility index.

  The steps shown in FIGS. 3, 4, 6 and 7 can be performed using the systems shown in FIGS.

Specific Examples Non-limiting specific examples of constructing the three formulas of the government bond volatility index using the method of the present invention are shown below. As mentioned above, the basis point bond price volatility index, percent bond price volatility index, basis point bond yield volatility index, and time-based basis point bond yield volatility index are calculated and published as shown in Figure 3. Performed by the publication system.

  In this specific example, data reflecting virtual market conditions is used. The data provided is a European-style forward put option and call option premium in decimal format for 10-year public bond (GB) forwards that mature in one month. The data for this example is shown in Table 1 below.

The first and second columns shown in Table 1 above show the strike price K and the percentage implied volatilities IV (K) of each strike price. The third and fourth columns show call option and put option premiums.

  Table 2 below provides information regarding specific examples of calculation of basis point bond price volatility index and percent bond price volatility index based on the formulas (BP_GBVI) and (PCT_GBVI), respectively.

  The second column of Table 2 shows at-the-money and out-of-the-money bonds that are entered into the formula for the exemplary public debt (GB) volatility index ( GB) Indicates the type (type) of the forward option. The third column shows the option premiums entered in the formula, the fourth and fifth columns show the weights given to each option premium for the final calculation of the index, and finally the sixth And the seventh column shows the out-of-the-money option premium multiplied by the appropriate weight, respectively. In “Basis point contribution”, each price in the third column is multiplied by the corresponding weight in the fourth column, and in “Percent contribution”, each price in the third column corresponds to each price in the fifth column. The weight is multiplied.

比較のため、アットザマネーのベーシスポイントインプライドボラティリティ及びパーセンテージインプライドボラティリティは、それぞれ、ＩＶ^ＢＰ（ＡＴＭ）＝５９７．９６及びＩＶ（ＡＴＭ）＝４．５３％である。 Thus, based on the data shown in this specific example, exemplary basis point bond price volatility index and percentage bond price volatility index were respectively calculated as follows.

For comparison, at-the-money basis point implied volatility and percentage implied volatility are IV ^BP (ATM) = 597.96 and IV (ATM) = 4.53%, respectively.

In this non-limiting example, by converting the 100 ² basis points index, multiplied by 100 to both the rate and the logarithm volatility, interest rates and market practice to express basis points implied volatility as the product of log volatility Imitating.

  In some embodiments of the present invention, the index calculated based on the embodiments of the present invention can indicate the value of underlying derivative contracts such as option and future contracts. Specifically, in embodiments of the present invention, the Government Bond Volatility Index (GB-VI) is designed to trade volatility in various maturities and underlying tenor public bond (GB) futures prices. Can serve as the basis for the underlying derivative contracts. In particular, futures and option contracts with various maturities based on the index may be traded on the OTC and / or listed on an exchange.

  The derivative product based on the above-described bond volatility index may be created as a standard exchange-type contract or an over-the-counter contract. Once the bond volatility index (GB-VI) based on bond futures / forward options is calculated, this index can be accessed for use in creating derivative contracts. Symbols can be assigned. In general, a GB-VI derivative contract may be assigned any unique symbol that serves as a standard identifier for the type of standardized GB-VI derivative contract. Information related to GB-VI and / or GB-VI derivative contracts may be sent for display, eg listed on trading platform by sending GB-VI index and / or GB-VI derivative information May be. Specific examples of the type of information transmitted for display include the settlement price of GB-VI derivatives, bids and offers associated with GB-VI derivatives, GB-VI index values, and / or GB- Contains the value of the underlying option with which the VI is associated.

  Typically, GB-VI derivative contracts may be listed on an electronic platform, a stand-alone platform, a hybrid environment that combines an electronic platform and a stand-alone platform, or any other platform known in the art. One specific example of a hybrid exchange environment is disclosed in US Pat. No. 7,613,650 filed Apr. 24, 2003, which is hereby incorporated by reference in its entirety. . Furthermore, a trading platform such as an exchange can communicate the liquidity provider's GB-VI derivative contract quotes to other market participants via a dissemination network. Liquidity providers include any entity that can present the price of a distributed derivative to a designated Primary Market Maker (DPM), market maker, local, specialist, trading authority holder, registered trader, member or trading platform be able to. The publication network may include networks such as Options Price Reporting Authority (OPRA), CBOE futures network, Internet website or e-mail notification via e-mail communication network. Market participants can include liquidity providers, brokers, general investors, or any entity that joins a public network.

  The trading platform can execute buy and sell orders for GB-VI derivatives, calculate the underlying option GB-VI, access the GB-VI index, GB-VI index and / or GB -Sending VI derivative information for display (listing GB-VI and / or GB-VI derivatives on the trading platform) and publishing GB-VI and / or GB-VI derivatives via the publication network And executing the GB-VI derivative buy and sell orders until the GB-VI derivative contract is settled.

  In some embodiments, the GB-VI derivative contract is via an exchange-operated parimutuel auction and cash settlement based on the underlying log-return GB-VI index. You can trade. Electronic Paris Mutuel or Dutch auction systems conduct regular auctions with all contracts settled in-the-money funded by premiums collected for contracts settled out-of-the-money.

  As described above, in the Paris Mutuel auction, all contracts settled in-the-money are funded by contracts settled out-of-the-money. Thus, the net exposure of the system is zero, and once the auction process is complete, no open interest is accumulated over time. Furthermore, the price of the Paris Mutuel auction contract is determined by relative demands, the higher the strike price demand, the higher the price. In other words, in the Paris Mutuel auction, pricing is independent of the market maker, and instead the price is continuously adjusted to reflect the stream of orders that flow into the auction. Typically, every time an order enters the system, it affects not only the strike price that is in demand, but all other strike prices that are valid at that auction. In such a scenario, if the price increases due to the more demanding exercise price, the system will adjust the less demanding exercise price downward. In addition, this process does not require the matching of a specific buy order against a specific sell order as in many conventional markets. Instead, all buy and sell orders enter a single liquid pool, where each order can provide liquidity to other orders at different strike prices, leaving system exposure at zero. , Fluidity is maintained. This format maximizes liquidity, which is an important feature when the underlying product is not tradeable.

  The following features of futures contracts illustrate one embodiment of futures trading with the index of the present invention as the underlying asset. These features are not intended to limit the invention and represent common features of futures.

  Contract size: The notional amount of contract unit can be defined as a multiple of the index level and may depend on the currency of the underlying index. In the case of an OTC transaction, a multiplier may be negotiated between related parties for each transaction.

  Contract month: The exchange can list contracts with a predetermined sequence of maturity dates, for example, every third Friday of every six months. Similarly, an OTC dealer can open a market in a predetermined sequence of maturity dates and can open a market for contracts that expire on other dates for each transaction.

  Quotes and Minimum Price Intervals: Futures based on the index may be quoted as a fraction or fraction representing the nominal principal per contract, and may define the minimum increment in which the price of the contract changes, Either may depend on the currency of the underlying index. The OTC market may employ different conventions for quotes and minimum ticks.

  Last transaction date: The last transaction date is specified for each contract.

  Final settlement date: The final settlement date is specified for each contract.

  Final settlement value: The final settlement value is based on the level of an index calculated at a predetermined time on the settlement date.

  Delivery: Settlement of futures based on the index takes the form of delivery of the cash settlement amount, and the payment date is specified in relation to the final settlement date.

  Additional specifications for exchange trading: When trading on an exchange, you can specify details such as trading platform, credit guarantee, trading time, cross-order rules, block trading rules, reporting rules, etc.

  The following features of the option contract illustrate one embodiment of an option contract with the index of the present invention as the underlying asset. These features are not intended to limit the invention and represent optional common features.

  Contract size: The nominal principal of the contract unit can be defined as a multiple of the index level and may depend on the underlying index currency. In the case of an OTC transaction, a multiplier may be negotiated between related parties for each transaction.

  Contract month: The exchange can list a contract with a predetermined sequence of due dates, such as the third Friday every six months. Similarly, an OTC dealer can open a market in a predetermined sequence of maturity dates, and can open a market for contracts that expire on other dates for each transaction.

  Strike Price: Exchange prices may be listed on the exchange, or quoted by OCT dealers, in-the-money, at-the-money and out-of-the-money for each currency, and new as the futures price increases or decreases You may trade the strike price. Depending on the underlying index currency, the exchange or OTC dealer community can fix the minimum increment between exercise prices.

  Quotes and Minimum Price Intervals: Index-based options may be quoted as a fraction or fraction representing the nominal principal per contract and may be the smallest increment that changes the price of the contract, Either may depend on the currency of the underlying index. The OTC market may employ different conventions for quotes and minimum ticks.

  Exercise style: Options written on GB-VI are not limited to the following, but many are European. Also, a US-type contract having the index of the present invention as an underlying asset is conceivable.

  Expiration date: An expiration date is specified for each contract.

  Last transaction date: The last transaction date is specified for each contract.

  Settlement of exercise: The final settlement value is based on the index level calculated at a pre-specified time on the settlement date. The cash settlement amount is the difference between the index level and the exercise price, the amount adjusted by a multiplier if possible, and the payment date is specified in association with the due date.

  Additional specifications for exchange trading: When trading on an exchange, you can specify details such as trading platform, credit guarantee, trading time, reporting rules, etc.

  In other embodiments of the invention, other financial instruments can be created that track or reference the indices of the invention. Such products include, but are not limited to: Exchange Traded Funds and Exchange Traded Notes listed on exchanges, and structured products sold by financial institutions. products).

  The specific embodiments of the present invention have been described above. However, it will be apparent that some or all of these advantages may be achieved by adding other variations and modifications to the embodiments described herein.

Claims (18)

In a computer system that calculates the bond volatility index,
A memory configured to store at least one program;
At least one processor communicatively coupled to the memory, and when the at least one program is executed by the at least one processor, the at least one processor is:
Receive data on bond derivative options,
Using data on the options of the bond derivatives, calculate the bond volatility index,
A computer system for transmitting data relating to the bond volatility index.   The computer system according to claim 1, wherein the data related to the option of the bond derivative includes data related to a price of the option of the bond derivative.   3. The computer system according to claim 2, wherein the data relating to the price of the option of the bond derivative includes data relating to the price of the option of the bond future or the bond forward. The bond volatility index is calculated by the following formula at time t,

t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the minimum strike price (strike) of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for the Z + 1 option,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, and Foundation put option and call option would limit at T _D The price of the bond derivative contract at time t
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
_{Call t (K i, T,} T D, T N) is based on bonds derivatives made on time at _{T D} with bonds the underlying maturing at _{T N,} exercised by _{K i,} deadline at T Is the price at time t of the call option
_{GB-VI (t, T,} T D, T N) are bonds volatility calculated based on the options that are deadline at T of bonds derivatives made on time at _{T D} based upon bonds that maturing at _{T N} The computer system according to claim 3, wherein the computer system is a value at an index time t. The bond volatility index is calculated by the following formula at time t,

t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, and Foundation put option and call option would limit at T _D The price of the bond derivative contract at time t
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
GB-VI ^bp (t, T, T _D , T _N ) is calculated based on the option that expires at T of the bond derivative that expires at T _D , with the underlying bond maturing at T _N The computer system according to claim 3, wherein the computer system is a value at a time t of the bond volatility index. If there is no interest incurred at time T, the bond volatility index is calculated by the following formula at time t:

And
t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
t _j is, T _D shows the first interest payment after the T indicates the maturity of the public debt derivatives to be the option of the foundation, is a T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, and Foundation put option and call option would limit at T _D The price of the bond derivative contract at time t
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
N is the total number of interest payments on bonds,
C _i is the amount of the i-th interest of the N interest payments on public debt,
n is the frequency of interest payment per year for government bonds,
y is the bond yield,
x is the bond yield,

The bond volatility index is calculated by the following formula at time t,

And
t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, and Foundation put option and call option would limit at T _D The price of the bond derivative contract at time t
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
N is the total number of interest payments on bonds,
C _i is the amount of the i-th interest of the N interest payments on public debt,
n is the frequency of interest payment per year for government bonds,
x is the bond yield,

The at least one processor further comprises:
Create standardized exchange derivative products based on the bond volatility index,
The computer system of claim 1, wherein the computer system transmits data relating to the standardized exchange trading derivative instrument.   9. The computer of claim 8, wherein the transmission of data relating to the standardized exchange trading derivative product includes transmission of data relating to one or more of a settlement price, a buy price, a selling price or a trading price of the standardized exchange trading derivative product. system. A non-volatile computer-readable medium having recorded thereon computer-executable instructions for configuring a computer to perform a method for calculating a bond volatility index when executed on the computer, the method comprising:
Receiving data on bond derivative options;
Calculating a bond volatility index using data on options of the bond derivative;
Transmitting data relating to the bond volatility index.   The non-volatile computer-readable medium of claim 10, wherein the data relating to the option of the bond derivative includes data relating to a price of the option of the bond derivative.   The non-volatile computer-readable medium of claim 11, wherein the data regarding the option price of the bond derivative includes data regarding the price of a bond future or bond forward option. The bond volatility index is calculated by the following formula at time t,

t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, and Foundation put option and call option would limit at T _D The price of the bond derivative contract at time t
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
GB-VI (t, T, T _D , T _N ) was calculated based on an option that expires at T of a bond derivative that expires at T _D , with the underlying bond maturing at T _N The non-volatile computer-readable medium according to claim 12, which is a value at a time t of a public debt volatility index. The bond volatility index is calculated by the following formula at time t,

t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, and Foundation put option and call option would limit at T _D The price of the bond derivative contract at time t
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
GB-VI ^bp (t, T, T _D , T _N ) is calculated based on the option that expires at T of the bond derivative that expires at T _D , with the underlying bond maturing at T _N 13. The non-volatile computer-readable medium according to claim 12, wherein the non-volatile computer-readable medium is a value at a time t of a bond volatility index. If there is no interest incurred at time T, the bond volatility index is calculated by the following formula at time t:

And
t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
t _j is, T _D shows the first interest payment after the T indicates the maturity of the public debt derivatives to be the option of the foundation, is a T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, and Foundation put option and call option would limit at T _D The price of the bond derivative contract at time t
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
N is the total number of interest payments on bonds,
C _i is the amount of the i-th interest of the N interest payments on public debt,
n is the frequency of interest payment per year for government bonds,
y is the bond yield,
x is the bond yield,

The bond volatility index is calculated by the following formula at time t,

And
t is the time when the bond volatility index is calculated,
T is the deadline for options on bond derivatives,
T _D indicates the maturity of the bond derivative underlying the option, T _D ≧ T,
_TN indicates the due date of the bond,
Z + 1 indicates the total number of options used in the exponent calculation,
K ₀ indicates the lowest strike of Z + 1 options,
K _i represents the i ^th highest strike of Z + 1 options,
K _Z represents the highest strike for Z + 1 options,
When i ≧ 1, ΔK _i = 1/2 (K _{i + 1} −K _i−1 ), and ΔK ₀ = (K ₁ −K ₀ ), ΔK _Z = (K _Z −K _Z−1 ),
If the price is observable at time _{t, F t (T D,} T N) has bonds the underlying maturing at T _N, and Foundation put option and call option would limit at T _D The price of the bond derivative contract at time t
If the price is not observable at time t, F _t (T _D , T _N ) is the strike price at which the difference between the put price and the call price is minimized,
If there is an option exercised at F _t (T _D , T _N ), K _* is equal to F _t (T _D , T _N )
In the absence of an option exercised at F _t (T _D , T _N ), K _* is the first valid strike price below F _t (T _D , T _N ),
P _t (T) is the price at the time t of the non-default discount bond with a maturity of T,
Put _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T It is the price at the time t of the put option that expires,
Call _t (K _i , T, T _D , T _N ) is exercised at K _i , based on a bond derivative that expires at T _D , with the underlying bond maturing at T _N , and at T The price at the time t of the call option that expires,
N is the total number of interest payments on bonds,
C _i is the amount of the i-th interest of the N interest payments on public debt,
n is the frequency of interest payment per year for government bonds,
x is the bond yield,

The at least one processor further comprises:
Create a standard exchange-type derivative product based on the bond volatility index,
The non-volatile computer-readable medium of claim 10, wherein the non-volatile computer readable medium transmits data related to the standardized exchange-type derivative product.   The transmission of data relating to the standardized exchange traded derivative product includes sending data relating to one or more of a settlement price, a buy price, a sell price or a trade price of the standardized exchange traded derivative product. The non-volatile computer-readable medium according to claim 17.

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