JP2014207002A - Reverse knock-out option premium calculation device and currency option premium calculation device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate the premium of a currency option subjected to evaluation.SOLUTION: As an option to be used for computing the premium of a currency option subjected to evaluation, in addition to an ATM plain option, a 25 forward delta call/put plain option of which the delta with a forward rate as a reference becomes 0.25 is applied and 25 delta risk reversal volatility Δσand 25 delta butterfly volatility Δσare acquired 58, 60. volatility σand σof 25 forward delta call/put plain option is computed 62. While using the volatility σ, an exercise price Kof the 25 forward delta call plain option is computed and while using the volatility σ, an exercise price Kof the 25 forward delta put plain option is computed 68 and used for computation 78 or the like of the premium for computing a correction value Zeta.

Description

The present invention relates to a premium computing device, a program and a recording medium for currency options.
A currency option premium calculation device for calculating a premium of a currency option to be evaluated, a currency option premium calculation program for causing a computer to function as the currency option premium calculation device, and a currency option premium calculation program are recorded. The present invention relates to a recording medium.

A currency option is a right to purchase (for call options) or sell (for put options) currency at a specified strike price (strike price) within a specified exercise date or period. For example, a holder of a dollar call option with an exercise price of $ 100 / dollar can exercise a right of $ 100 by exercising the option right even if the spot rate of the dollar / yen exchange rate exceeds $ 100 / $ 1 due to a rise in the dollar. You can buy dollars at the yen exchange rate. Therefore, while selling the dollar at a spot rate higher than $ 100 / dollar (for example, $ 105 / $ 1), you gain the foreign exchange gain by exercising the option rights and buying the dollar at the exchange rate of $ 100 / $ 1. be able to. Also, if the dollar-yen spot rate falls below 100 yen per dollar due to a drop in the dollar, the dollar can be purchased at the spot rate without exercising the option right.

Similarly, a holder of a dollar put option whose exercise price is 100 dollars will exercise the option right even if the spot rate of the dollar-yen exchange rate falls below 100 dollars due to the fall in dollars, and will exercise the option right. You can earn a foreign exchange gain by selling the dollar at the exchange rate of 100%, and if the spot rate of the dollar-yen exchange rate exceeds 100 yen per dollar, sell the dollar at the spot rate without exercising the option right be able to. In this way, currency options have the function of hedging the risk of loss associated with exchange rate fluctuations while ensuring the opportunity to obtain foreign exchange gains. Need to pay.

In order for currency options to be traded properly in the market, the currency option premium (
It is necessary to calculate and determine (price) so as to reflect the magnitude of the risk of the currency option risk undertaker (currency option seller). As a premium calculation method for currency options, the Garman = Korhalgen model, which is a modified version of the Black-Sholes model for currency options, or a framework based on this model (hereinafter referred to as the GK model). Is generally used). In the framework of the GK model, premiums for currency options are formulated with variables such as exercise price and exchange rate volatility (expected volatility). Since the exercise price is a given parameter and the volatility of the exchange rate is also presented in the market, the premium of the currency option can be easily calculated by using the framework of the GK model.

However, the Black-Scholes model and the GK model based on this model assume that fluctuations in underlying asset values such as exchange rates follow a probability distribution defined by a normal distribution, whereas actual exchange rates, etc. The probability distribution of fluctuations is different from the normal distribution. For this reason, even if the premium for the currency option is calculated using the Black-Scholes model or the GK model, the value of the premium that is obtained deviates from the actual probability distribution (risk), and a corrected premium cannot be obtained. There is a problem.

In order to solve the above-mentioned problem, the applicant of the present invention disclosed in Patent Document 1 an evaluation object option, an ATM (At The Money) plain option, a 25 delta call plain option, and a 25 delta put plain option for the same period as the evaluation object option. Vega, Volga, and Banna are calculated for the three types of plain options, and Vega, Volga, and Banna of the portfolio that combines the above three types of plain options are Vega,
Calculate the portfolio composition to match Volga and Banna,
Premiums calculated from ATM flat volatility σ _ATM and market values of volatility of 25 delta call plain option and 25 delta put plain option for plain option and 25 delta put plain option σ _C25 , σ _P25
A technique is proposed in which the difference between the premium calculated from (1) is calculated, and the premium of the option subject to evaluation calculated from σ _ATM is corrected by the weighted sum of the differences weighted by the above-mentioned composition ratio.

In addition, in connection with the above, Patent Document 2 creates a time series volatility curve indicating a change in volatility with respect to a period, and creates a smile curve indicating a volatility with respect to a delta value. Create a volatility curved surface model as a reference from the curve, set the appropriate price range in this volatility curved surface model, enter the appropriate price range by entering the volatility to be examined and set the appropriate price range Techniques for determining whether or not have been disclosed are disclosed.
JP 2002-230304 A JP 2002-288436 A

In the technique described in Patent Document 1, the strike price of each option is calculated in order to calculate Vega, Volga, and Banna of each option, and 25 delta call plain option and 25
The volatility at the spot rate (current volatility) is used to calculate the exercise price of the delta put plain option. However, short-term currency options traded in the market for less than one year are traded based on the spot rate, and the volatility based on the spot rate is also used as the market value of volatility. On the other hand, for long-term currency options of one year or longer, the forward rate is the exchange rate at the date of exercise of the currency option (this forward rate is the investment profit during the period (= interest rate x interest rate period) ) Can be calculated from the spot rate based on (1)), and the volatility based on the forward rate is also used as the market value of volatility.

For this reason, in the technique described in Patent Document 1, when the period of the currency option to be evaluated is a long period of one year or longer and the corresponding volatility market value is volatility based on the forward rate, the acquired volatility market The value is converted into volatility on a spot rate basis based on the interest rate and interest rate period, and then used to calculate the strike price. However, if the period of the currency option being evaluated is relatively long and the interest rate is relatively high, the discount factor (= interest rate and interest rate period: discount rate) used to convert the spot rate to the forward rate is 0.5 ( In this case, the strike price of the ATM plain option, 25 delta call plain option, and 25 delta put plain option is the same (25 ÷ 0.5 = 50 and the value of 25 delta is 50 delta) There is a problem that the premium cannot be calculated.

The present invention has been made in consideration of the above facts, and includes a currency option premium calculation device, a currency option premium calculation program, and a recording medium capable of avoiding a situation in which a premium of a currency option to be evaluated cannot be calculated. The purpose is to obtain.

To achieve the above object, the currency option premium computing device according to the first invention includes a first parameter capable of specifying an exercise date and an exercise period of a currency option to be evaluated and an exercise price of the currency option to be evaluated or First acquisition means for acquiring a second parameter representing delta, and storing the acquired first parameter and the second parameter in a first storage means;
The ATM flat volatility representing the market value of the volatility of the ATM plain option with the same exercise period and the exercise period of the currency option to be evaluated that can be specified from the first parameter, and the currency option and the exercise period are the same, A forward delta call plane in which a delta based on a forward rate, which is an exchange rate uniquely determined from a spot rate, an interest rate, and a period, is a predetermined value on the exercise date of the currency option to be evaluated that can be specified from the first parameter Obtain volatility information that represents the market value of volatility for options and forward delta putplane options,
A second acquisition unit for storing the acquired ATM flat volatility and the volatility information in a second storage unit, and reading out the second parameter from the first storage unit and reading out the ATM flat volatility from the second storage unit When the second parameter read from the first storage means represents the delta of the currency option to be evaluated, it is converted into the delta of the currency option to be evaluated represented by the second parameter by computer processing. After calculating the exercise price of the currency option to be evaluated on the basis of the ATM flat volatility read from the second storage means and the exercise price of the currency option to be evaluated by computer processing, the evaluation Target currency option premier A first premium calculating means for storing the calculated currency option premium in the third storage means, and reading the ATM flat volatility from the second storage means, and from the third storage means. The premium of the currency option to be evaluated is read out, and the second
Using the ATM flat volatility read from the storage means and the premium of the currency option to be evaluated read from the third storage means, a predetermined risk parameter is calculated for the currency option to be evaluated, and the calculated predetermined Risk parameter calculation means for storing the risk parameter in the fourth storage means, and the second storage means for the A
The TM flat volatility and the volatility information are read out, and the exercise price of the ATM plain option is calculated using the ATM flat volatility read out from the second storage means by computer processing, and is read out from the second storage means. The strike price of the forward delta call plan option is calculated using the volatility of the forward delta call plan option represented by the volatility information, and the forward delta represented by the volatility information read from the second storage means. Calculate the strike price of the forward delta / put plain option using the volatility of the put plain option and store the calculated strike price of each plain option in the fifth storage means The exercise price calculation means to be stored, the ATM flat volatility and the volatility information are read from the second storage means, the exercise price of each plain option is read from the fifth storage means, 2 using the ATM flat volatility read from the storage means and the strike price of the ATM plain option read from the fifth storage means
The premium of the M plain option is calculated, the volatility of the forward delta call plain option represented by the volatility information read from the second storage means, and the strike price of the forward delta call plain option read from the fifth storage means Is used to calculate the premium of the forward delta call plane option, and the volatility information of the forward delta / put plane option represented by the volatility information read from the second storage means and the forward read from the fifth storage means The forward delta / put plain option premium is calculated using the exercise price of the delta / put plain option, and the calculated premium of each plain option is calculated as the sixth premium. A second premium calculation means for storing each in the storage means; and a predetermined risk parameter of the currency option to be evaluated is read from the fourth storage means, and the ATM flat volatility and the volatility information are read from the second storage means And, the premium of each plain option is read from the sixth storage means, and the ATM flat volatility and the volatility information read from the second storage means by computer processing, the respective read from the sixth storage means The value of the predetermined risk parameter for the portfolio combining the respective plain options, obtained from the premium of the plain options, is the predetermined risk of the currency option to be evaluated read from the fourth storage means. A composition ratio calculating means for calculating the composition ratio of each plain option in the portfolio when the value is equal to a parameter value, and storing the calculated composition ratio in a seventh storage means; and the ATM flat from the second storage means The volatility is read, the strike price of each plain option is read from the fifth storage means, and the ATM flat volatility read from the second storage means and the forward read from the fifth storage means by computer processing The premium of the forward delta call plain option is calculated using the strike price of the delta call plain option, and the ATM flat volatility read from the second storage means and the read from the fifth storage means A third premium calculating means for calculating a premium of the forward delta / put plain option using an exercise price of the forward delta / put plain option, and storing the calculated premium of each plain option in an eighth storage means; The premium of each plain option is read from each of the 6 storage means and the 8th storage means, and the deviation between the premium read from the 6th storage means and the premium read from the 8th storage means is calculated by computer processing. Deviation calculation means for calculating for each plain option and storing the calculated deviation in the ninth storage means; reading out the deviation for each plain option from the ninth storage means; and the component ratio from the seventh storage means Read out to computer processing Ri, as a correction value for the premium currency option of the evaluation, the deviation of each of the said respective plain options ninth read from the storage means,
A correction value calculation unit that calculates a weighted and added value according to the configuration ratio read from the seventh storage unit, and stores the calculated correction value in the tenth storage unit, and the evaluation from the third storage unit The premium of the target currency option is read out, the correction value is read out from the tenth storage means, and the premium of the currency option to be evaluated read out from the third storage means by the calculation processing of the computer is stored in the tenth storage. Correcting with the correction value read out from the means and storing the corrected premium in the eleventh storage means; reading out the corrected premium from the eleventh storage means; and reading out the corrected premium read out, Output means for outputting as a premium of the currency option to be evaluated.

In the first invention, the first parameter that can specify the exercise date and the exercise period of the currency option to be evaluated and the second parameter that represents the exercise price or delta of the currency option to be evaluated are the first
Acquired by acquisition means. In addition, the AT with the same exercise period as the currency option to be evaluated
The exercise of the valuation target currency option, which is the same as the ATM flat volatility representing the market value of the volatility of the M-plan option, and the valuation target currency option is the same as the valuation target and the forward rate is uniquely determined from the spot rate, interest rate and period. The volatility information representing the market value of the volatility of the forward delta call plan option and the forward delta put plan option with a predetermined delta based on the exchange rate on the due date) is acquired by the second acquisition means.

As the forward delta call plane option, for example, as described in the eighth invention, a 25 forward delta call plane option with a delta based on the forward rate of 0.25 is preferable. As the put plain option, for example, as described in the eighth invention, the 25 forward delta / put plain option in which the delta based on the forward rate is 0.25 is preferable, but the present invention is not limited to this. Other forward delta plain options with rate-based delta values other than 0.25 may be applied.

If the second parameter represents the delta of the currency option to be evaluated by the first premium calculation means, the strike price of the currency option to be evaluated based on the delta of the currency option to be evaluated represented by the second parameter Is calculated, the premium of the currency option to be evaluated is calculated using the ATM flat volatility and the exercise price of the currency option to be evaluated. The risk parameter calculation means calculates a predetermined risk parameter for the currency option to be evaluated using the ATM flat volatility and the premium of the currency option to be evaluated. As the predetermined risk parameter, a parameter representing the risk of change in volatility is suitable, for example, as described in the sixth invention. Specifically, for example, as described in the seventh invention, , Vega which is the first derivative of currency option premium by volatility, Volga which is second derivative of currency option premium by volatility, and Banna which is first derivative of the Vega by spot rate. The present invention is not limited to this, and other parameters can be applied.

Further, the exercise price calculation means calculates the exercise price of the ATM plain option using the ATM flat volatility, and also uses the volatility of the forward delta call plan option represented by the volatility information to determine the exercise price of the forward delta call plan option. Further, the exercise price of the forward delta / put plain option is calculated using the volatility of the forward delta / put plain option represented by the volatility information. The second premium calculation means calculates the premium of the ATM plain option using the exercise price of the ATM flat volatility and the ATM plain option, and the volatility and forward delta call of the forward delta call plain option represented by the volatility information. The premium of the forward delta call plan option is calculated using the exercise price of the plain option, and the forward delta ・The premium for the put plain option is calculated.

In addition, the value of the predetermined risk parameter for the portfolio combining each plain option, which is obtained from the ATM flat volatility and volatility information, and the premium of each plain option by the component ratio calculation means, is the predetermined risk of the currency option to be evaluated. The composition ratio of each plain option in the portfolio when it becomes equal to the value of the parameter is calculated. More specifically, as described in the fifth aspect, the component ratio calculation means uses ATM flat volatility, volatility information, premiums of each plain option, ATM plain option, forward delta call plain option, and forward. After each of the predetermined risk parameters of the delta / put plain option is calculated, the composition ratio of each plain option in the portfolio can be calculated using the calculated predetermined risk parameter of each plain option. .

Furthermore, the third premium calculation means calculates the premium of the forward delta call plan option using the exercise price of the ATM flat volatility and the forward delta call plan option, The strike price is used to calculate the premium for the forward delta / put plain option. Further, the deviation calculating means calculates a deviation between the premium calculated by the second premium calculating means and the premium calculated by the third premium calculating means for each plain option. Further, the correction value calculating means weights the deviation for each plain option calculated by the deviation calculating means as a correction value for the premium of the currency option to be evaluated according to the composition ratio calculated by the composition ratio calculating means. The added value is calculated as a correction value. Further, the correction means corrects the premium of the currency option to be evaluated calculated by the first premium calculation means by the correction value calculated by the correction value calculation means, and the premium that has been corrected by the correction means is output by the output means. , Output as a premium for the currency option being evaluated.

Thus, in the first invention, for the forward delta call plane option,
Calculate the deviation of the premium using the forward delta call plan option volatility and the premium using the ATM flat volatility, and calculate the deviation. Premium with the volatility of plain options and A
Each premium is calculated by using TM flat volatility, and the deviation is calculated. When the value of the risk parameter is equal to the value of the predetermined risk parameter of the currency option to be evaluated, the correction value is calculated by weighting and adding according to the composition ratio of each option of the portfolio, and the ATM flat Since the premium of the currency option to be evaluated calculated by using the volatility is corrected by the correction value, a model used for calculating the premium of the currency option (for example, the Black Scholes model, It is possible to correct the error of the probability distribution assumed by the K model framework, etc., and as a premium for the currency option to be evaluated, an appropriate value that accurately reflects the magnitude of the risk underwriter of the currency option Can be obtained.

Further, in the first invention, as an option other than the ATM plain option used for calculating the correction value, the forward delta in which the exercise period is the same as the currency option to be evaluated and the delta based on the forward rate is a predetermined value.・ The call plain option and forward delta / put plain option are applied, and the second acquisition means obtains volatility information that represents the market value of the volatility of the above forward delta / call plain option and forward delta / put plain option. The strike price calculation means is
The forward delta call plain option exercise price is calculated using the forward delta call plain option volatility, and the forward delta put plain option exercise price is calculated using the forward delta put plain option volatility. . For this reason, when the currency option to be evaluated is a short-term currency option for which transactions are conducted based on the spot rate, a discount factor is used and parameters such as volatility are set in the technique described in Patent Document 1. On the contrary, it is necessary to convert the value based on the spot rate into the value based on the forward rate.

However, the discount factor is the product of the interest rate and the interest rate period. In the first invention, if the parameter needs to be converted from the value based on the spot rate to the value based on the forward rate, Since the period of the target currency option is short, the interest rate period is also small, and the discount factor cannot be as large as 0.5 (50%). Therefore, according to the first invention, it is possible to prevent the strike price of the ATM plain option and the strike price of the forward delta call plain option and the forward delta put plain option from being aligned. It is possible to avoid a situation in which the premium cannot be calculated.

In the first invention, as described in the second invention, for example, the exercise price calculation means is the currency option of the first currency and the second currency to be exchanged in the currency option to be evaluated. It is preferable that the exercise price in the reference currency in the premium payment is calculated, and the first to third premium calculation means are configured to calculate the premium in the reference currency. In general, the market value of volatility is a value based on the reference currency, and as described above, the base currency in the exercise price or premium to be calculated is matched with the reference currency in the market value of volatility. When acquiring the ATM flat volatility and the volatility information by the acquisition means, it is not necessary to convert the volatility because the reference currency is different, so that the premium of the currency option to be evaluated can be obtained more easily.

Further, in the first invention, the strike price calculating means, as described in the second invention, for example, the cumulative probability density function of the standard normal distribution is N (), the delta value based on the forward rate is Δ, the forward the volatility of the delta plain option sigma, the exercise period of the forward delta plain option when a T _e, the calculation processing of the computer, by searching the value of the variable D ₂ that satisfies the following formula (1) Decide

The spot rate is S ₀ , the interest rate of the base currency in the payment of the premium of the currency option out of the first currency and the second currency to be exchanged in the currency option to be evaluated is r _f , the first currency and the second currency Of the two currencies, when the interest rate of the non-reference currency is r _d and the interest rate period is T _d , the value of the variable D ₂ that satisfies the above-determined equation (1) is calculated as )

The exercise price K is calculated for the forward delta call plane option and the forward delta put plane option by performing the processing for calculating the exercise price K for the forward delta call plane option and the forward delta put plane option, respectively. can do.

In the first invention, the spot rate and interest rate are also used for calculating the currency option premium, etc. Considering that these pieces of information (particularly the spot rate) fluctuate in a short cycle, for example, As described in the invention, the first currency and the second currency to be exchanged with the currency option to be evaluated from another computer connected via a communication line
A third acquisition means for acquiring the spot rate of the currency, the interest rate of the first currency and the second currency, respectively, and storing the acquired spot rate, the interest rate of the first currency and the second currency in the twelfth storage means;
The first to third premium calculation means, risk parameter calculation means, strike price calculation means and component ratio calculation means are used to read the spot rate and interest rate from the twelfth storage means and also use the spot rate and interest rate read from the twelfth storage means It is preferable that each of the operations is performed.

The currency option premium calculation program according to the ninth invention is the first storage means to the eleventh
The computer having the storage means acquires the first parameter that can specify the exercise date and exercise period of the currency option to be evaluated and the second parameter that represents the exercise price or delta of the currency option to be evaluated, The first acquisition means for storing the first parameter and the second parameter in the first storage means, the volatility of the ATM plain option having the same exercise period and the exercise period of the currency option to be evaluated that can be specified from the first parameter Uniquely from the spot rate, interest rate, and period on the exercise date of the valuation target currency option that is the same as the valuation target currency option and the exercise period is the same as the valuation target currency option. Based on the forward rate, which is the fixed exchange rate Volatility information representing the market value of the volatility of the forward delta call plane option and the forward delta put plain option for which the predetermined delta is a predetermined value is acquired, and the acquired ATM flat volatility and the volatility information are stored in the second storage means. Second acquisition means for storing, reading the second parameter from the first storage means, reading the ATM flat volatility from the second storage means, and the second parameter read from the first storage means is the evaluation object Is calculated by calculating the strike price of the valuation target currency option based on the delta of the valuation target currency option represented by the second parameter by a computer calculation process. And calculating the premium of the currency option to be evaluated using the ATM flat volatility read from the second storage means and the exercise price of the currency option to be evaluated, and calculating the evaluation target. The first storage unit stores a premium of the currency option in the third storage means
The ATM calculation unit reads out the ATM flat volatility from the second storage unit, reads out the premium of the currency option to be evaluated from the third storage unit, and reads out the premium from the second storage unit by computer processing. Using the ATM flat volatility and the premium of the currency option to be evaluated read from the third storage means, a predetermined risk parameter is calculated for the currency option to be evaluated, and the calculated predetermined risk parameter is 4 The risk parameter calculation means to be stored in the storage means, the ATM flat volatility and the volatility information are read out from the second storage means, and the ATM flat box read out from the second storage means by computer calculation processing. The exercise price of the ATM plain option is calculated using the volatility and the exercise of the forward delta call plain option using the volatility of the forward delta call plain option represented by the volatility information read from the second storage means. The price is calculated, and further, the exercise price of the forward delta / put plain option is calculated using the volatility of the forward delta / put plain option represented by the volatility information read from the second storage means, and each calculated plain The exercise price calculation means for storing the option exercise price in the fifth storage means, the ATM flat volatility and the volatility information are read out from the second storage means, and the fifth storage means Reads the exercise price of the respective plain options, the calculation processes of the computer, the ATM read from the ATM flat volatility and the fifth memory means read out from said second memory means
The premium of the ATM plain option is calculated using the exercise price of the plain option, and the volatility of the forward delta call plain option represented by the volatility information read from the second storage means and the read from the fifth storage means The premium of the forward delta call plan option is calculated using the strike price of the forward delta call plan option, and the volatility of the forward delta / put plane option represented by the volatility information read from the second storage means and Using the strike price of the forward delta / put plain option read from the fifth storage means, the premium of the forward delta / put plain option is calculated, and the performance is calculated. The second premium calculation means for storing the premium of each plain option in the sixth storage means, the predetermined risk parameter of the currency option to be evaluated is read from the fourth storage means, and the second storage means AT
The M flat volatility and the volatility information are read out, the premium of each plain option is read out from the sixth storage means, and the ATM flat volatility and the volatility information read out from the second storage means by computer processing, The value of the predetermined risk parameter for the portfolio combining the plain options, obtained from the premium of each plain option read from the sixth storage means, is the currency option to be evaluated read from the fourth storage means. A composition ratio calculating means for calculating a composition ratio of each plain option in the portfolio when the value is equal to a predetermined risk parameter value, and storing the calculated composition ratio in the seventh storage means; The ATM flat volatility is read from the second storage means, the strike price of each plain option is read from the fifth storage means, and the ATM flat volatility read from the second storage means by the computer processing and the The premium of the forward delta call plane option is calculated using the strike price of the forward delta call plane option read from the fifth storage means, and the ATM flat volatility read from the second storage means and the fifth A premium of the forward delta / put plain option is calculated using the strike price of the forward delta / put plain option read from the storage means, and the calculated premium of each plain option is calculated. The premiums of the respective plain options are respectively read from the third premium calculation means, the sixth storage means and the eighth storage means for storing the medium in the eighth storage means, and are calculated from the sixth storage means by the calculation processing of the computer. Deviation calculating means for calculating a deviation between the read premium and the premium read from the eighth storage means for each plain option, and storing the calculated deviation in the ninth storage means; The deviation for each plain option is read out, the composition ratio is read out from the seventh storage means, and each of the read-out values from the ninth storage means as a correction value for the premium of the currency option to be evaluated by computer processing. Read the deviation for each plain option from the seventh storage means The weighted and added value is calculated according to the component ratio, and the calculated correction value is calculated as the tenth value.
A correction value calculation means to be stored in the storage means, a premium of the currency option to be evaluated is read out from the third storage means, and the correction value is read out from the tenth storage means, and the third memory is obtained by calculation processing of a computer. A premium of the currency option to be evaluated read from the means is corrected by the correction value read from the tenth storage means,
A correction means for storing the corrected premium in the eleventh storage means, and the corrected premium is read from the eleventh storage means, and the read premium after reading is used as a premium for the currency option to be evaluated. It functions as output means for outputting.

The currency option premium calculation program according to the ninth invention is the first storage means to the eleventh
A computer having storage means is connected to the first acquisition means, the second acquisition means, the first premium calculation means, the risk parameter calculation means, the exercise price calculation means, the second premium calculation means, the component ratio calculation means, and the third premium. Calculation means, deviation calculation means, correction value calculation means, correction means,
And the above-mentioned computer executes the currency option premium calculation program according to the ninth invention, so that the computer executes the currency option premium calculation according to the first invention. It will function as a device, and it can be avoided that the currency option premium to be evaluated falls into a state incapable of being calculated, as in the first invention.

According to a tenth aspect of the present invention, there is provided a recording medium according to a tenth aspect, wherein a computer including first storage means to eleventh storage means includes a first parameter capable of specifying an exercise date and an exercise period of an evaluation object currency option and the evaluation object currency option A second parameter representing the exercise price or delta of the first acquisition means for storing the acquired first parameter and the second parameter in the first storage means, the evaluation target that can be identified from the first parameter The ATM flat volatility representing the market value of the volatility of the ATM plain option with the same exercise period and the exercise period, and the currency option and the exercise period are the same and the first
Forward delta, call plain option, and forward delta with a predetermined delta based on the forward rate, which is the exchange rate uniquely determined from the spot rate, interest rate, and period, on the exercise date of the currency option to be evaluated that can be specified from the parameters A second acquisition means for acquiring the volatility information representing the market value of the volatility of the put plain option and storing the acquired ATM flat volatility and the volatility information in the second storage means; the second from the first storage means; When the parameter is read, the ATM flat volatility is read from the second storage means, and the second parameter read from the first storage means represents the delta of the currency option to be evaluated. After calculating the exercise price of the currency option to be evaluated based on the delta of the currency option to be evaluated represented by the second parameter by the computer calculation process, the calculation is read from the second storage unit by the computer calculation process. Further, the premium of the currency option to be evaluated is calculated using the ATM flat volatility and the exercise price of the currency option to be evaluated, and the calculated premium of the currency option to be evaluated is stored in the third storage means. The ATM premium volatility is read from the first premium calculation means and the second storage means, and the premium of the currency option to be evaluated is read from the third storage means, and is read from the second storage means by calculation processing of a computer. The ATM flat The predetermined risk parameter is calculated for the currency option to be evaluated using the utility and the premium of the currency option to be evaluated read from the third storage means, and the calculated predetermined risk parameter is stored in the fourth memory. The ATM flat volatility and the volatility information are read from the risk parameter calculating means and the second storage means to be stored in the means, and the ATM plain is read using the ATM flat volatility read from the second storage means by computer processing. Calculate the strike price of the option and
The exercise price of the forward delta call plane option is calculated using the volatility of the forward delta call plane option represented by the volatility information read from the storage means, and the volatility information read from the second storage means An exercise price calculating means for calculating the exercise price of the forward delta / put plain option using the volatility of the forward delta / put plain option, and storing the calculated exercise price of each plain option in the fifth storage means, Second
The ATM flat volatility and the volatility information are read from the storage means, the strike price of each plain option is read from the fifth storage means, and the ATM flat volatility read from the second storage means is calculated by computer processing. The premium of the ATM plain option is calculated using the strike price of the ATM plain option read from the fifth storage means, and the forward delta call plain option volatility represented by the volatility information read from the second storage means And a premium of the forward delta call plane option using the strike price of the forward delta call plane option read from the fifth storage means, The volatility of the forward delta put plain option volatility information read from said second memory means represents and the fifth
A second premium that calculates the premium of the forward delta / put plain option using the strike price of the forward delta / put plain option read from the storage means and stores the calculated premium of each plain option in the sixth storage means, respectively. The premium calculation means, the predetermined risk parameter of the currency option to be evaluated is read from the fourth storage means, the ATM flat volatility and the volatility information are read from the second storage means, and the sixth storage means The premium of each plain option is read out, and the ATM flat volatility and the volatility information read out from the second storage means and the respective plays read out from the sixth storage means by computer processing. The value of the predetermined risk parameter for the portfolio obtained by combining the plain options obtained from the premium of the option becomes equal to the value of the predetermined risk parameter of the currency option to be evaluated read from the fourth storage means. Calculating the composition ratio of each plain option in the portfolio, storing the calculated composition ratio in the seventh storage means, reading the ATM flat volatility from the second storage means, and The strike price of each plain option is read from the fifth storage means, and the ATM flat volatility read from the second storage means and the forward delta call play read from the fifth storage means by computer processing The premium of the forward delta call plane option is calculated using the strike price of the option, and the ATM flat volatility read from the second storage means and the forward delta / put plain option read from the fifth storage means A third premium calculation means, a sixth storage means, and an eighth calculation means for calculating a premium of the forward delta / put plain option using an exercise price and storing the calculated premium of each plain option in the eighth storage means. Each premium of each plain option is read from the storage means, and a deviation between the premium read from the sixth storage means and the premium read from the eighth storage means is calculated by computer processing. A deviation calculating means for calculating the deviation for each plane option, and storing the calculated deviation in the ninth storage means; reading out the deviation for each plain option from the ninth storage means; and reading out the component ratio from the seventh storage means The deviation for each plain option read out from the ninth storage means as a correction value for the premium of the currency option to be evaluated is calculated according to the component ratio read out from the seventh storage means. A weighted and added value is calculated, a correction value calculating means for storing the calculated correction value in the tenth storage means, a premium of the currency option to be evaluated is read from the third storage means, and the tenth The correction value is read out from the storage means, and read out from the third storage means by computer processing. The premium of the currency option of the evaluation, the first
0 is corrected by the correction value read from the storage means, and the corrected premium is the eleventh.
A currency that functions as an output unit that reads the corrected premium from the eleventh storage unit and outputs the read premium after the correction as a premium of the currency option to be evaluated. An optional premium calculation program is recorded.

A recording medium according to a tenth aspect of the invention is a currency option premium calculation program according to the ninth aspect of the invention, that is, a computer including the first storage means to the eleventh storage means.
Acquisition means, second acquisition means, first premium calculation means, risk parameter calculation means, strike price calculation means, second premium calculation means, component ratio calculation means, third premium calculation means, deviation calculation means, correction value calculation means, Since the program for functioning as the correcting means and the output means is recorded, the computer reads the premium calculation program for the currency option from the recording medium and executes it, so that the computer is the first invention. As in the first aspect of the invention, the premium of the currency option to be evaluated can be prevented from falling into a state where it cannot be calculated.

As described above, the present invention provides the ATM flat volatility representing the market value of the volatility of the ATM plain option having the same exercise period as the currency option to be evaluated, the currency option to be evaluated and the exercise period being the same, and forward. Forward delta call plane option and forward delta
Obtain volatility information that represents the market value of the volatility of the put plain option, calculate the strike price of the forward delta call plain option using the volatility of the forward delta call plain option represented by the volatility information, and forward the volatility information Calculate the strike price of the forward delta put plain option using the volatility of the delta put plain option and use the strike price to calculate the forward delta call plain option and forward delta
Since the calculation of the premium for the put plain option and the correction for the premium of the currency option to be evaluated is performed, the excellent effect of avoiding the situation that the premium of the currency option to be evaluated cannot be calculated is achieved. Have.

Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 shows a computer 10 according to this embodiment. The computer 10 includes a CPU 10A, ROM and R
A memory 10B made of AM or the like, a non-volatile storage unit 10C made of an HDD (Hard Disk Drive), a flash memory, or the like, and a communication control unit 10D are provided. The computer 10 includes a display 12 including a CRT, an LCD, etc., a keyboard 1 as various peripheral devices.
4 and mouse 16 are connected to each other. The communication control unit 10D of the computer 10
The exchange information providing system 20 is connected via a communication line. Exchange information provision system 2
0 is various parameters in the exchange rate (eg spot rate, interest rate, volatility, etc.)
Is a system that distributes the current market value to the outside as exchange information, a single computer,
Or it is comprised from the several computer mutually connected via networks, such as LAN.

The storage unit 10C of the computer 10 is provided with a currency exchange information table for registering currency exchange information acquired from the currency exchange information providing system 20, and includes a premium calculation program for performing premium calculation processing, which will be described later, and a spot rate. A volatility conversion program is also installed that has the function of converting the volatility of volatility into volatility at the forward rate. The premium calculation program corresponds to the premium calculation program of the currency option according to the present invention. The computer 10 functions as a premium calculation device of the currency option according to the present invention by the CPU 10A executing the premium calculation program, and the memory 10B includes Used as the first storage means to the eleventh storage means according to the present invention, and the storage section 12C is used as the twelfth storage means described as the fourth invention. The computer 10 corresponds to the computer described as the ninth and tenth inventions and can be constituted by a personal computer (PC), for example. However, the computer described as the ninth and tenth inventions is limited to a PC. For example, a workstation or a general-purpose host computer may be used.

Next, as an operation of this embodiment, the user operates the keyboard 14 and the mouse 16,
A premium calculation process realized by the computer 10 by executing a premium calculation program by the CPU 10A when a premium calculation is instructed for the currency option to be evaluated will be described with reference to FIG.

In the premium calculation process, first, in step 50, a message requesting input of various types of information that defines the currency option to be evaluated is displayed on the display 12, thereby allowing the user to input each of the above-described information regarding the currency option to be evaluated. . In the next step 52, it is determined whether or not each of the above information has been input, and step 52 is repeated until the determination is affirmed. When recognizing that the message is displayed on the display 12, the user uses the keyboard 1.
Operate 4 etc., and as the information to define the currency option to be evaluated, the type of the currency option to be evaluated (for example, the type of option such as plain option / reverse knockout option and whether it is call / put) Information indicating the type of the first and second currencies (for example, US dollars and Japanese yen) to be exchanged in the currency option to be evaluated, the exercise period T _e of the currency option to be evaluated (currency option The valuation date (today) to the exercise date of the currency option, etc., and the delta value of the currency option to be evaluated (the rate of change in the option value relative to the change in spot rate = the exchange rate of the option premium) First-order differential value) Δ ₀ , or the exercise price K ₀ of the currency option to be evaluated is also input. In addition, the currency option to be evaluated if the knock-out option, also knock out price K _V is input by the user.

When the above information is input by operating the keyboard 14 or the like by the user, the determination in step 52 is affirmed and the routine proceeds to step 54, where the exercise period T input by the user is entered.
Based on _e , the exercise date of the currency option to be evaluated is calculated, and the interest rate period T _d of the currency option to be evaluated (the transfer date of funds (usually two business days after the evaluation date))
Usually, the period up to 2 business days after the exercise date of the currency option) is calculated, and the calculated interest period _Td is stored in the memory 10B together with each information input by the user. In the following, a case will be described in which a reverse knockout option is designated as the type of currency option to be evaluated, and a premium of the reverse knockout option is calculated as a premium of the currency option to be evaluated. Options are not limited to reverse knockout options, but may be other exotic options or plain options.

In the next step 56, the types of the first currency and the second currency are read from the memory 10B and transmitted to the exchange information providing system 20, so that the current spot rates S ₀ , the current interest rate r _f of the _currency, the current interest rate r _d of the second currency exchange information providing system 2
0, the spot rate S ₀ received from the exchange information providing system 20, the interest rate r _f
, and stores the exchange information table provided a r _d in the storage unit 10C.

In the premium calculation processing according to the present embodiment, as will be described in detail later, the premium of the currency option to be evaluated is calculated based on the information of the plain option traded in the currency option market. In this embodiment, three types of plain options are used as the above-mentioned plain options: an ATM plain option with high market liquidity, a 25 delta call plain option, and a 25 delta put plain option. Where A
The TM plain option is an option with an equal strike price for call put delta values. The 25 delta call option has a delta of 25% as shown in FIG.
The 25 delta put option is a put option in which the exercise price is set at a point where the delta becomes 25%, as shown in FIG. These plain options are traded with quotes of volatility, and premium amounts calculated using the GK model from volatility and variables at the time of trading (spot rate, interest rate, etc.) are paid. That is, the volatility values for these plain options are available from the market.

For this reason, in the next step 58, the memory of the exercise period T _e of the currency option to be evaluated 1
It causes the display 12 is read from 0B, the indicated exercise period T _e and ATM flat volatility sigma _{ATM, 25} volatility .DELTA..sigma _RR risk reversal Delta same exercise period (same currency options exercise period evaluated) Then, a message requesting input of the 25 delta butterfly volatility Δσ _BF is displayed on the display 12 to allow the user to input the above information. In the premium calculation process according to the present embodiment, the first currency is used as the premium payment currency (the first currency is US dollar if the first / second currency is US dollar / Japanese yen), and the forward rate is used as the reference rate. Applying each, the premium of the currency option to be evaluated is calculated. In step 58 described above, more specifically, the volatility of the currency option whose reference rate is the forward rate in the first currency payment is input to the user. In the next step 60, it is determined whether or not each information is input, and step 60 is repeated until the determination is affirmed.

When the above message is displayed on the display 12, the user of the evaluation object displayed on the display 12 of the exercise period T _e of the same exercise period of currency options ATM flat volatility sigma _{ATM, 25} delta risk reversal of Obtain market values of volatility Δσ _RR and 25 delta butterfly volatility Δσ _BF (these market values can also be obtained online from the exchange information providing system 20), and use the obtained market values on the keyboard 14. Perform input operations via. However, long-term currency options that are traded on the market for one year or longer are traded based on the forward rate (for example, “25 Delta Options” has a delta value of 2 based on the forward rate).
5 (= 0.25) (hereinafter referred to as “25 forward delta” option), the corresponding volatility market value is volatility on the basis of the first currency payment and forward rate In contrast, short-term currency options of less than one year are traded based on the spot rate (for example, “25 Delta Options” is an option with a delta value of 25 (= 0.25) based on the spot rate , This option is referred to as the “25 Spot Delta” option), and the corresponding volatility market value is volatility on a spot rate basis, although it is the first currency payment.

For this reason, in this embodiment, a volatility conversion program having a function of converting spot rate based volatility into forward rate based volatility is installed in the storage unit 10C of the computer 10, and the exercise period T of the currency option to be evaluated.
_{If e} is a relatively short period (for example, less than one year) in which market transactions are conducted based on the spot rate, and the market value of the obtained volatility is the value based on the spot rate, the user The conversion program is executed by the CPU 10A, and the obtained spot rate-based volatility is input via the keyboard 14, whereby the spot rate-based volatility is converted into the forward rate-based volatility by the volatility conversion program. Then, by inputting the converted volatility based on the forward rate through the keyboard 14, the premium calculation processing (FIG. 2) receives the volatility σ _ATM , Δσ _RR , Δσ _{BF based} on the first currency payment and the forward rate. hand over.

When the market value of volatility (volatility σ _ATM , Δσ _RR , Δσ _{BF on the} basis of the first currency payment and forward rate) is input by the user as described above, the determination in step 60 is affirmed and the routine proceeds to step 62. Transition. Here, the market value of volatility available for 25 Delta is the 25 delta risk reversal volatility Δσ _RR , which is the difference between the volatility of the 25 delta call plain option and the volatility of the 25 delta put plain option, and the 25 delta call plain. Options and 25
Since the average value of the volatility of the delta put plain option and the volatility of the 25 delta butterfly Δσ _BF which is the deviation between the volatility of the ATM plain option, in step 62, the following (3), (4 ) To calculate the volatility σ _C25 and 25 of the 25 forward delta call plane option.
Each calculates the volatility σ _P25 of the forward delta / putplane option.
σ _C25 = σ _ATM + Δσ _BF + Δσ _RR / 2 (3)
σ _P25 = σ _ATM + Δσ _BF −Δσ _RR / 2 (4)
And the volatility σ of the calculated 25 forward delta call plan option σ
Volatility σ _{P25 of C25} and 25 forward delta putplane options
Are stored in the memory 10B together with the volatility of the ATM plain option input by the user.

In the above, the market value of the volatility is input to the user, but the present invention is not limited to this. The list of volatility is acquired from the exchange information providing system 20, and the currency option to be evaluated is determined from the acquired list. it exercise period may extract the same volatility of each plain option, the exercise period T _e of the currency option to be evaluated as well as notifies the exchange information providing system 20, the exercise period T _e which is the exercise period notified The exchange information providing system 20 may be queried for the same volatility of each plain option, and the corresponding volatility may be received from the exchange information providing system 20. In these modes, if the market value of the acquired volatility is a spot rate based value, the volatility conversion program is automatically activated to automatically convert the spot rate based volatility to the forward rate based volatility. Therefore, it is desirable to perform the calculations of the above formulas (3) and (4).

In the next step 64, the spot rate S ₀ and the interest rates r _f and r _d are read from the exchange information table, and the delta Δ ₀ or the exercise price K ₀ of the currency option to be evaluated, the exercise period T _e.
, Read interest period T _d , ATM flat volatility σ _ATM from memory 10B,
It calculates the premium P ₀ of the currency option to be evaluated using the information read out, and stores the premium P ₀ which is calculated in the memory 10B. In the framework of the GK model,
The premium P of the reverse knockout option is expressed by the following equation (5) regardless of whether it is a call option or a put option.

However, d1 to d8 and ξ in the equation (5) are expressed by the following equation (6).

Here, the above (5) and (6), K is the exercise price, K _V knockout price option rights disappears, N () is the cumulative probability density function of the standard normal distribution, strike K By using the exercise price K ₀ of the currency option to be evaluated as the volatility σ and the ATM flat volatility σ _ATM as the volatility σ, the above formulas (5) and (6) are used to calculate the currency to be evaluated as the reverse knockout option. it is possible to calculate the premium P ₀ of options. If the exercise price K ₀ of the currency option to be evaluated is entered by the user as information defining the currency option to be evaluated, the entered exercise price K ₀ is (5)
, (6), the strike price K can be used as it is, but when the delta value Δ ₀ of the currency option to be evaluated is entered instead of the strike price K ₀ , the entered delta value Δ ₀ is set as the predetermined value. After calculating the strike price K ₀ of the currency option to be evaluated by substituting
6) By substituting into the equation, it is possible to calculate the premium P ₀ of the currency option to be evaluated.

Specifically, the strike price K ₀ is calculated from the delta value Δ ₀ of the currency option to be evaluated, for example, instead of the delta value “0.25” in the following formula (9) or (11), After calculating the variable d ₂ by substituting the optional delta value Δ ₀ , substituting the calculated variable d ₂ into the following equation (10) or (12) and calculating the exercise price K it can.

In the next step 66 reads the spot rate S ₀ from the exchange information table, a premium P ₀ of the currency option to be evaluated was calculated in step 64, reading respectively ATM flat volatility sigma _ATM from the memory 10B, the information read Is substituted into the following equation (7) to calculate the Vega V, Volga V _σ , and Banna Vs of the currency option to be evaluated as the predetermined risk parameters of the currency option to be evaluated. , Volga V _σ and Banna Vs are stored in the memory 10B.

In the next step 68, an exercise price calculation process is performed for calculating the exercise prices of the ATM plain option, the 25 forward delta call plane option, and the 25 forward delta put plane option.

This strike price calculation process will be described with reference to FIG.
The spot rate S ₀ is read from the exchange information table, and the interest period T _d and the exercise period T
_e , the ATM flat volatility σ _ATM is read from the memory 10B, and the read information is substituted into the following equation (8) to calculate the exercise price K _ATM of the ATM plain option in the first currency payment, Calculated exercise price of ATM plain option K _ATM
Is stored in the memory 10B.

In the next steps 102 and 104, the strike price of the 25 forward delta call plane option is calculated. That is, First, in step 102, reads each volatility sigma _C25 and exercise period _{T e} of 25 forward delta call plain option from the memory 10B, respectively substituting each information read in the following equation (9), volatility sigma _C25 and obtaining a variable D ₂ that satisfies was substituted for exercise period T _e (9) equation.

Note that N () in the equation (9) is a cumulative probability density function of the standard normal distribution, and “0.25” in the equation (9).
“Represents a forward delta value. Since the value of the variable D ₂ that satisfies the equation (9) cannot be directly calculated, it is determined in step 102 whether or not the equation (9) is satisfied. By repeating this while changing the value of the variable D _2, the value of the variable D ₂ satisfying the expression (9) is searched for.See FIG. 4 for an example of the process for searching for the value of the variable D ₂ hereafter. To explain.

In the solution search process shown in FIG. 4, after the value of the variable D ₂ is narrowed down in steps 120 to 138, the solution of the variable D ₂ is searched by applying the Newton method in steps 142 to 152. That is, first, in step 120, assigns a predetermined initial value _{D init} variable _{D 2.} Note that, for example, a value of about “10” can be used as the initial value _Dinit . Step 122, the variable D ₂ is substituted into the arithmetic expression (equation (9)), calculates a value X ₀ of the right side of the expression. In the next step 124, the absolute value is determined or close enough whether zero values X ₀ obtained by calculation in step 122. In the example of FIG. 4, it is determined whether or not | X ₀ | is smaller than 1 × 10 ⁻¹² . If the determination is affirmative, the value of the variable D ₂ is narrowed down and the process proceeds to step 142. However, if the determination is negative, in step 126 the counter i
Substitute 1 for.

In the next step 128, it assigns a value obtained by adding the initial value _{D init} to the product of the counter i with variation width w to the variable _{D 2 (D 2 ← D init} + i × w) that is, varying the value of the variable _{D 2} Change only the width w. As the fluctuation width w, for example, a value of about “1” can be used. At step 130, it assigns the variable D ₂ which changes the value in step 128 to the arithmetic expression (equation (9)), calculates a value X _i of the arithmetic expression on the right side. In the next step 132, it is determined whether or not the absolute value of the value X _i obtained by the calculation in step 130 is sufficiently close to zero. In the example of FIG. 4, | X _i | is 1 × 10 ^−1.
2 and determines whether less than, but if the determination is affirmative, the process proceeds to exit the narrowing of the value of the variable D ₂ to step 142, if the determination is negative, the process proceeds to step 134 , Whether or not the signs of the value X _i and the previous value X _i−1 are different. If this determination is positive, the solution of the variable D _2, it can be determined that exists between the corresponding value to a value corresponding to the current i and (i-1), the value of the variable D ₂ of After narrowing down, the process proceeds to step 142.

If the determination in step 134 is negative, the process proceeds to step 136 to determine whether the value of the counter i has reached 30. If this determination is negative, the value of the counter i is incremented by 1 in step 138, and then the process returns to step 128. As a result, steps 128 to 13 are repeated until the determination of any of steps 132, 134, and 136 is positive.
8 is repeated. When the determination between steps 132 and 134 until the value of the counter i becomes 30 was not positive both, is affirmative determination in step 136 and proceeds to step 140, and outputs a free solution of the variable D ₂ To finish the process. In this case, the search for the solution of the variable D ₂ is
Another method (for example, a bisection method) can be applied. Needless to say, a value other than “30” may be applied as the upper limit value of the number of loops in steps 128 to 138.

On the other hand, if the determination in any of steps 124, 132, and 134 is affirmative, first, in step 142, 1 is assigned to the counter j. In addition step 144, it assigns the current variable D ₂ to the arithmetic expression (equation (9)), calculates a value X of the operation the right-hand side of the equation. In the next step 146, the absolute value of the value X obtained by the calculation in step 144 is sufficiently close to 0 (| X _i | <1 × 10 ⁻¹² ).
It is determined whether or not. Although the case where the determination in previous step 124 or step 132 has been affirmative this determination is affirmative, since the current value in this case is variable D ₂ can be determined as the solution of the variable D _2, at step 154 prints the current value of the variable D ₂ as the solution (to be stored in the memory 10B), the process ends. On the other hand, if the determination in step 146 is negative, step 14
8 and it is determined whether or not the value of the counter j has become 20. If this determination is negative, the process proceeds to step 150, updates the value of the variable D ₂ according to the following equation (10).
D ₂ ← D ₂ −X / F ′ (D ₂ ) ... (10)
However, F ′ (D ₂ ) in the equation (10) can be expressed by the following equation (11).

Since the search for the value of the variable D _{2 at} this time is for the purpose of calculating the strike price of the 25 forward delta call plane option, the volatility σ in the above equation (11) is
The volatility σ _C25 of the 25 forward delta call plane option can be used.

In the next step 152, the value of the counter j is incremented by 1, and the process returns to step 144. As a result, step 144 is continued until either of the determinations of steps 146 and 148 is affirmed.
Step 152 is repeated. When the determination between step 146 until the value of the counter j is 20 is not positive, it is affirmative determination in step 148 and proceeds to step 140, exit with an absence solutions of variable D ₂ To do. Step 144 to Step 1
Needless to say, a value other than “20” may be applied as the upper limit value of the number of loops of 52. In addition, although the determination in step 146 was initially denied, step 1 is thereafter performed.
If the determination in step 146 is affirmed before the determination in 48 is affirmed, step 154 is performed.
In output as the solution of the current value of the variable D ₂ (stored in the memory 10B), the process ends.
By performing the above process, it is possible to obtain the value of the variable D _2, thereby satisfying the expression (9).

In the exercise price calculation process (FIG. 3), subsequently, in step 104, the spot rate S ₀ and the interest rates r _f and r _d are read from the exchange information table, and the interest rate period T _d and the exercise period T _e.
, Variable D ₂ , 25 forward delta call plan option volatility σ _C2
5 is read from the memory 10B, and the read information is substituted into the following equation (12), whereby the strike price K _C2 of the 25 forward delta call plain option for the first currency payment
₅ is calculated, and the exercise price K _C25 of the calculated 25 forward delta call plane option of the first currency payment is stored in the memory 10B.

Subsequently, at steps 106 and 108, the strike price of the 25 forward delta / put plain option is calculated. That is, reading each volatility sigma _P25 and exercise period T _e of 25 forward delta call plain option in step 106 from the memory 10B, respectively substituting each information read in the following equation (13), the volatility sigma _P25 and exercise period obtained by substituting T _e (13) obtaining the variable D ₂ that satisfies the equation.

N () in equation (13) is a cumulative probability density function of standard normal distribution, and “0.25” in equation (13).
"Also represents the value of the forward delta. (13) can not be calculated directly the value of the variable D ₂ that satisfies the equation, even in step 106, performs the solution search process described above (FIG. 4) (where As the volatility σ in the above equation (11), the volatility σ _P25 of the 25 forward delta / put plain option is used), and the variable D satisfying the above equation (13)
Search for a value of ₂ .

In step 108, the spot rate S ₀ and the interest rates r _f and r _d are read from the exchange information table, respectively, and the interest period T _d , the exercise period T _e , the variable D ₂ , and the volatility σ _P25 of the put plain option of 25 deltas. By reading each information from the memory 10B and substituting each read information into the following equation (14), the _strike price K _P25 of the 25 forward delta / put plain option of the first currency payment is calculated, and the calculated first currency The _strike price K _P25 of the 25 forward delta putplane option of payment is stored in the memory 10B.

When the strike prices of the ATM plain option, the 25 forward delta call plane option, and the 25 forward delta put plain option are respectively calculated by the above exercise price calculation process, the process proceeds to step 70 of the premium calculation process (FIG. 2).

In step 70, the spot rate S ₀ and the interest rates r _f and r _d are read from the exchange information table, respectively, and the interest period T _d , the ATM plain option, the 25 forward delta call plain option and the 25 forward delta put plain option are exercised. The prices K _ATM , K _C25 , K _P25 , ATM flat volatility σ _ATM , 25 forward delta call plain option and 25 forward delta put plain option volatility σ _C25 , σ _P25 are read from the memory 10B, respectively, If the calculation target option is a call option, substitute it into equation (15), and if the calculation target option is a put option, substitute it into equation (16) to obtain an ATM plain option, 25 forward delta call. Rain options and 25 forward delta put plain option premium _{P ATM,} each calculates the _{P C25, P P25,} the calculated premium _{P ATM,} thereby each store _{P C25, P P25} in the memory 10B.

Incidentally, in the calculation step 70, 25 forward delta call at the time of calculation of plain option premium P _C25, as Boratiti, 25 forward delta call plain option volatility sigma _C25 is used, 25 forward delta put plain option premium at the time of the calculation of P _P25, as Boratiti, 25
The volatility σ _{P25 of the} forward delta / putplane option is used.

Subsequently in step 70, reads out each of the spot rate _{S 0} from the exchange information table, ATM plain option, 25 forward delta call plain option and 25 forward delta put plain option premium _{P ATM, P C25, P P
25} , volatility σ _ATM , σ _C25 , σ _P25 is read from the memory 10B, and the read information is substituted into the above equation (7), so that the V
_ATM , Volga V _{σ ATM} , _Vanna Vs _ATM , 25 Forward Delta Call Plan Option Vega V _C25 , Volga V _{σ C25} , _Vanna Vs _C25 , 25 Forward Delta Put Plain Option Vega V _P25 , Volga V _{σ P25} , _Vanna Vs _P25 Vega V _ATM , V _C25 , V _P25 , Volga V _σATM , V _σC25 ,
_VσP25 , _Vanna Vs _ATM , Vs _C25 and Vs _P25 are stored in the memory 10B, respectively.

In the next step 74, the currency option Vega V calculated in the previous step 66 is calculated.
, Volga V _σ and Banna Vs are read from the memory 10B, and the Vega V _ATM , V _C25 , V _P25 , Volga V _{ATM of} the ATM plain option, 25 forward delta call plain option, 25 forward delta put plain option calculated in step 70, Volga _{V σATM, V σC25, V σP25} , read Banna _{Vs ATM,} the _{Vs C25, Vs P25} from the memory 10B, ATM plain option, 25 forward delta call plain option, 25 forward delta put portfolio of Vega that a combination of plain option , Volga, Banner is Vega V currency options to be evaluated, Volga V _sigma, equal to Banner Vs (satisfying the relationship shown in the following equation (17)) of the time, the component ratio (the amount of each plain option _{Rate) A ATM, A C25,} calculates the _{A P25,} the calculated constituent ratio _{A A
TM} , A _C25 and A _P25 are stored in the memory 10B.

The composition ratios A _ATM , A _C25 , and A _P25 that satisfy the relationship of the above equation (17) can be obtained by calculating by substituting each data read from the memory into the following equation (18). it can.

In the next step 76, the spot rate S ₀ and the interest rates r _f and r _d are read from the exchange information table, respectively, and the strike period K of the interest rate period T _d , 25 forward delta call plain option and 25 forward delta put plain option _C25 , K _P25 , A
Each TM flat volatility σ _ATM is read from the memory 10B, and each read information is converted into the following equation (15) for the 25 forward delta call plane option: 25
By substituting the forward delta / put plain option into the equation (16), the premium P ′ of the 25 forward delta call plain option and the 25 forward delta / put plain option when the ATM flat volatility σ _ATM is used as the volatility σ. _C25 , P ′ _P25 is calculated, and the calculated premium P ′ _C25 , P ′
_P25 is stored in the memory 10B.

Thus, 25 the forward delta call plain option and 25 forward delta put plain option, using 25 forward delta call plain option volatility sigma _{C25, 25} forward delta put plain option volatility sigma _P25 as volatility sigma Calculated premium _PC25 ,
P _P25 and premiums P ′ _C25 and P ′ _P25 calculated using ATM flat volatility σ _ATM as volatility σ are respectively stored in memory 10B.

In step 78, 25 of the forward delta call plain option premium _{P C
25,} and P _'C25, 25 forward delta put plain option of premium _{P P
25} , P ′ _P25 is read from the memory 10B, two premiums of the 25 forward delta call plane option are substituted into the following equation (19), the deviation (difference) Zeta _C25 is calculated, and 25 forward delta・ Substitute the two premiums of the put plain option into the following equation (20), calculate the deviation (difference) Zeta _P25, and calculate the calculated deviation Zeta _C25
, Zeta _P25 is stored in the memory 10B.
_{Zeta C25 = P C25 -P 'C25} ... (19)
Zeta _P25 = P _P25− P ′ _P25 (20)
In step 80, the deviations Zeta _C25 and Zeta _P25 calculated in step 78 and the composition ratios A _C25 and A _P25 calculated in step 74 are read from the memory 10B, and the read information is _expressed by the following equation (21). The correction value Zeta is calculated by substituting each, and the calculated correction value Zeta is stored in the memory 10B.
Zeta = A _C25・ Zeta _C25 + A _P25・ Zeta _P25 ... (21)
By the way, in the knockout option, the probability of the option right extinction increases as the spot rate S ₀ approaches the knockout price K _{V at} which the option right expires, and the premium decreases as the probability of the option right extinction increases. Next step 8
In 2, for the purpose of further correcting the correction value Zeta depending on arrival probability to knock out price K _V spot rate S _0, Gap, arrival rate represents the arrival probability to knock out price K _V spot rate S ₀ R Is calculated. Gap arrival rate R is made to 0 (%) uniformly in plain option like that to knock out price K _V has not been set, when the currency option to be evaluated is the reverse knock-out option, etc., digital touch option (Digit
al Touch Option) can be calculated by calculating the premium.

As shown in FIG. 7, the digital touch option is an option that can receive a predetermined rebate Z when the spot rate S is at least the exercise price K (or less) before the option exercise date. It is. Of the digital touch options, as shown in FIG. 7 (A), those that can receive the rebate Z when the spot rate S becomes the exercise price K or more are call options, and the rebates when the spot rate S becomes the exercise price K or less. Those that can receive Z are called put options. The premium of the digital touch option reflects the probability of the spot rate S reaching the exercise price K, and as shown by the broken line in FIG. 7, the spot rate S approaches the exercise price K. If it is above or below the price K, it matches the rebate Z. That is, since the premium per unit rebate amount of the digital touch option can be regarded as representing the probability of reaching the strike price K of the spot rate S, the strike price K equal to the knockout price K _V of the option to be evaluated. Gap using a premium digital touch option with
The arrival rate R can be obtained.

In the GK model framework, the premium of the call digital touch option is expressed by the following equation (22), and the premium of the digital touch option of the put is expressed by the following equation (23).

However,

It is.

As described above, since the digital touch option for a call can receive a rebate Z when the exercise price is K or more before the exercise date, the premium for the digital touch option for a call with a rebate Z of “1” is , The probability that the spot rate S becomes the exercise price K or more before the exercise date. Then, OTM knock-out option of reverse knock-out option or put the call, the spot rate S is equal to or greater than the knock out price K _V the option of the right to disappear. Therefore, when the option to be evaluated is a reverse knockout option for calls or an OTM knockout option for puts, the spot rate S ₀ and the interest rates r _f and r _d are read from the exchange information table, and the interest rate period T _d and the option The period T _e , the exercise price K ₀ of the currency option to be evaluated, and the ATM flat volatility σ _ATM are read from the memory 10B, and the read information is (2
2) and (24) are substituted respectively, and 1 is substituted for Z, the interest period T _d and the option period T _e
Is the same as the currency option to be evaluated and the premium P of the digital touch option of the call whose rebate Z is “1” is calculated, and the calculated premium P is stored in the memory 10B as the Gap arrival rate R.

On the other hand, Put's digital touch option can receive a rebate Z when the exercise price falls below the exercise price K before the exercise date, so the premium of the put's digital touch option with a rebate Z of “1” is the spot rate. It represents the probability that S will be below the exercise price K before the exercise date. Then, when the spot rate S is equal to or lower than the knockout price K, the option right of the put reverse knockout option or the call OTM knockout option is lost. Therefore, when the option to be evaluated is a put reverse knockout option or a call OTM knockout option, the spot rate S ₀ and the interest rates r _f and r _d are read from the exchange information table, respectively, and the interest rate period T _d ,
The option period T _e , the exercise price K ₀ of the currency option to be evaluated, and the ATM flat volatility σ _ATM are read from the memory 10B, and the read information is assigned to the equations (23) and (24), respectively, and 1 is set to Z assignment, and identical to the currency option interest term T _d and optional period T _e is evaluated, and rebates Z is calculated premium P digital touch option put "1", Gap, arrival rate premium P which computed R is stored in the memory 10B.

In the next step 84, the correction value Zeta calculated in the previous step 80 and the GAP arrival rate R calculated in step 82 are read from the memory 10B, and the read information is substituted into the following equation (25) to obtain the correction value. Zeta correction calculation is performed, and the corrected correction value Zeta is stored in the memory 10B.
Zeta = (1-R) ・ Zeta ... (25)
(1-R) in equation (25) above indicates that the currency option being evaluated remains alive until the date of exercise
Represents a (right disappeared non) random, because in such plain option knockout price K _V is not set a GAP arrival rate R = 0 (%), ( 1-R) = 1 , and the above of the correction value of the correction value Zeta regardless of operation does not change, in such a barrier system options knockout options or knock-in options knockout price K _V is set, GAP
Since the arrival rate R> 0 (%), (1−R) <1, and the correction value Zeta after the above correction calculation becomes smaller as the probability that the evaluation-target currency option is alive until the due date becomes smaller. The value becomes smaller.

In the next step 86, the currency option premium P ₀ calculated in the previous step 80 and the correction value Zeta obtained through the correction calculation in step 84 are read from the memory 10B, respectively.
By calculating by substituting each information read in the following equation (26), a premium P ₀ of the currency option to be evaluated is corrected by the correction value Zeta, and stores the premium P ₀ after the correction in the memory 10B.
P ₀ = P ₀ + Zeta ... (26)
In step 88, the premium _{P 0} which has undergone the correction calculation step 84 the memory 10B
Read from, (to be displayed for example on the display 12) outputs a premium P ₀ read as premium currency option to be evaluated, and ends the premium calculation process.

Thus, in this embodiment, for the 25 forward delta call plan option, the premium _{PC 25} using the volatility σ _C25 of the 25 forward delta call plan option and the premium using the ATM flat volatility σ _ATM are used. Each of P ′ _C25 and its deviation Zeta _C25 are calculated, and for the 25 forward delta / put plain option, the premium _{PP 25} using the volatility σ _P25 of the 25 forward delta / put plain option and ATM
Flat volatility σ When premium _ATM is used, premium P ' _P25 is calculated and its deviation Zeta _P25 is calculated, and each deviation is calculated as ATM plain option, 25 forward delta call plain option and 25 forward delta put plain option. the combined portfolio of Vega V, Volga V _sigma, Banner Vs is, Vega V currency options to be evaluated, Volga V _sigma, when equal to Banner Vs, depending on the ratios of the plain option of the portfolio calculating a correction value Zeta by adding weighted, since the premium P ₀ of the currency option to be evaluated was calculated using the ATM flat volatility sigma _ATM is corrected by the correction value Zeta, calculation of currency option premium The model used for (G The error of the probability distribution assumed by the model framework) can be corrected, and an appropriate value that accurately reflects the magnitude of the risk underwriter of the currency option is obtained as the premium of the currency option to be evaluated. be able to.

In this embodiment, as an option other than the ATM plain option used for calculating the correction value Zeta, etc., 25 forward deltas in which the exercise period is the same as the currency option to be evaluated and the delta based on the forward rate is 0.25. Apply the call plain option and the 25 forward delta put plain option, and the 25 delta risk reversal volatility Δσ _RR and 2 representing the market value of the volatility of the 25 forward delta call plain option and the 25 forward delta put plain option
Obtain the 5-delta butterfly volatility Δσ _BF , calculate the _strike price K _C25 of the 25 forward delta call plan option using the volatility σ _C25 of the 25 forward delta call plan option, and use the 25 forward delta put plane option Since the exercise price K _P25 of the 25 forward delta / put plain option is calculated using the volatility σ _P25 of the ATM, the exercise price K _ATM of the ATM plain option, the 25 forward delta / call plain option and the 25 forward delta / put plain option are calculated. to avoid that it is possible to prevent that the option exercise price K _C25, K _P25 will all together, the situation in which the currency options of the premium to be evaluated becomes impossible calculation arise Door can be.

In the above description, the mode of applying the highly liquid 25 forward delta plain option and ATM plain option as the plain option used for calculating the correction value for the premium of the currency option to be evaluated has been described. If the liquidity is secured, it is possible to use a forward delta / callplane option with a delta based on the forward rate, such as a 10 forward delta / plane option. .

Further, in the above description, an embodiment using Vega, Volga and Banna as a predetermined risk parameter according to the present invention (more specifically, a parameter representing risk with respect to change in volatility) has been described, but the present invention is not limited to this. One or two parameters may be selected and used from other Vega, Volga and Banna, or another risk parameter (for example, a parameter representing the risk of changes in indicators other than volatility) may be used. , Vega,
The other risk parameter may be used in addition to Volga and Banna (or one or two parameters selected from these).

In the above description, the aspect in which the currency option premium calculation program according to the present invention is stored (installed) in advance in the storage unit 10C of the computer 10 has been described. It is also possible to provide the information recorded in a recording medium such as a ROM or a DVD-ROM. This aspect corresponds to the tenth invention.

It is a block diagram which shows schematic structure of the computer which concerns on this embodiment. It is a flowchart which shows the content of premium calculation processing. It is a flowchart which shows the content of the exercise price calculation process. It is a flowchart which shows the content of a solution search process. FIG. 6 is a diagram for explaining a 25 delta call plane option. It is a diagram for explaining a 25 delta put plane option. It is a diagram for explaining a digital touch option.

10 Computer 10B Memory 10C Storage Unit 12 Display 14 Keyboard 20 Exchange Information Providing System

Claims (8)

An input receiving unit for receiving an input of a spot rate, a first currency interest rate, a second currency interest rate, an interest period corresponding to the first currency interest rate, an exercise period, an exercise price, a knockout price, and standard volatility;
Based on the spot rate, the first currency interest rate, the second currency interest rate, the interest rate period, the right exercise period, the accounting exercise price, the knockout price, and the standard volatility received by the input reception unit. A premium calculation unit for calculating a knockout option premium;
Reverse knockout option premium calculator.   The reverse knockout option premium calculation device according to claim 1, wherein the interest rate period takes a value of one year or more. The input receiving unit further includes an exercise price calculation unit that calculates an exercise price by numerical calculation processing based on the delta value when a delta value is input,
The reverse knockout option premium calculation device according to claim 1, wherein the strike price calculation unit delivers the calculated strike price to the premium calculation unit.   The reverse knockout option premium calculation apparatus according to claim 1, wherein the standard volatility has a delta value of 50% based on a forward rate. Spot rate, first currency interest rate, second currency interest rate, interest period corresponding to the first currency interest rate, exercise period, first volatility related to a specific delta value, second volatility and standard related to the delta value An input reception unit that receives input of volatility;
A volatility calculation unit that calculates a volatility corresponding to the delta value based on the first volatility, the second volatility, and the standard volatility received by the input reception unit;
The volatility corresponding to the delta value calculated by the volatility calculation unit, the spot rate received by the input reception unit, the first currency interest rate, the second currency interest rate, the interest rate period, and the exercise period. Based on the strike price calculation unit for calculating the strike price corresponding to the delta value,
A currency option premium calculation device comprising: a premium calculation unit that calculates an option premium based on the volatility calculated by the volatility calculation unit and the exercise price calculated by the exercise price calculation unit.   When the first volatility related to the specific delta value received by the input receiving unit, the second volatility related to the delta value, and the standard volatility are numerical values based on a spot rate, the forward rate is used as a reference. The currency option premium calculation apparatus according to claim 5, further comprising a conversion unit that converts the numerical value into a numerical value. Spot rate, first currency interest rate, second currency interest rate, interest period corresponding to the first currency interest rate, exercise period, first volatility related to a specific delta value, second volatility and standard related to the delta value An input reception unit that receives input of volatility;
A volatility calculating unit that calculates a plurality of volatility corresponding to the delta value and the type of option based on the first volatility, the second volatility, and the standard volatility received by the input receiving unit;
A plurality of volatility corresponding to the delta value calculated by the volatility calculating unit, the spot rate received by the input receiving unit, the first currency interest rate, the second currency interest rate, the interest rate period, and the accounting exercise. A strike price calculation unit for calculating a plurality of strike prices corresponding to the delta value and the type of the option based on the period,
A premium calculation unit for calculating each option premium corresponding to the type of the option based on the plurality of volatility calculated by the volatility calculation unit and the plurality of exercise price calculated by the exercise price calculation unit; A currency option premium calculation device. When the first volatility related to the specific delta value received by the input receiving unit, the second volatility related to the delta value, and the standard volatility are numerical values based on a spot rate, the forward rate is used as a reference. The currency option premium calculation apparatus according to claim 7, further comprising: a conversion unit that converts the numerical value into a numerical value.

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