JP2002230304A - Method and system for computing premium of currency option, program making computer compute premium of currency option, and recording medium with program recorded thereon - Google Patents

Abstract

PROBLEM TO BE SOLVED: To compute the value of a premium very close to a market value as to a currency option that it has been difficult for a framework of a conventional GK model to properly evaluate the premium with. SOLUTION: Vega, Vega 2, and a vanner are computed (S102, S106) from ATM flat volatility σATM as to an object option to be evaluated and three kinds of play options and a portfolio constitution rate is computed (S108) so that the Vega, Vega 2, and vanner of the portfolio obtained by combining the object option to be evaluated and the three kinds of play options match one another. As for each play option, the difference between the premium computed from σATM and the premium computed from a volatility market value is computed (S110) and the premium of the object option to be evaluated which is computed from σATM is corrected with the sum of the difference amount weighted by the constitution ratio.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a method and system for calculating a premium for a currency option. The present invention also relates to a program for causing a computer to calculate a premium for a currency option, and a recording medium on which the program is recorded.

[0002]

2. Description of the Related Art A currency option is the right to purchase or sell a currency at a predetermined exercise price within a predetermined exercise date or period. For example, a buyer of a dollar call option with an exercise price of 100 yen per dollar can purchase a dollar at 100 yen per dollar even if the price rises and exceeds 100 yen per dollar. Thus, by selling $ 1 at prevailing rates above ¥ 100 (e.g., ¥ 105), while exercising options and buying $ 1 at ¥ 100,
Exchange gains can be obtained. If the dollar falls below 100 yen per dollar, the user can purchase the dollar at the spot rate without exercising the option. Similarly, a buyer of a dollar put option with a strike price of $ 100 can gain exchange gain by selling the dollar at $ 100 even if the dollar falls below $ 100. If you exceed 100 yen, you can sell dollars at the spot rate without exercising options. In this way, currency options have the function of hedging the risk of loss due to fluctuations in exchange rates while securing the opportunity to gain exchange gains. Have to pay.

In order for currency options to be properly traded in the market, it is necessary to present a premium that balances the profits of buyers and sellers of options. As a method of calculating such a premium, at present, the Garman = Korhalgen model in which the Black = Scholes model is modified for currency options, or a framework further modified based on the Garman = Korhalgen model (hereinafter referred to as a GK model framework) It has become common to use. In the framework of the GK model, the premium of the option is expressed using the volatility (expected volatility) of the exchange rate as a parameter. Since the volatility of exchange rates is presented on the market, the premium of currency options can be easily calculated by using the framework of the GK model.

[0004]

By the way, as currency options, not only simple options (plain options) in which only the exercise date or period and the exercise price are determined, but also exotic options that make them more complicated, are becoming popular. Is traded. For example, a knockout option, which is a typical example of an exotic option, is such that the option expires when the exchange rate reaches a predetermined knockout price even once by the exercise date of the option. The theoretical formula for calculating the premium of an exotic option such as knockout is derived based on the framework of the GK model. However, for example, in a reverse knockout option in which the knockout price is higher than the strike price of the option (ie, higher in the case of a call option, for example), the exchange rate is changed from the strike price to the knockout price. The premium calculated theoretically using ATM flat volatility based on the framework of the GK model increases the value of the option in the market, as the value of the option increases as the price approaches and decreases discontinuously to zero when the knockout price is reached. It is far away from the transaction value of the company, making it unsuitable for practical use.

[0005] The present invention has been made in view of the above points, and in addition to the out-of-the-money plain option, currency options such as a reverse knockout option can be properly evaluated in the framework of the conventional GK model. It is difficult to calculate the premium value of currency options that can calculate the value of the premium that closely approximates the market value, the premium calculation system of the currency option, and the program that allows the computer to calculate the premium of the currency option. It is an object of the present invention to provide a recorded recording medium.

[0006]

In order to achieve the above object, the invention described in claim 1 is a method for calculating a premium of a currency option by evaluating the premium,
A first step of acquiring ATM flat volatility and volatility smile-related information on volatility smile, and a first step of acquiring the acquired ATM flat volatility and volatility smile-related information.
A predetermined risk parameter relating to volatility for the option to be evaluated based on the ATM flat volatility stored in the first storage means, and calculating the result of the calculation in the second step. And a plurality of predetermined plain options having the same exercise date or exercise period as the option to be evaluated, with respect to the ATM flat volatility and the volatility smile related to the ATM flat volatility stored in the first storage means. The exercise price calculated based on the information and the AT stored in the first storage means.
A fourth step of calculating the value of the predetermined risk parameter based on the M flat volatility, and storing the calculated value in a third storage unit; and the predetermined plane stored in the third storage unit. The value of the predetermined risk parameter for the portfolio created by combining the predetermined plain options calculated based on the value of the risk parameter for the option is the evaluation target option stored in the second storage means. A fifth step of calculating a composition ratio of each of the plain options in the portfolio so as to be equal to the value of the predetermined risk parameter for the above, and storing the calculated value in fourth storage means; For each of the plain options, the ATM flags stored in the first storage means are stored. A sixth step of calculating a premium reflecting market conditions based on the volatility and volatility smile-related information; and for each of the plurality of predetermined plain options, the ATM flat volatility stored in the first storage means. A seventh step of calculating a premium based on the first and second predetermined plane options.
An eighth step of calculating a difference between the calculated value in the step and the calculated value in the seventh step; a difference calculated in the eighth step; A ninth step of calculating a correction value for the premium of the option to be evaluated based on the stored portfolio composition ratio of each plain option;
A tenth step of calculating the premium of the option to be evaluated based on the ATM flat volatility stored in the storage means, and correcting the calculated value with the correction value calculated in the ninth step; An eleventh step of outputting a correction result in the step as a premium evaluation value for the evaluation target option.

[0007] The invention described in claim 11 is a method of calculating a premium for a currency option as an evaluation object, wherein a first option for acquiring ATM flat volatility and information related to volatility smile relating to volatility smile. A second step of calculating predetermined risk parameters relating to volatility for the valuated option based on the ATM flat volatility obtained in the first step; and setting the same exercise date or exercise period as the valuated option. The strike price calculated based on the ATM flat volatility and the volatility smile related information stored in the first storage means for a plurality of predetermined plain options having the ATM plan information, and the ATM flag stored in the first storage means. A third step of calculating the value of the predetermined risk parameter based on the volatility, and the predetermined step calculated based on the value of the risk parameter for the predetermined plain option calculated in the third step. The value of the predetermined risk parameter for the portfolio created by combining the plain options is equal to the value of the predetermined risk parameter for the evaluation target option stored in the second storage means. A fourth step of calculating a composition ratio of each plain option in the portfolio; and a market condition of each of the plurality of predetermined plain options based on the ATM flat volatility and volatility smile related information input in the first step. Reflected A fifth step of calculating a premium, for each of said plurality of predetermined plain option, A entered in the first step
A sixth step of calculating a premium based on TM flat volatility; and for each of the plurality of predetermined plain options, a value between the calculated value in the fifth step and the calculated value in the sixth step. A seventh step of calculating the difference between the two, and correcting the premium of the option to be evaluated based on the difference calculated in the seventh step and the portfolio composition ratio of each plain option calculated in the fourth step. An eighth step of calculating the value, and the A input in the first step.
Calculate the premium of the option to be evaluated based on TM flat volatility, and
And a tenth step of outputting the correction result of the ninth step as a premium evaluation value for the evaluation target option. I do.

[0008] The invention described in claim 12 is a system for calculating a premium of a currency option as an evaluation object, and an acquisition means for acquiring volatility smile-related information on ATM flat volatility and volatility smile, and ATM acquired
First storage means for storing flat volatility and volatility smile related information; and first calculating means for calculating a predetermined risk parameter related to volatility for the option to be evaluated based on the ATM flat volatility stored in the first storage means. Calculation means, a second storage means for storing a value calculated by the first calculation means, and a first storage for a plurality of predetermined plain options having the same exercise date or exercise period as the evaluation target option. Calculating the value of the predetermined risk parameter based on the exercise price calculated based on the ATM flat volatility and the volatility smile related information stored in the means and the ATM flat volatility stored in the first storage means. 2 calculation means and the second Third storing the calculated values by means
And the predetermined risk for the portfolio created by combining the predetermined plain options calculated based on the value of the risk parameter for the predetermined plain options stored in the third storage means A third calculation for calculating a composition ratio of each plain option in the portfolio such that a value of the parameter is equal to a value of the predetermined risk parameter for the option to be evaluated stored in the second storage means; Means, fourth storage means for storing a value calculated by the third calculation means, and for each of the plurality of predetermined plain options, the ATM flat volatility and volatility smile stored in the first storage means. Calculate premiums that reflect market conditions based on information Fourth calculating means for calculating a premium for each of the plurality of predetermined plain options based on ATM flat volatility stored in the first storage means; and For each of the plain options, a sixth calculating means for calculating a difference between a calculated value by the fourth calculating means and a calculated value by the fifth calculating means, and a calculation by the sixth calculating means. A seventh calculating unit that calculates a correction value related to the premium of the evaluation target option based on the difference thus calculated and the portfolio composition ratio of each plain option stored in the fourth storage unit; The premium of the option to be evaluated is calculated based on the ATM flat volatility stored in the storage means, and the calculated value is calculated by the sixth And eighth computing means for correcting the correction value calculated by the calculation means, and an outputting means for outputting a correction result by the calculating means of said 8 as a premium evaluation value.

According to the inventions described in claims 1, 11 and 12, a plurality of predetermined exercises having the same exercise date or exercise period as the option to be evaluated are determined based on ATM flat volatility and volatility smile-related information obtainable from the market. The strike price is calculated for each of the plain options, and predetermined risk parameters for volatility are calculated. Next, the composition ratio of the portfolio is calculated such that the risk parameter value of the portfolio configured by combining the plurality of plain options is equal to the risk parameter value of the evaluation target option calculated using ATM flat volatility. That is, a portfolio is configured that is equivalent to the option to be evaluated with respect to a predetermined risk parameter. By the way, the volatility of plain options can be obtained from the market. Therefore, for the plain option, the difference between the premium calculated using the ATM flat volatility and the market value of the premium (that is, the premium value calculated from the market value of the volatility) can be calculated. Then, by using this difference, it is possible to calculate the difference between the calculated value using ATM flat volatility and the market value for the premium of the portfolio. The difference calculated for this portfolio is the difference between the premium calculated using ATM flat volatility for the valued option and the market value of the premium, since the portfolio is equivalent to the valued option with respect to the given risk parameters. Is considered to be close to Therefore, the premium value approximate to the market value can be obtained by correcting the premium value of the evaluation target option calculated from the ATM flat volatility obtainable from the market based on the calculated difference.

[0010] The volatility smile-related information includes, for example, a put option and a plain option of a call (for example, 25 delta put /
The volatility of the plain option and the 25 delta call plain option) can be used.

According to a second aspect of the present invention, in the method of the first aspect, the predetermined risk parameter is calculated in the third and fourth steps, and the sixth, seventh, and seventh steps are performed. The calculation of the premium in the ten steps is performed using a framework based on the Garman = Korhalgen model.

According to a third aspect of the present invention, in the method according to the first or second aspect, the plurality of predetermined plain options are a 25 delta put plain option, a 25 delta call plain option, and A
It is characterized by including a TM plane option.

According to a fourth aspect of the present invention, in the method according to any one of the first to third aspects, the predetermined risk parameter is a first-order derivative by premium volatility. Vega 2 which is the second derivative due to the volatility of the above, and Banna which is the first derivative due to the spot price of the Vega.

According to a fifth aspect of the present invention, in the method according to any one of the first to fourth aspects, the value of the predetermined risk parameter for the portfolio in the fifth step is set as: The calculation is performed as a weighted sum of the risk parameter values for each plain option, with the composition ratio of each plain option in the portfolio being weighted.

According to a sixth aspect of the present invention, in the method according to any one of the first to fifth aspects, in the ninth step, the correction value is obtained by changing the correction value of each of the plain options in the portfolio. The calculation is performed as a weighted sum of the differences for each of the plain options with the composition ratio as a weight.

According to a seventh aspect of the present invention, in the method according to any one of the first to sixth aspects, the strike price of the predetermined plain option is specified by a delta value, and In the step 4, the strike price of the plain option is calculated based on the market value of the volatility of the predetermined plain option and the delta value, and the calculated strike price and the calculated strike price are stored in the first storage means. Calculating the predetermined risk parameter for the predetermined plain option based on ATM flat volatility.

According to an eighth aspect of the present invention, in the method according to any one of the first to seventh aspects, the option to be evaluated disappears when the spot rate reaches a predetermined barrier point. Or, in the case of a barrier option that occurs, a second correction value is calculated according to the possibility that the spot rate will reach a barrier point by the exercise date of the option to be evaluated, and in the tenth step, The premium calculated based on the ATM flat volatility is calculated by using the correction value and the second
The correction value is used for the correction.

According to a tenth aspect of the present invention, in the method according to any one of the first to seventh aspects, in the ninth step, the option to be evaluated is such that the spot rate corresponds to the barrier point. If the option is a barrier option that disappears or occurs when it reaches,
The correction value is calculated based on the possibility that the spot rate will reach the barrier point by the exercise date of the option to be evaluated.

According to a thirteenth aspect of the present invention, in the system according to the twelfth aspect, when the option to be evaluated is a barrier option that disappears or occurs when the spot rate reaches a barrier point. Means for calculating a second correction value according to the possibility that the spot rate will reach the barrier point by the exercise date of the option to be evaluated, wherein the eighth calculation means is based on the ATM flat volatility. The premium calculation value is corrected by the correction value and the second correction value.

In the barrier option, as the spot rate approaches the barrier point, the possibility that the option disappears or occurs increases, and the premium takes a value reflecting the possibility that the option disappears or occurs. In the invention according to claims 8, 10 and 13, when the option to be evaluated is a barrier option, the possibility that the spot rate reaches the barrier point, that is, the possibility that the option disappears or occurs, is also considered. The premium calculated based on ATM flat volatility is corrected in this way, so even when the spot rate is close to the barrier point, it is possible to obtain a premium value that approximates the market value, reflecting the possibility that options will disappear or occur. it can.

According to a ninth aspect of the present invention, in the method of the eighth aspect, the second correction value is set to a premium of a digital touch option having an exercise price equal to a barrier point of the evaluation target option. It is characterized in that it is obtained based on

The digital touch option is an option that allows a predetermined rebate amount to be received when the spot rate reaches the strike price at least once before the option exercise date, and the premium per unit rebate amount is: It can be said that the spot rate indicates the possibility of reaching the strike price. Thus, based on a digital touch option having a strike price equal to the knockout price of the valuated option, as described in claim 9,
A second correction value can be determined.

According to a fourteenth aspect of the present invention, there is provided a program for causing a computer to execute the method according to any one of the first to eleventh aspects.
The invention according to claim 15 relates to a recording medium on which the program is recorded.

[0024]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a premium calculation system according to a first embodiment of the present invention will be described. In addition,
In the present embodiment, a case will be described in which the premium of the reverse knockout option is calculated based on the price of the plain option traded in the currency option market. The plain options underlying the premium calculation include ATMs (At The
Money) Three options are used: a plain option, a 25 delta put plain option, and a 25 delta call plain option. Here, the ATM plain option is an option in which the exercise price has the same delta value of the call put. Also, as shown in FIGS. 1 and 2, the 25 delta put option and the 25 delta call option are:
Put options and call options whose strike prices are set at a point where the delta (the rate of change of the option value with respect to the change in the exchange spot rate = the first derivative of the option premium at the exchange spot rate) becomes 25%.
These plain options are traded by quoted volatility, and the premium amount calculated using the GK model from the volatility and various variables at the time of trading (spot rate, interest rate, etc.) is paid and received. That is, the volatility values for these plain options are available from the market.

FIG. 3 is a configuration diagram of the premium calculation system of the present embodiment. As shown in FIG. 3, the system according to the present embodiment includes a central processing unit 10, a memory 12, a hard disk device 14, a floppy (registered trademark) disk, and a CD.
A drive device 16 for driving a recording medium 15 such as a ROM and a DVD-ROM, and an input device 1 such as a keyboard
8, a display device 20, and a printer 22 as a computer system. The premium calculation process is performed, for example, by the central processing unit 10 reading and executing a program stored in the hard disk device 14. Note that this program is recorded on a recording medium 15, and is read out from this recording medium via a recording medium drive device 16 and is read from the hard disk device 1.
4 is installed. However, the central processing unit 10 may directly read and execute the program recorded on the recording medium 15. Alternatively, the premium calculation system may be connected to a computer network such as the Internet, and the calculation program may be downloaded from the computer network and recorded on the hard disk device 14.

Next, the contents of the calculation processing executed in the system of this embodiment will be described. FIG. 4 is a flowchart showing the contents of the processing in this system.

As shown in FIG. 4, first, at step 100, ATM flat volatility, 25 delta
Risk reversal volatility and 25 delta
Each market value of butterfly volatility is entered,
Respectively stored and then the variables σ _ATM , σ _P25 , and σ
_C25 is calculated. Here, the ATM flat volatility corresponds to the volatility of the ATM plain option described above. The input of each volatility market value may be performed from the input device 18, or
If the computing system is connected to a computer network, the input may be made via the computer network.

Next, in step 102, for the reverse knockout option to be evaluated, Vega V, Vega 2V _σ , and Banna V _{S determine} the ATM flat volatility σ _ATM from the framework of the GK model for the reverse knockout option. It is calculated according to the following equations (1) to (3) using the volatility σ.

(Equation 1)

Here, S is the spot rate of the currency that is the target of the evaluation target option. P is a premium expressed in the framework of the GK model for the reverse knockout option, T is the period from the spot delivery date to the option delivery date, t is the period from the option signing date to the option exercise date, S ₀ spot rates in the option valuation date, (yen interest rate in the case of, for example, sell the dollar in the circle or buy options) Against the interest rate that corresponds to the period T in the option valuation date r _d, the period in the option valuation date r _f T (Eg, the dollar interest rate in the case of an option to sell or buy a dollar in yen), and σ is the volatility (as described above, AT
Using M flat volatility σ _ATM , K as the option strike price, V as the knockout price, and N (·) as the cumulative probability density function of the standard normal distribution, expressed by the following equation (4) (put option call option) Are the same.)

(Equation 2)

However,

(Equation 3) It is.

Next, in step 104, using the market values of volatility σ _P25 and σ _C25 of the 25 delta put option and the 25 delta call option, the 25 delta put plain option and the 25 delta option having the same exercise period as the option to be evaluated are used. The strike price of the call plane option is calculated.

That is, the framework of the GK model for the call plane option and the put plane option is as follows (in the case of the call option)

(Equation 4) (For put option)

(Equation 5) However, as mentioned above,

(Equation 6) And the value of the volatility σ in these equations (5) and (6) is given, the equation showing that the delta is 25% for each of equations (5) and (6)

(Equation 7) Or

(Equation 8) Thus, the strike price K can be calculated.

Next, in step 106, using the ATM flat volatility σ _ATM , the 25 delta put plane option, the 25 delta call plane option, and the ATM plane option vega,
Vega 2 and banna are calculated according to the above equations (1) to (3). At this time, the above expressions (5) and (6) representing the framework of the GK model for the plain option are used as the premium P in the expressions (1) to (3).
Also, the exercise price of each of the plain options of 25 delta put and 25 delta call is calculated as the above step 104.
Using the value calculated in (1), the strike price with the same call put delta value is used as the strike price of the ATM plain option. Vega, Vega 2, and banna of each option are represented by the following symbols.

V _P25 : Vega of 25 Delta Put Plain Option V _{σ P25} : Vega of 25 Delta Put Plain Option V _SP25 : _{Vanna of} 25 Delta Put Plain Option V _ATM : Vega of ATM Plain Option V _σATM : ATM Plain Optional Vega 2 V _SATM : ATM Plane Option _Vanna V _C25 : 25 Delta Call Plane Option Vega V _σC25 : 25 Delta Call Plane Option Vega 2 V _SC25 : 25 Delta Call Plane Option _Vanna

Next, in step 108, Vega, Vega2, and Banna of the hedge portfolio created by combining the 25 Delta Put Plan option, the 25 Delta Call Plan option, and the ATM Plan option are respectively evaluated. optional Vega V, Vega 2V _sigma, and Banner V _s becomes equal such amount ratios hedge portfolio is calculated. Specifically, the hedging amount ratios of the 25 delta put plain option, the ATM plain option, and the 25 delta call plain option are represented by A _P25 , A _ATM , and A
_{When C25} is set, the hedging amount ratios A _P25 , A _ATM , and A _C25 satisfying the following equation (7) are calculated.

(Equation 9) That is,

(Equation 10) As a result, A _P25 , A _ATM , and A _C25 are calculated.

Next, in step 110, the 25 delta put plane option and the 25 delta call
For plain option, and the premium was calculated using the market value as volatility, the difference ζ _P25 between the premium calculated using the ATM flat volatility as volatility, ζ _C25 is calculated.

That is, ζ _P25 = (Premium calculated from the framework of the GK model using the market value of volatility for the 25 delta put plain option) − (GK model using the ATM flat volatility for the 25 delta put plain option) 25 _C25 = Premium calculated from the framework of the GK model using the market value of volatility for the 25 delta call plain option for the 25 delta call plain option)-(using ATM flat volatility for the 25 delta call plain option) Premiums calculated by the framework of the GK model), the differences _ζP25 and _ζC25 are calculated.

Next, in step 112, A _P25 and A _C25 calculated in step 108 and the above step 1
Using _ζP25 and _ζC25 calculated in step 10, a correction value に 対_{す る} for the evaluation target option is calculated according to the following equation (9). ζ = A _P25 · ζ _P25 + A _C25 · ζ _C25 (9) For the ATM plain option, the market value of the volatility itself is the ATM flat volatility, so the above differences 差_P25 and ζ _C25 correspond. The deviation ζ _ATM becomes zero. Therefore, the expression (9) indicates that the ATM
Deviation for plain option ζ Does not include _ATM .

Lastly, in step 114, using the ATM flat volatility for the option to be evaluated, the premium P ₀ calculated based on equation (4) which is the framework of the GK model for the reverse knockout option is added to the above step. 112 correction value zeta value P _v = P ₀ + ζ plus calculated calculated as a premium evaluation value of the evaluation object Optionally, this premium evaluation value P _V is output to the display device 20 or printer 22.

As described above, in the system of this embodiment,
Based on the ATM flat volatility and smile-related information available from the market, strike prices are calculated for three types of plain options (25 delta put plain options, 25 delta call plain options, and ATM plain options) and volatility The values of the risk parameters Vega, Vega 2 and Banna are calculated, and each risk parameter value of the portfolio composed of these three types of plain options is set equal to each risk parameter value of the option to be evaluated. The composition ratio of the portfolio is calculated.

That is, with regard to Vega, Vega 2 and Bangna, the portfolio equivalent to the option to be evaluated is 3
It consists of different types of plain options. And
For each plain option, based on the difference between the premium calculated from the ATM flat volatility and the premium calculated from the market value of the volatility, for the above portfolio, the difference between the premium calculated from the ATM flat volatility and the market value Is calculated. As described above, since the portfolio is equivalent to the valuated option with respect to Vega, Vega 2 and Bangna, the difference calculated for the portfolio is the difference between the premium calculated from the ATM flat volatility and the market value for the valuated option. Is considered to be close to the difference. Therefore, by adding this difference to the premium of the evaluation target option calculated from the ATM flat volatility, a premium value that closely approximates the market value can be obtained.

FIG. 5 shows, for some reverse knock output options and reverse knock out call options that are evaluation options, premiums traded on the market and premiums calculated by the present system (hereinafter referred to as the premium calculated by the present system). ) And premiums calculated from the framework of the GK model using ATM flat volatility as before (hereinafter referred to as previously calculated premiums). In FIG. 5, the transaction conclusion date,
Knockout price, exercise date, transaction amount, strike price, this system calculated value of premium, buy order value of premium presented in the market, sell order value of premium presented in the market, previously calculated value of premium, presented in the market The average value of the buy order value and the sell order value (hereinafter referred to as the premium market average value), the difference between the previously calculated premium value and the market average value, and the premium calculated by the system and the market average value Are shown. The value of each premium is shown as a percentage of the option for one dollar.

As can be seen from FIG. 5, among the 15 types of options exemplified, No. 3, No. 4, no. For twelve options except 14, the difference between the system calculated value and the market average is smaller than the previously calculated value, and the premium calculated by the system is closer to the market value. You can see that.

As described above, according to the system of the present embodiment, it is possible to calculate an accurate value suitable for the market situation for the premium of the reverse knockout option, which is difficult to accurately evaluate with the framework of the GK model. . In other words, since it is possible to obtain the appropriate market price of the premium for the reverse knockout option,
By using this system, it is possible to evaluate the appropriate price of the reverse knockout option.

In the above-described embodiment, the 25 delta plain option and the ATM plain option having high liquidity are used as the plain options which are the basis of the premium calculation. It is considered that a more accurate model can be constructed using other plane options such as the Delta plane option.

Further, in the above embodiment, Vega, Vega 2 and Bangna are used as risk parameters relating to volatility. However, other risk parameters may be defined and used.

Next, a second embodiment of the present invention will be described. In the knockout option, the possibility of the option disappearing increases as the spot rate approaches the knockout price, and the premium takes a value reflecting the possibility of the option disappearing. In the present embodiment, by further correcting the correction value の of the above embodiment based on the possibility of reaching the knockout price, even when the spot rate is close to the knockout price, the premium calculation value approximate to the market prevailing value is obtained. I am getting it. In the present embodiment, as an example, a case will be described in which the reverse knockout option and the OTM knockout option are options to be evaluated.

In the present embodiment, the calculation processing is executed in the system shown in FIG. 3 according to the flowchart shown in FIG. As shown in FIG. 6, in the present embodiment, steps 100 to 11 are performed similarly to the flowchart shown in FIG.
In step 2, a correction value ζ is calculated. At the same time, the Gap arrival rate R representing the possibility of reaching the knockout price is calculated (step 120), and the correction value ζ is corrected with the Gap arrival rate R (step 122). Ga in step 120
p reach rate R is the digital touch option (Digital To
uch Option) by calculating the premium evaluation value.

As shown in FIG. 7, the digital touch option means that a predetermined rebate amount Z can be received in the event that the spot market price is at least once (or below) the exercise price before the option exercise date. This is a possible option. For the digital touch option,
As shown in FIG. 7 (A), those that can receive the rebate amount Z above the strike price are called call options, and those that can receive the rebate amount Z below the strike price are put options. The premium of the digital touch option reflects the reachability of the spot rate to the strike price, and as shown by the broken line in FIG. 7, the closer the spot rate is to the strike price, the more the rebate amount Z
, And when the strike price is equal to or greater than or equal to the strike price, it matches the rebate amount Z. That is, since the premium per unit rebate amount of the digital touch option can be said to indicate the possibility of reaching the strike price, the Gap attainment rate is calculated using the premium of the digital touch option having the strike price equal to the knockout price of the evaluation target option. R can be obtained.

The frameworks of the GK model for the call and put digital touch options are:
The following equations (10) and (11) are used. (For call option)

[Equation 11] (For put option)

(Equation 12) However,

(Equation 13) It is.

As in the first embodiment, T is the period from the spot delivery date to the option delivery date, t is the period from the option signing date to the option exercise date,
S ₀ is the spot rate in the option valuation date, r _d is Against the interest rate that corresponds to the period T in the option valuation date, r _f is underline grayed interest rate corresponding to the period T in the option valuation date, σ the ATM flat volatility, N (•) is the cumulative probability density function of the standard normal distribution, and K is the option strike price, which is equal to the knockout price of the evaluation target option in the present embodiment as described above.

As described above, since the digital touch option of the call is such that the rebate Z can be received if the exercise price is equal to or more than the exercise price before the exercise date, the premium of the option where the rebate Z is “1” is Represents the possibility that the spot rate will be higher than the exercise price before the exercise date. Then, the reverse knockout option for the call or the OTM knockout option for the put disappears when the spot rate becomes equal to or higher than the knockout price. Therefore, when the option to be evaluated is the reverse knockout option of the call or the OTM knockout option of the put, the premium of the digital touch option of the call calculated by Expression (10) is set as the Gap arrival rate R.

On the other hand, the put digital touch option is such that if the exercise price falls below the strike price before the exercise date, the rebate Z can be received. Represents the possibility of falling below the strike price. And put reverse knockout option or call OTM
Knockout options disappear when the spot rate falls below the knockout price. Therefore,
When the option to be evaluated is the put reverse knockout option or the call OTM knockout option, the digital touch option of the put calculated by Expression (11) is defined as the Gap arrival rate R.

In calculating the premium of the digital touch option by the formulas (10) and (11), the evaluation target is defined as a period t from the date of concluding the option to the date of exercising the option and a period T from the date of spot delivery to the date of option delivery. A value equal to the option shall be used.

Step 12 of the flowchart shown in FIG.
In step 2, the correction value に よ り is corrected by ζ = ζ · (1−R) using the Gap arrival rate R calculated in this manner. In step 114, the premium P ₀ calculated based on the framework of the GK model is corrected. Then, a value obtained by adding the correction value の after the correction to the above is calculated as the premium evaluation value of the option to be evaluated.
That is, in the present embodiment, the correction value ζ and the second
The premium P ₀ is calculated using the Gap arrival rate R, which is the correction value of
Is corrected.

FIG. 8 shows reverse knockout and OTM.
With respect to the knockout option, a calculation example in the case where the spot rate is near the knockout price will be described. Specifically, knockout prices are 111.5 and 1
Spot rate 11 for 13.5 options
An example in the case of 2.5 is shown. In FIG. 8, in order from the left column, the knockout price, the remaining period up to the exercise date (number of months), the exercise price, the option type (reverse knockout option rko or OTM knockout option k)
o), put / call, premium calculated value according to the present embodiment, premium calculated value according to the first embodiment,
Premium buy order value presented in the market, premium sell order value presented in the market, previously calculated premium value, premium sell / buy market average value, and deviation from the market average value for each calculated value , The percentage (deviation rate) of each deviation width with respect to the market average value, and the off-market value for each calculated value. The off-market value is
If the calculated value is between the buy order value and the sell order value of the premium in the market, the value is defined to be 0, and if the calculated value is out of the range, the difference is defined as a percentage of the market average value.

FIG. 8 also shows the divergence width, the divergence rate, and the average value of the off-market value of each calculated value. As can be seen from this average value, the calculated value in the present embodiment has a smaller divergence width, divergence rate, and off-market value than any of the calculated value in the first embodiment and the previously calculated value, It can be seen that even when the spot rate is close to the knockout price, a premium evaluation value that closely approximates the market value is obtained.

In the above description, the case where the option to be evaluated is the reverse knockout option or the OTM knockout option has been described. However, the calculation method according to the present embodiment can be applied to various other barrier options such as knockin. is there.

[0059]

As described above, according to the present invention,
Using the volatility of plain options that can be easily obtained from the currency option market, premiums such as out-of-the-money plain options and reverse knockout options are also appropriate with the conventional ATM flat volatility method applied to the GK model framework. It is possible to calculate an appropriate value that is close to the market value, which has been difficult to evaluate.

Further, by considering the possibility that the spot rate will reach the barrier point for the barrier-related options, even when the spot rate is close to the barrier point, the actual market value reflecting the possibility of the disappearance of the option is obtained. An approximate premium value can be obtained.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining a 25 delta put plane option.

FIG. 2 is a diagram for explaining a 25 delta call plane option.

FIG. 3 is a configuration diagram of a premium calculation system according to an embodiment of the present invention.

FIG. 4 is a flowchart illustrating a process executed in the premium calculation system according to the embodiment.

FIG. 5 is a diagram showing a premium calculation result by the premium calculation system of the present embodiment in comparison with a calculation result by a conventional method.

FIG. 6 is a flowchart illustrating a process executed in a second embodiment of the present invention.

FIG. 7 is a diagram illustrating a digital touch option.

FIG. 8 shows a calculation result of a premium in the present embodiment.
FIG. 9 is a diagram showing a comparison between the first embodiment and a calculation result obtained by a conventional method.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 Central processing unit 12 Memory 14 Hard disk device 15 Recording medium 18 Input device 20 Display device 22 Printer

 ──────────────────────────────────────────────────続 き Continuation of the front page (54) [Title of Invention] A method for calculating a premium for a currency option, a premium calculation system for a currency option, a program for allowing a computer to calculate a premium for a currency option, and a record of the program. Recording medium

Claims (15)

[Claims] 1. A method for calculating a premium of a currency option with respect to a valuation object, comprising: a first step of obtaining ATM flat volatility and volatility smile-related information relating to volatility smile; A second step of storing the volatility smile-related information in a first storage means, and calculating a predetermined risk parameter relating to volatility for the option to be evaluated based on the ATM flat volatility stored in the first storage means. A third step of storing the calculation result in the second storage means, and a plurality of predetermined plain options having the same exercise date or exercise period as the evaluation target option, stored in the first storage means. ATM A strike price calculated on the basis of Tsu preparative volatility and volatility smile related information stored in said first storage means A
A fourth step of calculating the value of the predetermined risk parameter based on the TM flat volatility, and storing the calculated value in a third storage unit; and the predetermined plane stored in the third storage unit. The value of the predetermined risk parameter for the portfolio created by combining the predetermined plain options calculated based on the value of the risk parameter for the option is the evaluation target option stored in the second storage means. A fifth step of calculating a composition ratio of each of the plain options in the portfolio so as to be equal to the value of the predetermined risk parameter for the above, and storing the calculated value in fourth storage means; For each of the plain options,
A sixth step of calculating a premium reflecting market conditions based on ATM flat volatility and volatility smile related information stored in the first storage means; and for each of the plurality of predetermined plain options,
A seventh step of calculating a premium based on the ATM flat volatility stored in the first storage means, and for each of the plurality of predetermined plain options,
An eighth step of calculating a difference between the calculated value in the sixth step and the calculated value in the seventh step; a difference calculated in the eighth step; A ninth step of calculating a correction value relating to the premium of the option to be evaluated based on the portfolio composition ratio of each plain option stored in the storage means, and an ATM flat volatility stored in the first storage means. A tenth step of calculating the premium of the evaluation target option based on the correction value calculated by the correction value calculated in the ninth step, and calculating the correction result in the tenth step based on the evaluation target option. 1st output as premium evaluation value for
A method comprising the steps of: 2. The method of claim 1, wherein said third
And calculating the predetermined risk parameter in the fourth step and calculating the premium in the sixth, seventh and tenth steps by Garman = Korh
A method characterized in that the method is performed using a framework based on an algen model. 3. The method according to claim 1, wherein the plurality of predetermined plain options include a 25 delta put plain option, a 25 delta call plain option, and an ATM plain option. . 4. The method according to claim 1, wherein the predetermined risk parameter is Vega which is a first derivative by premium volatility and Vega 2 which is a second derivative by premium volatility. ,
And a banna which is a first derivative of the vega spot price. 5. The method according to claim 1, wherein the value of the predetermined risk parameter for the portfolio in the fifth step is determined by calculating a composition ratio of each plain option in the portfolio. A method of calculating a weighted sum of the values of the risk parameters for each of the plain options as weights. 6. The method according to claim 1, wherein in the ninth step, the correction value is obtained by weighting a composition ratio of each plain option in the portfolio. And calculating as a weighted sum of the differences. 7. The method according to claim 1, wherein an exercise price of the predetermined plain option is defined by a delta value, and in the fourth step, the predetermined plain option is determined. The exercise price of the plane option is calculated based on the market value of the volatility of the above and the delta value, and the predetermined plane is calculated based on the calculated exercise price and the ATM flat volatility stored in the first storage means. Calculating the predetermined risk parameter for an option. 8. The method according to claim 1, wherein the option to be evaluated is a barrier option in which the option disappears or occurs when the spot rate reaches a barrier point. A second correction value is calculated according to the possibility that the spot rate will reach the barrier point by the exercise date of the option to be evaluated, and in the tenth step, the premium calculation value based on the ATM flat volatility is corrected by the correction. A method comprising: correcting by a value and said second correction value. 9. The method of claim 8, wherein the second
Calculating the correction value of the digital touch option having a strike price equal to the barrier point of the evaluated option. 10. The method according to claim 1, wherein, in the ninth step, the option to be evaluated is:
If the option is a barrier option that disappears or occurs when the spot rate reaches the barrier point, the correction value is calculated based on the possibility that the spot rate will reach the barrier point by the exercise date of the option to be evaluated. A method characterized by calculating. 11. A method for calculating a premium of a currency option as an evaluation object, comprising: a first step of obtaining ATM flat volatility and volatility smile-related information relating to volatility smile; Calculating a predetermined risk parameter related to volatility for the evaluated option based on the determined ATM flat volatility; and for a plurality of predetermined plain options having the same exercise date or exercise period as the evaluated option, The strike price calculated based on the ATM flat volatility and the volatility smile related information stored in the first storage means, and the A stored in the first storage means.
A third step of calculating the value of the predetermined risk parameter based on TM flat volatility; and the predetermined step of calculating based on the value of the risk parameter for the predetermined plane option calculated in the third step. The value of the predetermined risk parameter for the portfolio created by combining the plain options is equal to the value of the predetermined risk parameter for the evaluation target option stored in the second storage means. A fourth step of calculating a composition ratio of each plain option in the portfolio; and for each of the plurality of predetermined plain options,
A fifth step of calculating a premium reflecting market conditions based on the ATM flat volatility and volatility smile related information input in the first step; and for each of the plurality of predetermined plain options,
A sixth step of calculating a premium based on the ATM flat volatility input in the first step, and for each of the plurality of predetermined plain options,
A seventh step for calculating a difference between the calculated value in the fifth step and the calculated value in the sixth step; a difference calculated in the seventh step; and a fourth step. An eighth step of calculating a correction value related to the premium of the option to be evaluated based on the portfolio composition ratio of each plain option calculated in step (b); A ninth step of calculating the premium of the option and correcting the calculated value with the correction value calculated in the eighth step; and calculating the correction result in the ninth step as a premium evaluation value of the option to be evaluated. The tenth to output as
The steps of: 12. A system for calculating a premium for a currency option as an evaluation object, comprising: an acquisition unit for acquiring volatility smile-related information on ATM flat volatility and volatility smile; and the acquired ATM flat volatility and volatility smile-related information. First storage means for storing a predetermined risk parameter relating to volatility for the evaluation target option based on the ATM flat volatility stored in the first storage means; and Second storage means for storing a value calculated by the first calculation means; and ATM flags stored in the first storage means for a plurality of predetermined plain options having the same exercise date or exercise period as the option to be evaluated. A strike price that is calculated based on the bets volatility and volatility smile related information stored in said first storage means A
A second calculating means for calculating the value of the predetermined risk parameter based on TM flat volatility; a third storing means for storing a value calculated by the second calculating means; and a third storing means. The value of the predetermined risk parameter for the portfolio created by combining the predetermined plain options, calculated based on the stored value of the risk parameter for the predetermined plain option, is stored in the second storage unit. Third calculating means for calculating a composition ratio of each plain option in the portfolio so as to be equal to the value of the predetermined risk parameter for the stored evaluation target option; and a value calculated by the third calculating means. Fourth storage means for storing a plurality of predetermined plain options. ,
Fourth calculating means for calculating a premium reflecting market conditions based on ATM flat volatility and volatility smile related information stored in the first storing means; and for each of the plurality of predetermined plain options,
A fifth calculating means for calculating a premium based on the ATM flat volatility stored in the first storing means, and for each of the plurality of predetermined plain options,
A sixth calculating means for calculating a difference between the value calculated by the fourth calculating means and the calculated value by the fifth calculating means; a difference calculated by the sixth calculating means; A seventh calculating means for calculating a correction value relating to the premium of the option to be evaluated based on the portfolio composition ratio of each plain option stored in the storing means of No. 4, and an ATM stored in the first storing means. Eighth calculating means for calculating a premium of the option to be evaluated based on flat volatility, and correcting the calculated value with a correction value calculated by the sixth calculating means; and a correction result by the eighth calculating means. And an output unit for outputting as a premium evaluation value. 13. The system according to claim 12, wherein, when the option to be evaluated is a barrier option that disappears or occurs when the spot rate reaches a barrier point, by the exercise date of the option to be evaluated. Means for calculating a second correction value according to the possibility that the spot rate reaches the barrier point, wherein the eighth calculation means calculates a premium calculation value based on the ATM flat volatility by the correction value and the second correction value. 2. A system wherein the correction is performed using the correction value of 2. 14. A program for causing a computer to execute the method according to claim 1. Description: 15. A recording medium on which the program according to claim 14 is recorded.