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CN105339973A - Methods and systems for creating a government bond volatility index and trading derivative products based thereon - Google Patents

Methods and systems for creating a government bond volatility index and trading derivative products based thereon Download PDF

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CN105339973A
CN105339973A CN201380075864.3A CN201380075864A CN105339973A CN 105339973 A CN105339973 A CN 105339973A CN 201380075864 A CN201380075864 A CN 201380075864A CN 105339973 A CN105339973 A CN 105339973A
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bond
government
price
government bond
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A.米尔
Y.奥巴亚希
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Applied Academics LLC
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Priority claimed from US13/842,197 external-priority patent/US20130317963A1/en
Priority claimed from US13/931,114 external-priority patent/US20140040164A1/en
Priority claimed from US13/970,193 external-priority patent/US20130332333A1/en
Application filed by Applied Academics LLC filed Critical Applied Academics LLC
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    • G06COMPUTING; CALCULATING OR COUNTING
    • G06QINFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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Abstract

A computer system for calculating a government bond volatility index comprising memory configured to store at least one program; and at least one processor communicatively coupled to the memory, in which the at least one program, when executed by the at least one processor, causes the at least one processor to receive data regarding options on government bond derivatives; calculate, using the data regarding options on government bond derivatives, the government bond volatility index; and transmit data regarding the government bond volatility index.

Description

Method and system for creating government bond volatility index and trading derivatives based on government bond volatility index
RELATED APPLICATIONS
This application is a continuation of pending U.S. application No. 13/931,114, filed on 28.6.2013 as a continuation of pending U.S. application No. 13/842,197 filed on 15.3.2013, and pending U.S. application No. 13/842,197 claims priority (now expired) to U.S. provisional application No. 61/650,150 filed on 22.5.2012, each of which is incorporated herein by reference in its entirety. All parent documents, parent application and references cited anywhere in this specification are incorporated herein by reference in their entirety.
Technical Field
The present disclosure relates to a fixed revenue derived investment market.
Background
A derivative is a financial instrument whose value depends, at least in part, on the value and/or characteristics of another security called a subject asset (underpingasset). Examples of subject assets include, but are not limited to: interest rate financial instruments (e.g., bonds), securities, commodities, electronic trading funds, and indices. Two exemplary and notable derivatives are options and futures contracts.
Derivatives such as options and futures contracts may be traded off-site and/or on other trading platforms such as organized exchanges (e.g., the corporate chicago option exchange ("CBOE")). In an off-site transaction, the parties to the transaction can customize each transaction to meet each party's individual needs. Through trading derivative by the trading platform or exchange, the buy and sell orders of the standardized derivative contracts are submitted to the exchanges where they are matched and implemented. Typically, modern exchange exchanges have exchange-specific computer systems that allow orders to be submitted electronically via an electronic communication network, such as the internet. An example of an exchange-specific computer system is illustrated in fig. 1.
Once matched and implemented, the implemented transaction is transmitted to a clearing house (clearing corporation) between the holder of the derivative contract and the seller. When the exchange trade derivative is exercised, cash or tender assets are delivered to the settlement company as necessary, and the settlement company dispenses the appropriate assets and as dictated by the outcome of the trade.
Option contracts give the contract holder the right to buy or sell a subject asset at a particular price at or before a certain date, rather than obligation, depending on the type of option (e.g., U.S. or europe). Option contracts, in turn, mandate that the seller of the contract, depending on the option type (e.g., U.S. or europe), deliver the subject asset at a particular price at or before a certain date. The american option may be exercised at any time prior to its expiration. The european option can only be exercised at its expiry, i.e. at a single predefined point in time.
There are generally two types of options: subscription and maintenance. The option is granted the right to purchase the subject asset at a specific price (i.e., the performance price) with the holder, and the seller is obligated to deliver the subject asset to the holder at the performance price. The put option gives the holder the right to sell the subject asset at a particular price (i.e., a performance price) and places the seller obligation to purchase the subject asset at the performance price.
There are generally two types of settlement processes: physical settlement and cash settlement. In the physical settlement process, funds are transferred from one party to another party in the exchange for delivery of the subject asset. In the course of cash settlement, funds are delivered from one party to another party according to calculations incorporating data about the subject asset.
Futures contracts impose on the buyer of futures the obligation to receive the delivery of the subject good or asset on a fixed date in the future. Thus, the seller of the futures contract is obligated to deliver the goods or assets on the specified date at a given price. Futures may be settled using physical or cash settlement. Both options and futures contracts can be based on abstract market indicators, such as indices, and are typically traded at exchanges. Throughout this application, the term "term of subject bond" refers to the time of expiration of a bond that is the subject of a futures, and thus the subject of a futures option (because the option is written in relation to futures and not directly in relation to bonds).
The forward contract places an obligation on the forward buyer to receive delivery of the subject good or asset on a fixed date in the future. Therefore, the seller of the forward contract is obligated to deliver the goods or assets on the specified date at a given price. The forwards term may be settled using physical or cash settlement. Forward contracts can be based on abstract market indicators such as indices and are typically traded OTC-wise. Throughout this application, the term "term of subject bond" refers to the time of expiration of a bond that is the subject of a futures, and thus the subject of a futures option (because the option is written in relation to futures and not directly in relation to bonds).
An index is a statistically aggregated value used to indicate the market or the performance of the market over different time periods, i.e., used as a performance benchmark. Examples of indices include Doujones Industrial average index, national securities trader Association automatic quote Table ("NASDAQ") composite index, and Standard pulAs mentioned above, options relating to indices are typically settled in cash. For example, using cash settlement, the holder of the index subscription option receives the right to purchase an amount of cash that is not the index itself, but is equal to the value of the index multiplied by a multiplier (e.g., $ 100). Thus, if the holder of the index underwriting option exercises the option, the option seller must pay the holder the difference between the current value of the index and the performance price multiplied by the multiplier, if the option is real.
The indices on which the derivation may be based are those that measure the volatility of the market or market segment. For example, CBOE creates and distributes CBOE market volatility indices orWhich is formed by S&A key measure of market expectation of recent volatility conveyed by the P500 stock index option price. In addition, the first and second substrates are,the CBOE provides exchange traded derivative products (both futures and options) that use VIX as a subject asset. Volatility indexes and derivative products on this basis have been widely accepted by the financial industry as both a useful tool for hedging positions and a means for expressing investment views of the direction of volatility.
Government bonds are bond securities issued by governing entities. Bonds have different expiration dates and periodic fixed or floating interest payments, i.e. coupons, can be made. Government bonds are circulated under different names depending on the deadline for issuing the government or bonds, including but not limited to short term national library volume, medium term national library volume, long term national library volume, german national bond, german bobl, german schatz, japanese national bond (JGB), ukdilt, etc.
Disclosure of Invention
The inventors have recognized that while there are several volatility indices, there currently is no implementation of a volatility metric for the Government Bond (GB) market that theoretically coincides with the price prevailing in the existing market for GB-derived options such as for futures and forwards. In particular, there is no standard benchmark to estimate the volatility in the GB market over a given investment deadline and a deadline for a subject bond. Because there is currently no standardized benchmark reflecting the fair market value within options for expected GB volatility, traders, other market participants, and/or currency managers currently trade options for GB forwards and options for hedge other financial positions, stock market makes prosperous weather, and/or takes specific investment positions related to market volatility. However, the strategy employed in attempting to hedge risk via trading of options for GB futures does not necessarily result in precise gains and losses due to the trend of gains and losses being influenced by price dependencies, i.e., the generation of paths moved by prices between the start of trade and expiration date, rather than the absolute price level prevailing at the expiration of the options.
Accordingly, some embodiments of the present invention provide techniques for calculating an effective volatility index associated with the GB market. Additionally, some embodiments of the present invention provide techniques for instantiating and/or facilitating a trading derivative product based on such an index.
In some embodiments, techniques are provided for: creating and distributing one or more volatility indices calculated using data from government bond-derived options such as futures and forwards (i.e., options given their owner the right to join a subject bond-derived contract rather than obligations); and facilitating electronic creation and trading of derivative products based on one or more indices related to volatility.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention will be realized and attained by the methods particularly pointed out in the written description and claims hereof as well as the appended drawings.
To achieve these and other advantages and in accordance with the purpose of the present invention, as embodied and broadly described, the present invention provides a computer system for calculating a government bond volatility index, comprising a memory configured to store at least one program; and at least one processor communicatively coupled to the memory, wherein the at least one program, when executed by the at least one processor, causes the at least one processor to: receiving data regarding options derived from government bonds; calculating a government bond volatility index using data on options derived from government bonds; and transmitting data regarding the government bond volatility index.
In some embodiments, the data regarding government bond-derived options includes data regarding prices of government bond-derived options.
In one embodiment, the data regarding prices of options derived from government bonds includes data regarding prices of options on government bond futures or government bond forwards.
In further embodiments, the data regarding prices of options derived from government bonds includes data regarding prices of euro options for future on government bonds.
In some embodiments, the data regarding prices of options derived from government bonds includes data regarding prices of options that are not euro options of government bond forwards.
In some embodiments, when the data regarding prices of options derived from a government bond includes data regarding prices of options that are euro options that are not government bond forwards, the data regarding prices of options that are euro options that are not government bond forwards is converted into data regarding prices of euro options that are government bond forwards.
In some embodiments, calculating the government bond volatility index includes evaluating a set of options derived from the government bond that are required for model-independent pricing of the government bond-derived variance exchange contract.
In some embodiments, the government bond volatility index is calculated at time t according to the following equation:
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(Td,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a non-defaultable (non-defaultable) bond that expires at T;
Putt(Ki,t,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivativesLiving and harmony at TNA price at time t of the call option of the subject bond at expiration; and
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index at time T calculated at an option expiring at time T for a subject bond that expires.
In some embodiments, the government bond volatility index is calculated at time t according to the following equation
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,t,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration; and
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index at time T calculated at an option expiring at time T for a subject bond that expires.
In some embodiments, when there is no coupon due (accudcoupon) at time T, the government bond volatility index is calculated at time T according to the following equation:
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
wherein
P ^ ( y ) &equiv; &Sigma; i = 1 N C i n ( 1 + y n ) - i + 100 ( 1 + y n ) - N ;
And, the coupon to be accounted for when there is a time T and at the time TjCalculating a government bond volatility index at time t according to the following equation at the time of the next coupon due
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
Wherein
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
And is
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
And is
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
tjis a first ticket payment at or after T;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,t,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration;
n represents the total number of coupon payments for government bonds;
Cian amount of an ith coupon among the N coupons representing the government bond;
n represents the frequency of annual coupon payments for government bonds;
y represents a profit of the government bond;
x represents a benefit of a government bond;
is a bond price corresponding to a bond benefit of a bond of the subsidiary government;
is thatThe inverse of the function of (a);
is a bond price at time T corresponding to bond profit for a bond of the subsidiary government;
is thatThe inverse of the function of (a);
dc (year) is the number of days in a year based on a day count convention for government bonds;
dc (T-T) is the number of days between T and T based on a day count convention for government bonds;
is based on at TDTime expired government bond derivatives and at TNOption calculation for a targetted bond that expires at TA value of a government bond volatility index of the base point yield volatility at an outgoing time t;
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of a basepoint price volatility at time T calculated at an option expiring at T for a target bond at time of expiration; and
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of the percentage price volatility at time T calculated for options expiring at T for a target bond at expiration.
In some embodiments, the government bond volatility index is calculated at time t according to the following equation:
G B - VI Y d b p ( t , T , T D , T N ) &equiv; 100 &times; ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) &times; G B - VI b p ( t , T , T D , T N ) &Sigma; i = j N C i n ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t i - T ) d c ( y e a r ) ( d c ( t i - T ) d c ( y e a r ) ) + 100 ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t N - T ) d c ( y e a r ) ( d c ( t N - T ) d c ( y e a r ) )
wherein
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
And is
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
And is
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) The option of performing the contract is set up,then K is*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,t,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration;
n represents the total number of coupon payments for government bonds;
Cian amount of an ith coupon among the N coupons representing the government bond;
n represents the frequency of annual coupon payments for government bonds;
x represents a benefit of a government bond;
is a bond price corresponding to a bond benefit of a bond of the subsidiary government;
is thatThe inverse of the function of (a);
dc (year) is the number of days in a year based on a day count convention for government bonds;
dc (T-T) is the number of days between T and T based on a day count convention for government bonds;
tjis a first ticket payment at or after T;
is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index for a basepoint yield volatility at time T calculated for an option expiring at T for a target bond at time of expiration;
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of a basepoint price volatility at time T calculated at an option expiring at T for a target bond at time of expiration;
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of the percentage price volatility at time T calculated for options expiring at T for a target bond at expiration.
In some embodiments, the at least one processor is further caused to: creating a standardized exchange trading derivative instrument based on the government bond volatility index; and transmitting data relating to the standardized exchange transaction derivative.
In some embodiments, transmitting data regarding the standardized exchange trading derivative includes transmitting data regarding one or more of a settlement price, a bid price, or a trading price of the standardized exchange trading derivative instrument.
In further embodiments, a non-transitory computer readable storage medium has computer executable instructions recorded thereon that, when executed on a computer, configure the computer to perform a method of calculating a government bond volatility index, the method comprising: receiving data regarding options derived from government bonds; calculating a government bond volatility index using data on options derived from government bonds; and transmitting data regarding the government bond volatility index.
In some embodiments of the non-transitory computer readable storage medium, the data regarding government bond-derived options includes data regarding prices of government bond-derived options.
In one embodiment of the non-transitory computer readable storage medium, the data regarding prices of options derived from government bonds includes data regarding prices of options on government bond futures or government bond forwards.
In some embodiments of the non-transitory computer readable storage medium, the data regarding prices of options derived from government bonds includes data regarding prices of euro options for government bond forwards.
In some embodiments of the non-transitory computer readable storage medium, the data regarding prices of options derived from a government bond includes data regarding prices of options that are euro options that are not government bond forwards.
In some embodiments of the non-transitory computer readable storage medium, when the data regarding prices of options derived from the government bond includes data regarding prices of options that are euro options that are not government bond forwards, the data regarding prices of options that are euro options that are not government bond forwards is converted into data regarding prices of euro options that are government bond forwards.
In some embodiments of the non-transitory computer readable storage medium, calculating the government bond volatility index includes valuing a set of options derived from the government bond required for model-independent pricing of the government bond-derived variance exchange contract.
In some embodiments of the non-transitory computer readable storage medium, the government bond volatility index is calculated at time t according to the following equation:
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,t,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration; and
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index at time T calculated at an option expiring at time T for a subject bond that expires.
In some embodiments of the non-transitory computer readable storage medium, the government bond volatility index is calculated at time t according to the following equation:
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, thenFt(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,t,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration; and
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index at time T calculated at an option expiring at time T for a subject bond that expires.
In some embodiments of the non-transitory computer readable storage medium, when there is no coupon to be charged at time T, the government bond volatility index is calculated at time T according to the following equation
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
Wherein
P ^ ( y ) &equiv; &Sigma; i = 1 N C i n ( 1 + y n ) - i + 100 ( 1 + y n ) - N ;
And, when there is an information ticket to be charged at time T and at time TjCalculating a government bond volatility index at time t according to the following equation at the time of the next coupon due
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
Wherein
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
And is
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
And is
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
tjis a first ticket payment at or after T;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,t,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration;
n represents the total number of coupon payments for government bonds;
Cian amount of an ith coupon among the N coupons representing the government bond;
n represents the frequency of annual coupon payments for government bonds;
y represents a profit of the government bond;
x represents a benefit of a government bond;
is a bond price corresponding to a bond benefit of a bond of the subsidiary government;
is thatThe inverse of the function of (a);
is corresponding toBond price at time T of bond profit of the bond of the subsidiary government;
is thatThe inverse of the function of (a);
dc (year) is the number of days in a year based on a day count convention for government bonds;
dc (T-T) is the number of days between T and T based on a day count convention for government bonds;
is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index for a basepoint yield volatility at time T calculated for an option expiring at T for a target bond at time of expiration;
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of a basepoint price volatility at time T calculated at an option expiring at T for a target bond at time of expiration; and
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of the percentage price volatility at time T calculated for options expiring at T for a target bond at expiration.
In some embodiments of the non-transitory computer readable storage medium, the government bond volatility index is calculated at time t according to the following equation:
G B - VI Y d b p ( t , T , T D , T N ) &equiv; 100 &times; ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) &times; G B - VI b p ( t , T , T D , T N ) &Sigma; i = j N C i n ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t i - T ) d c ( y e a r ) ( d c ( t i - T ) d c ( y e a r ) ) + 100 ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t N - T ) d c ( y e a r ) ( d c ( t N - T ) d c ( y e a r ) )
wherein
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
And is
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
And is
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,t,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration;
n represents the total number of coupon payments for government bonds;
Cian amount of an ith coupon among the N coupons representing the government bond;
n represents the frequency of annual coupon payments for government bonds;
x represents a benefit of a government bond;
is a bond price corresponding to a bond benefit of a bond of the subsidiary government;
is thatThe inverse of the function of (a);
dc (year) is the number of days in a year based on a day count convention for government bonds;
dc (T-T) is the number of days between T and T based on a day count convention for government bonds;
tjis a first ticket payment at or after T;
is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index for a basepoint yield volatility at time T calculated for an option expiring at T for a target bond at time of expiration;
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNBase point price at time T calculated from option expiring at time T for subject bond at expirationA value of a government bond volatility index of volatility;
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of the percentage price volatility at time T calculated for options expiring at T for a target bond at expiration.
In some embodiments of the non-transitory computer readable storage medium, the at least one processor is further caused to: creating a standardized exchange trading derivative instrument based on the government bond volatility index; and transmitting data relating to the standardized exchange transaction derivative.
In some embodiments of the non-transitory computer-readable storage medium, transmitting data regarding the standardized exchange trading derivative includes transmitting data regarding one or more of a settlement price, a bid price, or a trading price of the standardized exchange trading derivative instrument.
The foregoing is a non-limiting summary of the invention, some embodiments of which are defined by the appended claims.
Drawings
FIG. 1 is a computerized trading system of a financial exchange;
FIG. 2 is a back end transaction system of a financial exchange;
FIG. 3 is a flow chart of a method of calculating a base point GB price volatility index;
FIG. 4 is a flow chart of a method of calculating a percentage GB price volatility index;
FIG. 5 is a diagram of a general purpose computer system that may be modified via computer hardware or software to be customized or specialized to be suitable for use in a financial exchange computerized trading system;
FIG. 6 is a flow chart of a method of calculating a base point GB gain volatility index; and
FIG. 7 is a flow chart of a method of calculating a modified duration-based base point GB revenue volatility index.
Detailed Description
Some embodiments of the invention may be implemented on financial transaction systems and/or other known financial industry systems, whether now known or later developed. Typically, financial transaction systems and other known financial industry systems utilize a combination of computer hardware (e.g., client and server computers, which may include computer processors, memory, storage, input and output devices, and other known components of computer systems, electronic communication devices, such as electronic communication lines, routers, switches, etc., electronic information storage systems, such as network-attached storage and storage area networks), and computer software (i.e., instructions that cause the computer hardware to function in a particular manner) to achieve desired system performance. It should be noted that the financial transaction system may be a floor-based public pricing system, a pure electronic system, or some combination of floor-based public pricing systems and pure electronic systems.
Fig. 1 illustrates an electronic trading system 100 that may be used to create and distribute GB futures-based indices (such as GB volatility indices) and/or to create, list, and trade derivative contracts based on GB futures indices. Those skilled in the art will readily appreciate that the system 100 described in detail below will be implemented using a combination of computer hardware and software as described in the paragraphs above. It will be appreciated that the described system may implement the method described below.
The system 100 includes components operated by the exchange and by others who access the transaction so they conduct the transaction. The components shown within the dashed lines are those operated by the exchange. Components outside the dashed line are operated by others, but are required for operation of the exchange to exercise responsibility. The exchange component 122 of the trading system 100 includes the electronic trading platform 120, the member interface 108, the matching engine 110, and the backend system 112. The back-end systems not operated by the exchange but necessary to process the transaction and settlement contract are settlement company system 114 and member company back-end system 116.
The market maker (markmaker) may access the transaction platform 120 directly through the personal input device 104 in communication with the member interface 108. Market makers may offer prices for derivative contracts (e.g., GB volatility index derivative contracts) of the present invention. However, the non-member customers 102 must access the exchange through a member company (memberfirm). The customer orders are routed through the member company routing system 106. The member company routing system 106 forwards the order to the exchange via the member interface 108. The member interface 108 manages all communications between the member company routing system 106 and the market maker's personal input device 104; determining whether the order can be processed by the trading platform; and determining an appropriate matching engine to process the order. Although only a single matching engine 110 is shown in the system 100, the transaction platform 120 may include multiple matching engines. Products traded by different exchanges may be assigned to different matching engines for efficient execution of the trade. When the member interface 102 receives an order from the member company routing system 106, the member interface 108 determines the appropriate matching engine 110 to process the order and forwards the order to the appropriate matching engine. The matching engine 110 performs the transaction by pairing corresponding marketable buy/sell orders. Non-orderable orders are placed in an electronic order book.
When the order is executed, the matching engine 110 sends the details of the executed transaction to the exchange back-end system 112, the clearing house system 114, and the member company back-end system 116. The matching engine also updates the order book to reflect changes in the marketplace based on the executed trades. Previously unaffordable orders may become available due to changes in the market. If so, the matching engine 110 also executes the orders.
The exchange back-end system 112 performs many different functions. For example, the contractual definition and listing data is initiated by the exchange back-end system 112. The GB futures options index of the present invention (e.g., the GB volatility index described below) and pricing information of derivative contracts associated with the index of the present invention are distributed from the exchange back-end system to market data providers 118. The customer 102, market makers 104, and others may access market data regarding the index of the present invention and derivative contracts based on the index of the present invention, for example, via a proprietary network, an online service, and the like.
The exchange back-end system also evaluates the subject asset or assets upon which the derivative contract of the present invention is based. Upon expiration, the back-end system 112 determines the appropriate settlement amount and provides the final settlement data to the settlement company 114. The settlement company 114 acts as a bank of the exchange and performs final market-rate adjustments to the member company surplus accounts based on the positions taken by the members company' customers. The final per-market adjustment reflects the derivative contract of the present invention and the final settlement amount for the account of the corresponding settlement company debit/credit member company. These data are also forwarded to member company system 116 so that they can also update their customer accounts.
Fig. 2 illustrates an embodiment of an exchange backend system 112 for creating and distributing an index (e.g., GB volatility index) of the present invention and/or creating, listing, and trading derivative contracts based on the index of the present invention. The derivative contract of the present invention has provisions stored in module 202 that contain all relevant data related to the derivative contract to be traded on trading platform 120, including, for example, contract symbols, provisions for the subject asset or assets associated with the derivative, or a deadline for the computational period associated with the derivative. The pricing data aggregation and distribution module 204 receives contract information from the derivative contract provisioning module 202 and transactional data from the matching engine 110. The pricing data aggregation and distribution module 204 provides market data regarding public bids and offers and recent deals to the market data providers 118. The pricing data aggregation and distribution module 204 also forwards the trading data to the settlement company 114 so that the settlement company 114 can adjust the member company's account by market price at the end of each trading day taking into account the current market price of the derivative contract of the present invention. Finally, the settlement calculation module 206 receives input from the derivative monitoring module 208. On the settlement day, settlement calculation module 206 calculates a settlement amount based on a value associated with the subject asset or assets (e.g., a value of the GB volatility index). The settlement calculation module 206 forwards the settlement amount to the settlement company 114, and the settlement company 114 performs final market-price adjustment on the account of the member company to settle the derivative contract of the present invention.
Referring to FIG. 5, an exemplary embodiment of a general-purpose computer system that may be used for one or more components shown in FIG. 1 or in any other transaction system configured to perform the methods described in more detail below is shown and designated 500. The computer system 500 may include a set of instructions that can be executed to cause the computer system 500 to perform any one or more of the methods or computers based on the functionality described herein. Computer system 500 may operate as a standalone device or may be connected, for example using a network, to other computer systems or peripheral devices.
In a networked arrangement, the computer system may operate in the capacity of a server or as a client user computer in a server-client user network environment, or as a peer computer system in a peer-to-peer (or distributed) network environment. The computer system 500 may also be implemented as, or incorporated into, a variety of devices, such as a personal computer ("PC"), a tablet PC, a set-top box ("STB"), a personal digital assistant ("PDA"), a mobile device, a palmtop computer, a desktop computer, a network router, switch or bridge, or any other machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that machine. In particular embodiments, computer system 500 may be implemented using electronic devices that provide voice, video, or data communication. Additionally, although a single computer system 500 is illustrated, the term "system" shall be taken to include any collection of systems or subsystems that individually or jointly execute a set or multiple sets of instructions to perform one or more computer functions.
As shown in fig. 5, computer system 500 may include a processor 502, such as a central processing unit ("CPU"), a graphics processing unit ("GPU"), or both. Moreover, the computer system 500 may include a main memory 504 and a static memory 506, which may communicate with each other via a bus 508. As shown, the computer system 500 may also include a video display unit 510, such as a liquid crystal display ("LCD"), an organic light emitting diode ("OLED"), a flat panel display, a solid state display, or a cathode ray tube ("CRT"). In addition, the computer system 500 may include an input device 512, such as a keyboard, and a cursor control device 514, such as a mouse. The computer system 500 may 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 a particular embodiment, as shown in FIG. 5, the disk drive unit 516 may include a computer-readable medium 522 in which one or more sets of instructions 524, such as software, may be implemented. Additionally, the instructions 524 may implement one or more methods or logic as described herein. In particular embodiments, the instructions 524 may reside, completely or at least partially, within the main memory 504, the static memory 506, and/or within the processor 502 during execution thereof by the computer system 500. The main memory 504 and the processor 502 may also include computer-readable media.
In alternative embodiments, hardware devices such as application specific integrated circuits, programmable logic arrays, and other hardware implementations may be constructed in such specific hardware implementations to implement one or more of the methodologies described herein. Applications that may include the apparatus and systems of different embodiments may broadly include a variety of electronic and computer systems. One or more embodiments described herein may implement functions using two or more specific interconnected hardware modules or devices and related control and data signals that may be communicated between and through the modules or as part of an application-specific integrated circuit. Accordingly, the present system encompasses software, firmware, and hardware implementations.
According to various embodiments of the present disclosure, the methods described herein may be implemented by software programs executable by a computer system. Additionally, in an exemplary, non-limiting embodiment, implementations can include distributed processing, component/object distributed processing, and parallel processing. Alternatively, a virtual computer system may be constructed to implement one or more of the methods or functions described herein.
The present disclosure contemplates a computer-readable medium that includes instructions 524 or receives and executes instructions 524 in response to a propagated signal so that a device connected to network 526 can communicate voice, video, or data over network 526. Additionally, the instructions 524 may be transmitted or received over a network 526 via the network interface device 520.
While the computer-readable medium is shown to be a single medium, the term "computer-readable medium" includes a single medium or multiple media, such as a centralized or distributed database, that stores one or more sets of instructions, and/or associated caches and servers. The term "computer-readable medium" shall also be taken to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by a processor or that cause a computer system to perform any one or more of the methodologies or operations disclosed herein.
In a specific, non-limiting, exemplary embodiment, 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. Additionally, the computer-readable medium may be random access memory or other volatile rewritable memory. Additionally, the computer readable medium may include magneto-optical or optical media, such as a disk or tape or other storage device, to capture information communicated over a transmission medium. A digital file attachment to an email or other self-contained information archive or collection of archives can be considered a distribution medium equivalent to a tangible storage medium. Accordingly, the disclosure is considered to include any one or more of a computer-readable medium or a distribution medium and other equivalents and successor media, in which data or instructions may be stored.
Although this specification describes components and functions that may be implemented in particular embodiments with reference to particular standards and protocols that are common among investment management companies, the present invention is not limited to these standards and protocols. For example, standards for Internet and other packet-switched network transport (e.g., TCP/IP, UDP/IP, HTML, HTTP) represent examples of the state of the art. Such criteria are periodically replaced by more efficient equivalents having substantially the same function. Accordingly, replacement standards and protocols having the same or similar functionality as those disclosed herein are considered equivalents thereof.
According to one embodiment, a system and method for calculating and distributing a GB volatility index is provided. The GB volatility index ("GB-VI") may be calculated and distributed using the systems shown in fig. 1, 2, and 5 and described in detail above. In general, GB-VI reflects the fair value of a contract for achieved volatility for delivery of GB futures of any duration, and reflects the expected volatility of GB futures prices within any investment duration. The index may also be interpreted as the fair value of the contract for delivery of GB forward realized volatility and reflects the expected volatility of the GB forward price within any investment horizon, as the realized and expected volatility of futures and forward are mathematically equivalent in the framework of the index design. GB-VI may be calculated for GB in any country and currency where there is a bond futures (or forwards) and bond futures (or forwards) options market, according to some embodiments of the present invention. According to some embodiments of the invention, GB-VI is calculated based on data relating to the market for the options of GB futures or forwards. For example, GB-VI will currently be particularly well suited for the GB futures (or forward) options market for bonds issued by the united states, germany, uk, japan, and other governments.
According to some embodiments of the present invention, GB-VI is calculated for each expiration-term combination on the "volatility surface" (i.e., the expiration of an option and the term of a subject bond that becomes the subject future or forward of the option) by aggregating the equal-present and null hold of bond futures and the price of buy options (i.e., the option "bias", "volatility bias"), such as into a single formula that may be independent of any option pricing model. These GB-VI match the prevailing market practice of the opening price volatility in interest rate markets in terms of base point price volatility or percentage price volatility. (unless otherwise indicated herein, references to volatility should be interpreted as price volatility and not revenue volatility). In addition, GB-VI is also proposed in terms of a base point yield volatility (i.e. with respect to price volatility) or a modified duration-based base point yield volatility based on a model-independent conversion from price volatility to yield volatility. Moreover, GB-VI described herein may reflect the fair market value of the contract for future delivery of GB volatility at each point of the volatility surface (i.e., over any arbitrary expiration and target period).
The uncertainty associated with the GB market is related to the change in the structure of interest rates. Mathematically, negotiable government bond Bt(TN) Is of value to
B t ( T N ) &equiv; &Sigma; i = i t N C i n P t ( T i ) + P t ( T N )
Wherein t is the date of valuation; t isi(i∈[it,N]) Is the coupon payment date, where T1Is at T0The first ticket payment after issuance of the time,is the first invoice date T, and TNIs the expiration of the bond at the time of the last coupon payment by reimbursement of the principal; ciN is at TiA coupon payment of time; and P ist(Ti) Is the time TiThe zero-coupon in time may not delinquent the price at time t when the bond is due and represents a major source of uncertainty in the GB price.
In the forward agreement for GB, one party agrees to deliver the GB to the other party at a fixed price on a future date. At TNLong term price F at time T of T time delivery of expired bondt(T,TN) Is given by
F t ( T , T N ) = B t ( T N ) P t ( T )
It may be a contract that allows the seller to choose from a set of multiple "deliverable" GB, in which case the subject bond Bt(TN) Can be interpreted as tracking the "cheapest delivery" GB and proposing prices in terms of trade flat or adjusted prices based on some heading "conversion factor".
The forward price is at a "forward probability" defined by "Lower halter strap
dQ F T d Q | I T = exp ( - &Integral; t T r ( s ) d s ) P t ( T )
Wherein r(s) is a short term rate over time s, ITRepresents a collection of information up to time T.
Under the long-term probability, GB long-term price dynamic satisfaction
dF s ( T , T N ) F s ( T , T N ) = v s ( T , T N ) dW F T ( s )
Wherein,is that(ii) brownian motion of and vs(T,TN) Is the instantaneous fluctuation rate.
A "government bond variance interchange agreement" is a contract that party A agrees at time T to pay party B the following amount at time T
Vt(T,TN)-S(t,T,TN),T≤TN
Wherein,and S (T, T)N) Is a fixed performance at time t, which hasHas the following fair value
S ( t , T , T N ) = 1 P t ( T ) E t &lsqb; exp ( - &Integral; t T r s d s ) V t ( T , T N ) &rsqb; = E t Q F T &lsqb; V t ( T , T N ) &rsqb; - E t Q F T &lsqb; ln F T ( T , T N ) F t ( T , T N ) &rsqb; = 1 2 E t Q F T &lsqb; V t ( T , T N ) &rsqb; = 1 2 S ( t , T , T N )
Wherein E istIs an expectation at risk neutral probability Q, andis at a distant probabilityThe following two desires are obtained on the condition that the information up to the time t is obtained. The last term is generated by options having the following relationship
E t Q F T &lsqb; l n F T ( T , T N ) F t ( T , T N ) &rsqb; = - 1 P t ( T ) &lsqb; &Integral; 0 F t ( T , T N ) Put t ( K , T , T N ) K 2 d K + &Integral; F t ( T , T N ) &infin; Call t ( K , T , T N ) K 2 d K &rsqb;
Wherein Putt(t,T,TN) Is about the bond term T with an expiration T and a targetNThe GB of forward date has a price of European put option with fulfillment K and expiration T, and Callt(t,T,TN) Is about the bond term T with an expiration T and a targetNHas a contract K and an expiration T, which results in fair contract performance
S ( t , T , T N ) = 2 P t ( T ) &lsqb; &Integral; 0 F t ( T , T N ) Put t ( K , T , T N ) K 2 d K + &Integral; F t ( T , T N ) &infin; Call t ( K , T , T N ) K 2 d K &rsqb;
In fact, there is a finite set of performance rates traded at any given moment, and therefore the points will be replaced by discrete finite summations as follows:
S ( t , T , T N ) &equiv; 2 P t ( T ) &lsqb; &Sigma; i : K i < F t ( T , T N ) Put t ( K i , T , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; F t ( T , T N ) Call t ( K i , T , T N ) K i 2 &Delta;K i &rsqb;
wherein, K0Represents the lowest performance of the Z +1 options; kiRepresents the ith highest performance in the Z +1 options; kZRepresents the highest performance in the Z +1 options; and for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1)。
In some embodiments, the "percentage government bond price volatility index" is expressed as:
G B - V I ( t , T , T N ) &equiv; 100 &times; S ( t , T , T N ) T - t
the continuous case:
= 100 &times; 2 P t ( T ) ( T - t ) &lsqb; &Integral; 0 F t ( T , T N ) Put t ( K , T , T N ) K 2 d K + &Integral; F t ( T , T N ) &infin; Call t ( K , T , T N ) K 2 d K &rsqb;
discrete case:
= 100 &times; 2 P t ( T ) ( T - t ) &lsqb; &Sigma; i : K i < F t ( T , T N ) Put t ( K i , T , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; F t ( T , T N ) Call t ( K i , T , T N ) K i 2 &Delta;K i &rsqb;
discrete case with long term adjustment:
= 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T , T N ) - K * K * ) 2 &rsqb;
Eq.(PCT_GBVI)
wherein the forward adjustment handles the case where there is no option to fulfill the ATM forward price, and K*Is lower than the current forward price Ft(T,TN) The first available performance. If the forward price is not observable at time t, Ft(T,TN) Is the performance when the difference between the purchase and withdrawal prices is minimal.
More generally, for any constant multiplier CM
G B - V I ( t , T , T N ) &equiv; C M &times; S ( t , T , T N ) T - t
The continuous case:
= C M &times; 2 P t ( T ) ( T - t ) &lsqb; &Integral; 0 F t ( T , T N ) Put t ( K , T , T N ) K 2 d K + &Integral; F t ( T , T N ) &infin; Call t ( K , T , T N ) K 2 d K &rsqb;
discrete case:
= C M &times; 2 P t ( T ) ( T - t ) &lsqb; &Sigma; i : K i < F t ( T , T N ) Put t ( K i , T , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; F t ( T , T N ) Call t ( K i , T , T N ) K i 2 &Delta;K i &rsqb;
discrete case with long term adjustment:
= C M &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T , T N ) - K * K * ) 2 &rsqb; which is the fair value of the scaling of the GB variance exchange agreement.
The above contracts are designed and also for options expansion index formulas with a GB forward that expires later than the option, for example:
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
wherein, TDIndicating the time of expiration of a targeted government bond future that becomes an option that expires at T, where TD≥T。K*Is lower than the current forward price Ft(TD,TN) The first available performance. If the forward price is not observable at time t, Ft(TD,TN) Is the performance when the difference between the purchase and withdrawal prices is minimal.
A "government bond basepoint variance exchange agreement" is a contract for party A to agree at time T to pay party B the following amount at time T
V t b p ( T , T N ) - S b p ( t , T , T N ) , T &le; T N
Wherein V l b p ( T , T N ) &equiv; &Integral; t T F s 2 ( T , T N ) | | v s ( T , T N ) | | 2 d s And Sbp(t,T,TN) Is a performance fixed at time t with a fair value
S b p ( t , T , T N ) = E t Q F T &lsqb; V t b p ( T , T N ) &rsqb; = E t Q F T &lsqb; F T 2 ( T , T N ) &rsqb; - F t 2 ( T , T N )
Wherein,is at the probability conditioned on the information up to time tThe following expectations. The last term is generated by options having the following relationship
E t Q F T &lsqb; F T 2 ( T , T N ) &rsqb; - F t 2 ( T , T N ) = 2 P t ( T ) &lsqb; &Integral; 0 F t ( T , T N ) Put t ( K , T , T N ) d K + &Integral; F t ( T , T N ) &infin; Call t ( K , T , T N ) d K &rsqb;
Wherein Putt(t,T,TN) Is about the bond term T with an expiration T and a targetNThe GB of forward date has a price of European put option with fulfillment K and expiration T, and Callt(t,T,TN) Is about the bond term T with an expiration T and a targetNHas a contract K and an expiration T, which results in fair contract performance
S b p ( t , T , T N ) = 2 P t ( T ) &lsqb; &Integral; 0 F t ( T , T N ) Put t ( K , T , T N ) d K + &Integral; F t ( T , T N ) &infin; Call t ( K , T , T N ) d K &rsqb;
In fact, there is a finite set of performance rates traded at any given moment, and therefore the points will be replaced by discrete finite summations as follows:
S b p ( t , T , T N ) &equiv; 2 P t ( T ) &lsqb; &Sigma; i : K i < F t ( T , T N ) Put t ( K i , T , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; F t ( T , T N ) Call t ( K i , T , T N ) K i &rsqb;
in some embodiments, the "benchmark government bond price volatility index" is expressed as:
G B - VI b p ( t , T , T N ) &equiv; 100 &times; 100 &times; S b p ( t , T , T N ) T - t
the continuous case:
= 100 2 &times; 2 P t ( T ) ( T - t ) &lsqb; &Integral; 0 F t ( T , T N ) Put t ( K , T , T N ) d K + &Integral; F t ( T , T N ) &infin; Call t ( K , T , T N ) d K &rsqb;
discrete case:
= 100 2 &times; 2 P t ( T ) ( T - t ) &lsqb; &Sigma; i : K i < F t ( T , T N ) Put t ( K i , T , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; F t ( T , T N ) Call t ( K i , T , T N ) &Delta;K i &rsqb;
discrete case with long term adjustment:
= 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T N ) &Delta;K i &rsqb; - ( F t ( T , T N ) - K * ) 2 &rsqb; E q . ( B P _ G B V I )
which is the fair value of the scaling of the BPGB variance exchange protocol.
More generally, for any constant multiplier CM
G B - VI b p ( t , T , T N ) &equiv; C M &times; S b p ( t , T , T N ) T - t
The continuous case:
= C M &times; 2 P t ( T ) ( T - t ) &lsqb; &Integral; 0 F t ( T , T N ) Put t ( K , T , T N ) d K + &Integral; F t ( T , T N ) &infin; Call t ( K , T , T N ) d K &rsqb;
discrete case:
= C M &times; 2 P t ( T ) ( T - t ) &lsqb; &Sigma; i : K i < F t ( T , T N ) Put t ( K i , T , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; F t ( T , T N ) Call t ( K i , T , T N ) &Delta;K i &rsqb;
discrete case with long term adjustment:
= C M &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T N ) &Delta;K i &rsqb; - ( F t ( T , T N ) - K * ) 2 &rsqb;
the above contracts are designed and also for options spread index formulas with GB forwards that expire later than the option, for example:
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
wherein, TDIndicating the time of expiration of a targeted government bond future that becomes an option that expires at T, where TD≥T。K*Is lower than the current forward price Ft(TD,TN) The first available performance. If the forward price is not observable at time t, Ft(TD,TN) Is the performance when the difference between the purchase and withdrawal prices is minimal.
Although the volatility in the GB market is typically measured and traded at most in terms of price volatility, another formula for GB bond futures volatility, the base point yield volatility, may also be considered.
Defining intrinsic bond price B*(TN) So that
GB-VIbp(t,T,TN)=B*(TN)×GB-VI(t,T,TN
And its corresponding profit yB*(TN) So that
G B - VI Y b p ( t , T , T N ) = 100 &times; y B * ( T N ) &times; G B - V I ( t , T , T N ) y B * ( T N ) : B * ( T N ) = G B - VI b p ( t , T , T N ) G B - V I ( t , T , T N ) = P ^ ( y B * ( T N ) )
And is
P ^ ( y ) &equiv; &Sigma; i = 1 N C i n ( 1 + y n ) - i + 100 ( 1 + y n ) - N
Or when there is a coupon due at time T and at time TjWhen the next coupon is due,
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
where dc (year) is the number of days in a year based on the day count convention for government bonds, and dc (T-T) is the number of days between T and T based on the day count convention for government bonds.
Then, in some embodiments, the "Basidiom bond profit volatility index" may be expressed as
G B - VI Y b p ( t , T , T N ) &equiv; 100 &times; P ^ - 1 &lsqb; G B - VI b p ( t , T , T N ) G B - V I ( t , T , T N ) &rsqb; &times; G B - V I ( t , T , T N )
Or the coupon due when there is a time T and at time TjWhen the next coupon is due,
G B - VI Y b p ( t , T , T N ) &equiv; 100 &times; P ^ T - 1 &lsqb; G B - VI b p ( t , T , T N ) G B - V I ( t , T , T N ) &rsqb; &times; G B - V I ( t , T , T N )
Eq.(BPY_GBVI)
wherein,is thatIs inverse to the function of (A), andis thatIs inverse to the function of (a).
Options for GB forwards with expiry later than the option extend the above exponential formula, for example:
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
and is
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
Wherein, TDIndicating the time of expiration of a targeted government bond future that becomes an option that expires at T, where TD≥T。
In some embodiments, the "modified duration-based benchmark government bond profit volatility index" may be defined as:
G B - VI Y d b p ( t , T , T D , T N ) &equiv; 100 &times; ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) &times; G B - VI b p ( t , T , T D , T N ) &Sigma; i = j N C i n ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t i - T ) d c ( y e a r ) ( d c ( t i - T ) d c ( y e a r ) ) + 100 ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t N - T ) d c ( y e a r ) ( d c ( t N - T ) d c ( y e a r ) )
Eq.(MDBPY_GBVI)
which has the representation defined in the above paragraph.
For PCT _ GBVI, BP _ GBVI, BPY _ GBV, and MDBPY _ GBVI, when the expiration of the option is shorter than the target GB duration, i.e., T < TDAn adjustment deadline may be calculated to account for the impact of the expired discrepancy. The four adjusted index equations are as follows:
G B - VI a d j ( t , T , T D , T N ) &equiv; 100 &times; ( T - t ) &times; ( G B - V I ( t , T , T D , T N ) / 100 ) 2 + C ( t , T , T D , T N ) T - t
G B - VI a d j b p ( t , T , T D , T N ) &equiv; 100 2 &times; ( T - t ) &times; ( G B - VI b p ( t , T , T D , T N ) / 100 2 ) 2 + C b p ( t , T , T D , T N ) T - t
G B - VI Y , a d j b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ T - 1 &lsqb; G B - VI a d j b p ( t , T , T D , T N ) G B - VI a d j ( t , T , T D , T N ) &rsqb; &times; G B - VI a d j ( t , T , T D , T N )
G B - VI Y d , a d j b p ( t , T , T D , T N ) &equiv; 100 &times; ( 1 + P ^ T - 1 &lsqb; G B - VI a d j b p ( t , T , T D , T N ) G B - VI a d j ( t , T , T D , T N ) &rsqb; ) &times; G B - VI a d j b p ( t , T , T D , T N ) &Sigma; i = j N C i n ( 1 + P ^ T - 1 &lsqb; G B - VI a d j b p ( t , T , T D , T N ) G B - VI a d j ( t , T , T D , T N ) &rsqb; ) - d c ( t i - T ) d c ( y e a r ) ( d c ( t i - T ) d c ( y e a r ) ) + 100 ( 1 + P ^ T - 1 &lsqb; G B - VI a d j b p ( t , T , T D , T N ) G B - VI a d j ( t , T , T D , T N ) &rsqb; ) - d c ( t N - T ) d c ( y e a r ) ( d c ( t N - T ) d c ( y e a r ) )
wherein
C ( t , T , T D , T N ) &equiv; 2 ( &Integral; 0 F t ( T D , T N ) C 1 t ( K , T , T D , T N ) 1 K 2 d K + &Integral; F t ( T D , T N ) &infin; C 2 t ( K , T , T D , T N ) 1 K 2 d K ) - C 0 t ( T , T D , T N )
C b p ( t , T , T D , T N ) &equiv; 2 ( &Integral; 0 F t ( T D , T N ) C 1 t ( K , T , T D , T N ) d K + &Integral; F t ( T D , T N ) &infin; C 2 t ( K , T , T D , T N ) d K ) - C 0 t b p ( T , T D , T N )
C 0 t ( K , T , T D , T N ) &equiv; Cov t Q F T ( V t ( T , T D , T N ) , P t ( T ) P t ( T D ) e - &Integral; T T D r s d s )
C 0 t b p ( K , T , T D , T N ) &equiv; Cov t Q F T ( V t b p ( T , T D , T N ) , P t ( T ) P t ( T D ) e - &Integral; T T D r s d s )
C 1 t ( K , T , T D , T N ) &equiv; Cov t Q F T ( ( K - F T ( T D , T N ) ) + , P t ( T ) P t ( T D ) e - &Integral; T T D r s d s )
C 2 t ( K , T , T D , T N ) &equiv; Cov t Q F T ( ( F T ( T D , T N ) - K ) + , P 1 ( T ) P t ( T D ) e - &Integral; T T D r s d s )
V t ( T , T D , T N ) &equiv; &Integral; T | | v s ( T D , T N ) | | 2 d s
V t b p ( T , T D , T N ) &equiv; &Integral; t T F s 2 ( T D , T N ) | | v s ( T D , T N ) | | 2 d s
G B - VI a d j b p ( t , T , T D , T N ) = B * , a d j ( t , T , T D , T N ) &times; G B - VI a d j ( t , T , T D , T N )
And C0tC1t、C2tMay be calculated based on a specification of interest rate dynamics.
C (T, T) may also be added when there is no option price to fulfill with real valueD,TN) Is replaced byAnd using K in the constraint of all integrals (or summations in the discrete case) in the exponential formula*Alternative Ft(TD,TN) To adjust GB-VIadjIn which K is*Is less than Ft(TD,TN) The first performance of (1). Similarly, C can also be obtained bybp(t,T,TD,TN) Is replaced by Cbp(t,T,TD,TN)-(Ft(TD,TN)-K*)2And using K in the constraint of all integrals (or summations in the discrete case) in the exponential formula*Alternative Ft(TD,TN) To adjustWherein K*Is less than Ft(TD,TN) The first performance of (1). Conversely, GB-VI may be used when there is no ATM option price presentadjAndto calculate the performance adjustment version ofAnd
the mathematical formulation and formula given above for the government bond volatility index uses the price of the european option for the GB term. However, options with other exercise types or GB-derived options with other targets may be used directly in the above formula if it is determined that the prices of these options are not substantially different from the equivalent prices of the european options for the GB term. For example, the price of a nominal American option for a government bond futures may not differ substantially from an otherwise equivalent European option for a government bond forward, as may be concluded from Flesaker, B's 1993 work on "testing the Heaath-Jarrow-Morton/Ho-Leemodelo interest RateContentingClaimping" (journal of financial and quantitative analysis28) and Bikbov, R and M.Chernov's 2011 work on "Young's economic and social issues options" (journal of financial instruments 9).
The current practice of some exchanges is to list the american options for GB futures. In the case of a scenario where the price of the american option that causes GB futures is substantially different from the european option of GB forwards, the inventors developed a technique to convert the U.S. bond option price to the corresponding european bond forward price, which may be performed by: (1) selecting a model of interest rate dynamics and using historical data to estimate its parameters; (2) defining and calibrating risk prices such that the difference between observed option prices and option prices implied by the model in (1) is minimized; and calculating a euro option implied by the model of government bond forwards using the calibrated risk price in (2).
In one example technique, the price of the U.S. options for government bond futures may be transformed into the price of the U.S. options for government bond forwards. The example technique performs as follows:
step 1, selecting a Vasicek (1977) model of interest rate
dr t = &kappa; ( &mu; - r 1 ) d t + &sigma;dW t p
Wherein r istIs the instantaneous interest rate at time t, andis the brownian motion under the physical probability measurement P. The parameters (κ, μ, σ) will be estimated using historical interest rate data.
Step 2, dynamically defining the risk neutrality of the short-term rate as follows:
dr t = &kappa; ( r &OverBar; - r t ) d t + &sigma;dW t , r &OverBar; &equiv; &mu; - &lambda; &sigma; &kappa;
wherein, WtIs brownian motion under risk neutral probability measurement, and λ is the risk price. By findingOr solving minimization problem 2A or 2B to calibrate the risk price:
minimization problem 2A:
&lambda; ^ = arg min &lambda; &Element; &Lambda; &Sigma; j = 1 M ( O mod e l ( K j ; &lambda; ) - O m a r k e t ( K j ) ) 2 w ( K j )
wherein,is a compact set; k is option performance; o ismodel(K; λ) are model implied option prices for performance K and for risk price λ; o ismodel(K) Is the observed option price for fulfillment K; and w (K) is a weighting function; m represents the number of observable option prices.
Minimization problem 2B:
for each fulfillment K, findMake the option price implied by the modelJust match the observed option price Omodel(K)Result in a function ofThe defined risk guarantees a deviation of the gold, so that for each K, O mod e l ( K ; &lambda; ^ ( K ) ) = O m a r k e t ( K ) .
model price of American options for government bond futures O in both 2A and 2Bmodel(K; lambda) isIn which C iss(rs(ii) a K) Is that C s ( r s ; K ) = m a x { &psi; ( F ~ s ( r s ; T , T N ) ) , exp ( - r s &Delta; s ) E &lsqb; C s + &Delta; s ( r s + &Delta; s ; K ) &rsqb; } Wherein for option subscription, the profit isAnd for put options, profit isΔsIs an increment time after time s, which is the time at which the option can be exercised; e is the expectation under risk neutral probability measurement; and calculating the future price according to the following formula
F ~ t ( r t ; T , T N ) - E t &lsqb; B T ( r T , T N ) &rsqb; = &Sigma; i = i t N C &OverBar; i &times; exp ( a t F ( T , T i ) - b t F ( T , T i ) r t )
C &OverBar; i &equiv; C i / N , i = 1 , ... , N - 1 , C N = 1 + C N / N
a t F ( T , T i ) &equiv; a T ( T i ) - ( 1 - exp ( - &kappa; ( T - t ) ) ) r &OverBar; b T ( T i ) + ( &sigma; 2 ( 1 - exp ( - 2 &kappa; ( T - t ) ) ) b T 2 ( T i ) / 4 &kappa;
b t F ( T , T i ) &equiv; exp ( - &kappa; ( T - t ) b T ( T i ) )
a t ( T ) &equiv; ( 1 - exp ( - &kappa; ( T - t ) ) &kappa; - ( T - t ) ) ( r &OverBar; - 1 2 ( &sigma; &kappa; ) 2 ) - &sigma; 2 4 &kappa; 3 ( 1 - exp ( - &kappa; ( T - t ) ) ) 2
b t ( T ) &equiv; 1 &kappa; ( 1 - exp ( - &kappa; ( T - t ) ) )
Step 3. in case of 2AUsed under the condition ofAnd use in the case of 2BTo calculate the price of European options for government bond forwards using the formula Jamshidian (1989)
Call t ( K , T , T N ) = &Sigma; i = 1 N C &OverBar; i &times; Call t &OverBar; ( T ; P t ( T t ) , K i * ( K ) , &upsi; t )
And is
Put t ( K , T , T N ) = Call t ( K , T , T N ) + P t ( T ) K - B t ( T N )
Wherein
K i * ( K ) = P T ( r * ( K ) , T i )
Call t &OverBar; ( T ; P t ( T i ) , K i * ( K ) , &upsi; i ) = P i &Phi; ( d 1 , i ) - K i * ( K ) P t ( T ) &Phi; ( d 1 , i - &upsi; i )
d 1 , i = ln P i K i * ( K ) P t ( T ) + 1 2 &upsi; i 2 &upsi; i , &upsi; i = &sigma; 1 - exp ( - 2 &kappa; ( T - t ) ) 2 &kappa; b T ( T i )
P t ( r , T ) = exp ( a t ( T ) - b t ( T ) r , B t ( r t , T ) &equiv; &Sigma; i = 1 N C i &OverBar; P t ( r t , T i )
And r is*(K) So that BT(r*(K),TN)=K。
In the case of 2B, to use the risk deposit that is calibrated to the expirations in the formula of the future option, the risk deposit is biased by the following transformationIs inclined to
K i * * = K i F t ( r t ; T , T N ) F ~ t $ ( T , T N )
Wherein, Ft(rt;T,TN) Is a model-based forward price, andis the market futures price.
Use ofTo calculate a forward price Ft(rt;T,TN) Wherein the following fixed point problem is found K a t m * * = F t ( r t ; T , T N ) :
&lambda; ^ ( i ) = &lambda; ^ ( F t ( i ) ) , F t ( i + 1 ) = F t ( r t ; T , T N ; &lambda; ^ ( i ) ) &lambda; ^ ( 0 ) = Initial guess
And isBy ensuring that the risk is equal toThe model of time predicts the forward price.
For GB long term and long term options markets that trade within a period based on a standardized roll date (roldate) (e.g., cycling quarterly through march, june, september, and dodecamonth), two or more long term options with different expirations may be used in combination to calculate an index with an expiration corresponding to any of the expirations between the shortest and longest expirations used.
In the case where GB long and long options are traded with an expiration period, as a first non-limiting example, the index may be calculated by the last and next cycle dates using a "sandwich combination" such that the volatility index with an m-month time limit is calculated as
I t &equiv; 1 ( m / 12 ) &lsqb; x t V t ( T i ) + ( 1 - x t ) V t ( T i + 1 ) &rsqb; , t &Element; &lsqb; T i - 1 , T i &rsqb;
Wherein T isi-Ti-1=Ti+1-TiM × d, and Ti+1Ti-12m × d, d is the number of days in a month, Vt(Ti) Equal to S (T, T) in the case of percentage government bond price volatility indexi,TN) And S under the condition of price fluctuation rate index of basic point government bondbp(t,Ti,TN) (ii) a And xtIs a weight such that
x t T i - t 12 d + ( 1 - x t ) T i + 1 - t 12 d = m 12 , t &Element; &lsqb; T i - 1 , T i &rsqb;
Which results in the following expression
I t &equiv; 1 ( m / 12 ) &lsqb; ( T i + 1 - t m &times; d - 1 ) V t ( T i ) + ( 2 - T i + 1 - t m &times; d ) V t ( T t + 1 ) , t &Element; &lsqb; T i - 1 , T i &rsqb;
For the case of the benchmark revenue government bond volatility index, the combination of the sandwich structure at time t may be expressed as
I Y b p &equiv; 100 &times; P ^ - 1 &lsqb; I t B P I t P e r c &rsqb; &times; I t p e r c
And for the case of a modified duration-based benchmark revenue government bond volatility index, the sandwich structure combination at time ttime can be expressed as
I Y d , t b p &equiv; 100 &times; ( 1 + P ^ T - 1 &lsqb; I t b p I t p e r c &rsqb; ) &times; I t b p &Sigma; i = j N C i n ( 1 + P ^ T - 1 &lsqb; I t b p I t p e r c &rsqb; ) - d c ( t i - T ) d c ( y e a r ) ( d c ( t i - T ) d c ( y e a r ) ) + 100 ( 1 + P ^ T - 1 &lsqb; I t b p I t p e r c &rsqb; ) - d c ( t N - T ) d c ( y e r a r ) ( d c ( t N - T ) d c ( y e a r ) )
Wherein,is a sandwich structure combination of the price fluctuation rate index of the basic government bond,is a sandwich structure combination of percentage government bond price volatility index.
In the case where GB forwards and forwards options are traded with an expiration cycle, as a second non-limiting example, the volatility index may be calculated based on the deviation of a particular futures option contract from an expired contraction time. For example, if the index is based on expiring options within three months of a ten year bond, the index on the first day will reflect the expected volatility of the next three months, the next three months minus the expected volatility of one day, and so on, until the index naturally expires at the expiration of the options in the three months. The same approach may be used in the case of GB futures and futures options.
Fig. 3 is a flowchart outlining an embodiment of the steps for calculating and distributing a benchmark government bond price volatility index in accordance with the present invention. In step 302, data is electronically received from an electronic data source. Included in the received data is data regarding GB options. At step 304, the data is cleaned up and normalized according to known techniques and GB option price data is created as input to the index formula for all available expiration/term/performance combinations. If the option prices are not prices for euro bond options, they may optionally be converted to prices for the corresponding euro bond options at step 306. At step 308, the price for each expiration and term combination for all available performances is entered into the equation BP _ GBVI shown above to calculate the cardinal point GB volatility index.
Figure 4 is a flowchart outlining an embodiment of the steps for calculating and distributing a percentage government bond price volatility index in accordance with the present invention. At step 402, data is electronically received from an electronic data source. Included in the received data is data on GB options. At step 404, the data is cleaned up and normalized according to known techniques and GB option price data is created as input to the index formula for all available expiration/term/performance combinations. If the option prices are not prices for euro bond options, they may optionally be converted to prices for the corresponding euro options at step 406. At step 408, the price for each expiration and term combination for all available performances is entered into the equation PCT _ GBVI shown above to calculate the percentage government bond price volatility index.
FIG. 6 is a flowchart outlining an embodiment of the steps for calculating and distributing a benchmark government bond yield volatility index in accordance with the present invention. At step 602, data is electronically received from an electronic data source. Included in the received data is data on GB options. At step 604, the data is cleaned up and normalized according to known techniques and GB option price data is created as input to the index formula for all available expiration/term/performance combinations. If the option prices are not prices for euro bond options, they may optionally be converted to prices for the corresponding euro options at step 606. At step 608, the price for each expiration and term combination for all available performances is entered into the equation BPY _ GBVI shown above to calculate the Baseline government bond yield volatility index.
FIG. 7 is a flowchart outlining an embodiment of the steps for calculating and distributing a modified duration-based benchmark government bond volatility index in accordance with the present invention. In step 702, data is electronically received from an electronic data source. Included in the received data is data on GB options. At step 704, the data is cleaned up and normalized according to known techniques and GB option price data is created as input to the index formula for all available expiration/term/performance combinations. If the option prices are not prices for euro bond options, they may optionally be converted to prices for the corresponding euro options, step 706. At step 708, the price for each expiration and term combination for all available performances is entered into the equation MDBPY _ GBVI shown above to calculate a modified duration-based benchmark government bond revenue volatility index.
The steps shown in fig. 3, 4, 6 and 7 may be performed using the systems illustrated in fig. 1, 2 and 5.
Implementation examples
The following are non-limiting examples of how the method of the present invention may be used to construct three formulas of a government bond volatility index. As described above, the actual calculation and distribution of the benchmark government bond price volatility index, the percentage government bond price volatility index, the benchmark government bond profit volatility index, and the modified duration-based benchmark government bond profit volatility index is performed by a calculation and distribution system, an example of which is illustrated in fig. 3.
The present example utilizes data that reflects hypothetical market conditions. The data provided is a warranty gold for european forward hold and call options for a ten year GB forward term that expires in one month, expressed in decimal terms. The data for this example is provided below in table 1:
table 1
As indicated above, the first two columns of Table 1 report the performance price K and the percent internal volatility IV (K) for each performance price. The third and fourth columns provide subscription and withdrawal options guarantees.
As shown below, table 2 provides information calculated according to this example for the base and percentage government bond price volatility indices according to equations (BP _ GBVI) and (PCT _ GBVI), respectively.
Table 2
The second column of table 2 shows the types of equi-current and imaginary GB options that are added in the calculation of the example of the GB volatility index. The third column shows the option guaranty added to the calculation; the fourth and fifth columns report the weight of each option deposit interest for the final calculation of the index; and finally, the sixth and seventh columns report each of the imaginary value option margins multiplied by the appropriate weights. Each price in the third column is multiplied by a corresponding weight in the fourth column as a "base contribution" and each price in the third column is multiplied by a corresponding weight in the fifth column as a "percentage contribution".
Thus, according to the data provided in this example, embodiments of the basepoint and percent government bond price volatility indices are calculated as follows:
G B - VI B P = 100 2 &times; 1 0.9980 2 ( 1 / 12 ) &times; 1.7757 &CenterDot; 10 - 4 = 653.4751
and
G B - V I = 100 &times; 1 0.9980 2 ( 1 / 12 ) &times; 1.0268 &CenterDot; 10 - 4 = 4.9692.
the scaling factor inside the square root (1/0.9980) is the inverse of a zero-coupon bond that expires within a month. The benchmark revenue government bond volatility index value may then be calculated by: solving for
B * = G B - VI b p G B - V I = 653.4751 4.9692 = 131.5121
Then the hypothesis N-1, N-10 and C are obtainedi4r ═ 4rWhich leads to the intrinsic yield of
G B - VI Y b p = 100 &times; 7.2226 &times; 10 - 3 &times; 4.9692 = 3.5891
And is
G B - VI Y d b p = 100 &times; 4.9692 8.6048 = 57.749
For comparison purposes, the iso-value intrinsic base point and percent volatility are IVBP(ATM) ═ 597.96 and iv (ATM) ═ 4.53%.
In this non-limiting example, the base point index is in accordance with 1002Readjusted to simulate market practice, whereby the baseline intrinsic volatility is expressed as a product of the rate times the logarithmic volatility, where both the rate and the logarithmic volatility are multiplied by 100.
According to some embodiments of the invention, the index calculated according to embodiments of the invention may be used as a target value for derivative contracts such as options and futures contracts. More specifically, according to embodiments of the invention, a government bond volatility index (GB-VI) may be used as a target reference for derivative contracts designed for the volatility of GB futures prices trading various expirations and target periods. In particular, futures and option contracts with different expirations based on the index may be traded and/or listed in trade on the OTC.
Derivative instruments based on the above disclosed government bond volatility index may be created as standardized exchange traded contracts as well as off-board contracts. When a government bond volatility index (GB-VI) based on government futures/forwards options is calculated, the index may be accessed for use in creating derivative contracts, and the derivative contracts may be assigned unique symbols. In general, a GB-VI derived contract may be assigned any unique symbol that serves as a standardized identifier for the type of standardized GB-VI derived contract. Information associated with the GB-VI and/or GB-VI derivative contracts can be communicated for display, such as information to list GB-VI indices and/or GB-VI derivatives on a trading platform. Examples of the types of information that may be conveyed for display include settlement prices of the GB-VI derivative, bids or offers associated with the GB-VI derivative, and/or the value of subject options associated with the GB-VI.
In general, the GB-VI derivative contract may be listed on an electronic platform, a public price calling platform, a hybrid environment that combines an electronic platform and a public price calling platform, or any other type of platform known in the art. One example of a hybrid trading environment is disclosed in U.S. patent No. 7,613,650, filed 24/4/2003, which is incorporated herein by reference in its entirety. In addition, trading platforms such as exchanges may transmit the liquidity provider's GB-VI derived contract offers to other market participants through a distribution network. Liquidity providers may include designated master market makers ("DPMs"), market makers, local residents, experts, trading privilege holders, registered traders, members, or any other entity that may provide variance-derived quotes to a trading platform. The distribution network may include a network such as an option price reporting agency ("OPRA"), a CBOE futures network, an internet website, or an email alert via an email communication network. Market participants may include liquidity providers, economic companies, normal investors, or any other entity that may subscribe to a distribution network.
The trading platform may execute GB-VI derived buy and sell orders and may repeat the following steps: calculating GB-VI of the subject option, accessing the GB-VI index, transmitting the GB-VI index and/or GB-VI derivative information for display (listing the GB-VI and/or GB-VI derivatives on a trading platform), distributing the GB-VI and/or GB-VI derivatives over a distribution network, and executing the GB-VI derived buy and sell orders until the GB-VI derivative contract settles.
In some implementations, GB-VI derivative contracts may be traded by a discounted auction and cash settlement operated on exchanges of the GB-VI index that earn a pair of benefits based on the equity of the bid. The electronic auction or Dutch auction system conducts a periodic auction in which all contracts for real value settlement are funded by those collected margins for virtual value settlement.
As mentioned, in a discounted auction, all contracts for real-value settlement are funded by those for virtual-value settlement. Thus, the net position (netissue) of the system is zero at the completion of the auction process and there is no accumulation of outstanding interest (openinterest) over time. In addition, pricing of contracts in a reduced price auction depends on relative demand; the more popular the performance, the higher its value. In other words, a discounted price auction does not depend on the bidder setting the price; but the price is continually adjusted to reflect the flow of orders into the auction. Typically, as each order enters the system, it affects not only the price at which performance is sought, but also all other performance available in the auction. In such a case, the system adjusts the price down for less popular performance because the price rises for multiple sought performance. In addition, the process does not require matching of a particular buy order with a particular sell order as in many conventional markets. Alternatively, all buy and sell orders enter a single pool of liquidity, and each order may provide liquidity for other orders of different performance prices, and the liquidity is maintained so that the system capacity remains zero. This format maximizes liquidity, a key feature when there is no tradable target instrument.
The following features of futures contracts illustrate one example of futures contracts having the index of the present invention as the subject asset. This feature is not intended to limit the invention, but rather to illustrate the general features of futures:
contract size: a unit of tentative payment for a contract may be defined as a number of index levels, which may depend on the currency of the subject index. When OTC's are transacted, the multipliers are negotiated transaction by transaction between the parties involved.
Contract month number: the exchange may list contracts having a predetermined sequence of dates, for example, the third friday of each of the next 6 months. Similarly, OTC traders may market in a predetermined sequence of expiration dates, but may also market for contracts that expire on other dates on a trade-by-trade basis.
Quote and minimum price interval: index-based futures may be quoted in points and decimal numbers or fractions representing some tentative amount of money per contract, and there may be minimum increments by which the pricing of contracts may vary, both of which may depend on the currency of the target index. The OTC market may employ different conventions for quotes and minimum credit.
The final transaction date: for each contract, a last transaction date will be specified.
Final settlement date: for each contract, a final settlement date will be specified.
Final settlement value: the final settlement value will be based on the level of the index calculated at a pre-specified time of the settlement date.
Delivering: the settlement of futures based on the index will take the form of the delivery of a cash settlement amount and will specify a payment date in relation to the final settlement date.
Additional provisions at the exchange trade: when traded at the exchange, trading platform, surplus demand, hours traded, order line rules, batch trading rules, reporting rules, and other details may be specified.
The following features of the option contract illustrate one example of an option contract having the index of the present invention as the subject asset. The described features are not intended to limit the invention, but rather to set forth general features of options:
contract size: a unit of tentative payment for a contract may be defined as a number of index levels, which may depend on the currency of the subject index. When OTC's are transacted, the multipliers are negotiated transaction by transaction between the parties involved.
Contract month number: the exchange may list contracts having a predetermined sequence of expiration dates, for example, the third friday of each of the next 6 months. Similarly, OTC traders may market in a predetermined sequence of expiration dates, but may also market for contracts expiring on other dates on a trade-by-trade basis.
Price of performing the contract: for each currency, performance prices, which are real, equal, present, and imaginary values, may be listed by the trade or quoted by the OTC trader, and new performance prices may be traded as the futures price increases or decreases. The exchange or OTC trader group may fix the minimum increment between performance prices in terms of the currency of the target index.
Quote and minimum price interval: index-based futures may be quoted in points and decimal numbers or fractions representing some tentative amount of money per contract, and there may be minimum increments by which the pricing of contracts may vary, both of which may depend on the currency of the target index. The OTC market may employ different conventions for quotes and minimum credit.
The exercise type: options written on GB-VI may be, but are not limited to, euros. It is envisioned that American contracts may also have the index of the present invention as the subject asset.
Expiration date: for each contract, an expiration date will be specified.
The final transaction date: for each contract, a last transaction date will be specified.
And (3) settlement of exercise: the final settlement value will be based on the level of the index calculated at a pre-specified time of the settlement date. The cash settlement amount will be the difference between the index level and the performance price, which may be adjusted by some multiplier, and will specify the payment date in relation to the expiry date.
Additional provisions at the exchange trade: when traded at the exchange, trading platform, surplus demand, trading hours, reporting rules, and other details may be specified.
According to other embodiments of the invention, other financial products may be created that track or reference the index of the invention. Such products include, but are not limited to, funds traded at exchanges listed in the trade and exchange-traded instruments and structured products sold by financial institutions.
The foregoing description has been directed to specific embodiments of this invention. It will be apparent, however, that other variations and modifications may be made to the described embodiments, which achieve some or all of their advantages.

Claims (18)

1. A computer system for calculating a government bond volatility index comprising:
a memory configured to store at least one program; and
at least one processor communicatively coupled to a memory, wherein the at least one program, when executed by the at least one processor, causes the at least one processor to:
receiving data regarding options derived from government bonds;
calculating a government bond volatility index using data on options derived from government bonds; and
data is communicated regarding a government bond volatility index.
2. The computer system of claim 1, wherein the data regarding government bond-derived options comprises data regarding prices of government bond-derived options.
3. The computer system of claim 2, wherein the data regarding prices of options derived from government bonds comprises data regarding prices of options on government bond futures or government bond forwards.
4. The computer system of claim 3, wherein the government bond volatility index is calculated at time t according to the following equation:
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest of the Z +1 optionsPerforming a contract;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration; and
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNTime-expired markThe value of the government bond volatility index at time T calculated for the option expiring at time T of the bond of (a).
5. The computer system of claim 3, wherein the government bond volatility index is calculated at time t according to the following equation:
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDgovernment bond derivatives representing subject matter to be optionsTime of birth due, wherein TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNTime of put option of subject bond on expiry time tThe price of (c);
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration; and
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index at time T calculated at an option expiring at time T for a subject bond that expires.
6. The computer system of claim 3,
wherein when there is no coupon due at time T, the government bond volatility index is calculated at time T according to the following equation:
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
wherein
P ^ ( y ) &equiv; &Sigma; i = 1 N C i n ( 1 + y n ) - i + 100 ( 1 + y n ) - N ;
And, wherein there is a coupon due when there is a time T and at the time TjCalculating a government bond volatility index at time t according to the following equation for the next coupon due:
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
wherein
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
And is
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
And is
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
tjis a first ticket payment at or after T;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration;
n represents the total number of coupon payments for government bonds;
Cian amount of an ith coupon among the N coupons representing the government bond;
n represents the frequency of annual coupon payments for government bonds;
y represents a profit of the government bond;
x represents a benefit of a government bond;
is a bond price corresponding to a bond benefit of a bond of the subsidiary government;
is thatThe inverse of the function of (a);
is a bond price at time T corresponding to bond profit for a bond of the subsidiary government;
is thatThe inverse of the function of (a);
dc (year) is the number of days in a year based on a day count convention for government bonds;
dc (T-T) is the number of days between T and T based on a day count convention for government bonds;
is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index for a basepoint yield volatility at time T calculated for an option expiring at T for a target bond at time of expiration;
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNThe option of the expired subject bond expiring at T is calculatedThe value of the government bond volatility index of the base point price volatility at time t; and
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of the percentage price volatility at time T calculated for options expiring at T for a target bond at expiration.
7. The computer system of claim 3, wherein the government bond volatility index is calculated at time t according to the following equation:
G B - VI Y d b p ( t , T , T D , T N ) &equiv; 100 &times; ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) &times; G B - VI b p ( t , T , T D , T N ) &Sigma; i = j N C i n ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t i - T ) d c ( y e a r ) ( d c ( t i - T ) d c ( y e a r ) ) + 100 ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t N - T ) d c ( y e a r ) ( d c ( t N - T ) d c ( y e a r ) )
wherein
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
And is
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
And is
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is in timetIs not observable, then Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration;
n represents the total number of coupon payments for government bonds;
Cian amount of an ith coupon among the N coupons representing the government bond;
n represents the frequency of annual coupon payments for government bonds;
x represents a benefit of a government bond;
is bond yield corresponding to bond of subsidiary governmentThe bond price of (a);
is thatThe inverse of the function of (a);
dc (year) is the number of days in a year based on a day count convention for government bonds;
dc (T-T) is the number of days between T and T based on a day count convention for government bonds;
tjis a first ticket payment at or after T;
is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index for a basepoint yield volatility at time T calculated for an option expiring at T for a target bond at time of expiration;
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of a basepoint price volatility at time T calculated at an option expiring at T for a target bond at time of expiration;
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of the percentage price volatility at time T calculated for options expiring at T for a target bond at expiration.
8. The computer system of claim 1, wherein the at least one processor is further caused to:
creating a standardized exchange trading derivative instrument based on the government bond volatility index; and
data relating to the standardized exchange trade derivative is communicated.
9. The computer system of claim 8, wherein transmitting data regarding the standardized exchange-traded derivative instrument comprises transmitting data regarding one or more of a settlement price, a bid price, or a trading price of the standardized exchange-traded derivative instrument.
10. A non-transitory computer readable storage medium having computer executable instructions recorded thereon that, when executed on a computer, configure the computer to perform a method of calculating a government bond volatility index, the method comprising:
receiving data regarding options derived from government bonds;
calculating a government bond volatility index using data on options derived from government bonds; and
data is communicated regarding a government bond volatility index.
11. The non-transitory computer readable storage medium of claim 10, wherein the data regarding government bond-derived options includes data regarding prices of government bond-derived options.
12. The non-transitory computer readable storage medium of claim 11, wherein the data regarding prices of options derived from government bonds comprises data regarding prices of options on government bond futures or government bond forwards.
13. The non-transitory computer readable storage medium of claim 12, wherein the government bond volatility index is calculated at time t according to the following equation:
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration; and
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index at time T calculated at an option expiring at time T for a subject bond that expires.
14. The non-transitory computer readable storage medium of claim 12, wherein the government bond volatility index is calculated at time t according to the following equation:
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA target time t-time price for the time-out of hold and call options, whichWinning government bond at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration; and
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index at time T calculated at an option expiring at time T for a subject bond that expires.
15. The non-transitory computer readable storage medium of claim 12,
wherein, when there is no coupon due at time T, the government bond volatility index is calculated at time T according to the following equation:
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
wherein
P ^ ( y ) &equiv; &Sigma; i = 1 N C i n ( 1 + y n ) - i + 100 ( 1 + y n ) - N ;
And wherein there is a coupon to be billed at time T and at time TjCalculating a government bond volatility index at time t according to the following equation for the next coupon due:
G B - VI Y b p ( t , T , T D , T N ) &equiv; 100 &times; P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; &times; G B - V I ( t , T , T D , T N )
wherein
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
And is
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
And is
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
tjis a first ticket payment at or after T;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is a zero coupon that expires at TTime of non-defaulting bondtThe price of the hour;
Putt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration;
n represents the total number of coupon payments for government bonds;
Cian amount of an ith coupon among the N coupons representing the government bond;
n represents the frequency of annual coupon payments for government bonds;
y represents a profit of the government bond;
x represents a benefit of a government bond;
is a bond price corresponding to a bond benefit of a bond of the subsidiary government;
is thatThe inverse of the function of (a);
is a bond price at time T corresponding to bond profit for a bond of the subsidiary government;
is thatThe inverse of the function of (a);
dc (year) is the number of days in a year based on a day count convention for government bonds;
dc (T-T) is the number of days between T and T based on a day count convention for government bonds;
is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index for a basepoint yield volatility at time T calculated for an option expiring at T for a target bond at time of expiration;
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of a basepoint price volatility at time T calculated at an option expiring at T for a target bond at time of expiration; and
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of the percentage price volatility at time T calculated for options expiring at T for a target bond at expiration.
16. The non-transitory computer readable storage medium of claim 12, wherein the government bond volatility index is calculated at time t according to the following equation:
G B - VI Y d b p ( t , T , T D , T N ) &equiv; 100 &times; ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) &times; G B - VI b p ( t , T , T D , T N ) &Sigma; i = j N C i n ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t i - T ) d c ( y e a r ) ( d c ( t i - T ) d c ( y e a r ) ) + 100 ( 1 + P ^ T - 1 &lsqb; G B - VI b p ( t , T , T D , T N ) G B - V I ( t , T , T D , T N ) &rsqb; ) - d c ( t N - T ) d c ( y e a r ) ( d c ( t N - T ) d c ( y e a r ) )
wherein
P ^ T ( x ) &equiv; &Sigma; i = j N C i n ( 1 + x ) - d c ( t i - T ) d c ( y e a r ) + 100 ( 1 + x ) - d c ( t N - T ) d c ( y e a r )
And is
G B - V I ( t , T , T D , T N ) &equiv; 100 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) K i 2 &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) K i 2 &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * K * ) 2 &rsqb;
And is
G B - VI b p ( t , T , T D , T N ) &equiv; 100 2 &times; 1 ( T - t ) &lsqb; 2 P t ( T ) &lsqb; &Sigma; i : K i < K * Put t ( K i , T , T D , T N ) &Delta;K i + &Sigma; i : K i &GreaterEqual; K * Call t ( K i , T , T D , T N ) &Delta;K i &rsqb; - ( F t ( T D , T N ) - K * ) 2 &rsqb;
Wherein:
t represents the time to calculate the government bond volatility index;
t represents the time of expiration of an option derived from a government bond;
TDrepresenting the time of expiration of a derivative of a subject government bond to be an option, where TD≥T;
TNTime of expiry of the government bond;
z +1 represents the total number of options used in the index calculation;
K0represents the lowest performance of the Z +1 options;
Kirepresents the ith highest performance in the Z +1 options;
KZrepresents the highest performance in the Z +1 options;
for i ≧ 1,and Δ K0=(K1-K0),ΔKZ=(KZ-KZ-1);
If the price is observable at time t, Ft(TD,TN) Is to make the government bond derivative contract at TDA bid time T price for the pending and subscription options at expiration, wherein the winning government bond is at TNThe time expires;
if the price is not observable at time t, Ft(TD,TN) Is a performance when the difference between the purchase and withdrawal prices is minimal;
if present with Ft(TD,TN) Option to fulfill, K*Is equal to Ft(TD,TN);
If not present with Ft(TD,TN) Option to fulfill, K*Is less than Ft(TD,TN) The first available performance of (1);
Pt(T) is the price at time T of a bond for which zero coupons expired at T cannot be breached;
Putt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the put option of the subject bond on expiration;
Callt(Ki,T,TD,TN) Is at KiFulfilling, expiring at T and having a status at TDGraceful target government bond derivatives and at TNA price at time t of the call option of the subject bond at expiration;
n represents the total number of coupon payments for government bonds;
Cian amount of an ith coupon among the N coupons representing the government bond;
n represents the frequency of annual coupon payments for government bonds;
x represents a benefit of a government bond;
is a bond price corresponding to a bond benefit of a bond of the subsidiary government;
is thatThe inverse of the function of (a);
dc (year) is the number of days in a year based on a day count convention for government bonds;
dc (T-T) is the number of days between T and T based on a day count convention for government bonds;
tjis a first ticket payment at or after T;
is based on at TDTime expired government bond derivatives and at TNIn the meantime toA value of a government bond volatility index of a base point yield volatility at time T calculated at an option expiring at T for an underlying bond;
GB-VIbp(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of a basepoint price volatility at time T calculated at an option expiring at T for a target bond at time of expiration;
GB-VI(t,T,TD,TN) Is based on at TDTime expired government bond derivatives and at TNA value of a government bond volatility index of the percentage price volatility at time T calculated for options expiring at T for a target bond at expiration.
17. The non-transitory computer readable storage medium of claim 10, wherein the at least one processor is further caused to:
creating a standardized exchange trading derivative instrument based on the government bond volatility index; and
data relating to the standardized exchange trade derivative is communicated.
18. The non-transitory computer-readable storage medium of claim 17, wherein transmitting data regarding the standardized exchange-traded derivative instrument comprises transmitting data regarding one or more of a settlement price, a bid price, or a trade price of the standardized exchange-traded derivative instrument.
CN201380075864.3A 2013-03-15 2013-11-21 Methods and systems for creating a government bond volatility index and trading derivative products based thereon Pending CN105339973A (en)

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US13/931,114 2013-06-28
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US13/970,193 US20130332333A1 (en) 2012-05-22 2013-08-19 Methods and Systems for Creating a Government Bond Volatility Index and Trading Derivative Products Based Thereon
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