TWI502534B - A method, an electronic equipment and a readable medium of computers for static hedging american down-and-out call options - Google Patents

Description

Static hedging method for American lower limit failure type call right, electronic design using the method Ready and computer readable recording media

The present invention relates to a method for hedging a choice, an electronic device using the method, and a computer-readable recording medium; in particular, a static hedging method for an American lower limit failure type purchase right, an electronic device using the same, and Computer readable recording media.

Among the many new financial products (such as: futures, options, etc.) derived from the development of the capital market, the options are available for investors to leverage or hedge, and often become derivatives in the portfolio. financial product. In particular, the option is to have a rights contract between the buyer and the seller. When the buyer pays the premium, it can be on the contract expiration date (European Options) or any day before the expiration (American Options). , according to the agreed strike price (Strike Price) to buy (Call) or sell (Put) a certain number of agreed subject matter (such as stocks, precious metals or grains), and because the value of the option will be regarded as The subject matter fluctuates due to price changes during the agreed period. Therefore, the investor can profit from trading at the trading place via the spread between the strike price and the spot price (ie, Intrinsic Value).

Among them, due to the growing boom in the selection of commodity transactions, the Barrier Option, which is different from the Plain Vanilla Option, has been developed. The Trigger Price is stipulated outside the performance price of the option. Once the spot price of the subject matter touches the price of the card within the entitlement period, the contract of the barrier option will take effect immediately (commonly known as the effective barrier option, Knock -In Option), or terminate immediately (commonly known as Knock-Out Option), where the latter can be divided into Up-and-Out Option and Lower Limit-Failed depending on the failure requirements. Down-and-Out Option), if the spot price of the subject reaches an upper level price or a lower level price, the contract is terminated immediately (eg, buy or sell option). Therefore, investors can further reduce the investment risk through the Hedging strategy to increase the flexibility of the investment strategy when conducting investment operations. Moreover, before issuing the option, the brokers can first assess the issue risk to avoid Risk strategy.

Among them, when investors actually operate a combination of options, they often need to use a large amount of information to make investment strategies in a short period of time. Nowadays, solutions have been developed to obtain transaction information or hedging using computers and networks, such as: Republic of China Patent Announcement No. I364721 "Methods for predicting the price of goods subject to the right, electronic devices using them, and computer-readable record media" patent cases, or Republic of China Patent Notice No. I223172 "Common funds traded on the exchange or Patent case for other portfolio basket products. However, Patent No. I364721 can only predict the price for the above-mentioned standard option, but cannot be applied to more complicated obstacle selection rights (such as the US lower limit failure type call), and neither patent reveals the option. Safe haven strategy.

Moreover, although some scholars have studied the valuation methods of American failure-type obstacles, for example: "Boyle, PP, and YSTian. "Pricing Lookback and Barrier Options under the CEV Process." Journal of Financial and Quantitative Analysis, 34 ( 1999), pp.241-264, but the method described in this paper must frequently calculate the price of the US-type barrier-type option (Dynamic Hedging) as the underlying asset fluctuations or market interest rates change. Those of ordinary skill in the art can understand that as the number of times the price is repeatedly calculated, the option issuer or investor will increase the risk of mistakes and consume a lot of computing resources. Therefore, it is necessary to develop a failure barrier that can be applied to the US lower limit. A static hedging solution for type-of-calls, where option issuers and investors fully grasp the risks, costs and potential gains and losses, and avoid financial problems caused by undervalued risks.

The main object of the present invention is to provide a static hedging method for the US-type lower limit failure type call right, which can reduce the risk of required computing resources and errors without frequent operations.

A second object of the present invention is to provide a computer readable recording medium that can be completed when a computer is loaded into a computer program stored in the recording medium and executed.

Another object of the present invention is to provide an electronic device capable of loading a computer program stored in a computer readable recording medium to perform the above method.

The invention provides a static hedging method for an American type lower limit failure type purchase right, which is executed by a processor, and includes: setting a spot price, a strike price, a barrier price, a one-year risk-free interest rate, and a one-year spot. Volatility, a spot interest yield and a portfolio quantity, wherein the barrier price is less than the strike price; and based on the above spot price, strike price, barrier price, annualized risk-free rate, annualized spot volatility, spot interest The rate of return and the number of portfolios establish a static hedging portfolio of the above-mentioned US lower limit failure barriers, as shown in the following formula: Among them, SHP _{n is} the value of the static hedging portfolio; n is the number of the portfolio, and a period T can be divided into n+1 time points t _i according to the value of n (i=n-1, n-2, .. ., 0)~t _n , time t ₀ =0, time point t _n-1 =T-Δt, Δt=T/n, time point t _n =T; S _{0 is} the spot price; B ₀ ,..., B _{n -2} and B _{n -1} are the early performance boundaries of time points t ₀ ,..., t _n-2 , t _n-1 , respectively; w ₀ ,..., w _{n -2} , w _{n -1} are time points t ₀ Weights of European call rights for , ..., t _n-2 , t _n-1 ; ,..., , The weight value of the European selling rights for the time points t ₀ ,..., t _n-2 , t _{n -1} respectively; X is the performance price; H is the price of the obstacle; σ is the annualized spot volatility; r is the year The risk-free interest rate; q is the spot interest rate; C ^E (.) is the price of the European call, C ^E ( S , X , σ, r , q , τ) = Se ^{- q τ} N ( d ₁ ) - Xe ^{-r τ} N ( d ₂ ), P ^E (.) is the price of the European selling rights, P ^E ( S , X , σ, r , q , τ) = Xe ^{-r τ} N (- d ₂ )- Se ^{-q τ} N (- d ₁ ), where , , S is the spot price, τ is the expiration time, N(.) is the cumulative distribution function of the standard normal distribution, the above spot price, performance price, obstacle price, annualized risk-free interest rate, annualized spot volatility, spot interest The rate of return and the number of portfolios are defined by a failure boundary function, a value equivalence condition function and a smooth matching condition function. The failure boundary function, the value equivalence condition function and the smooth matching condition function are based on Newton's approximation method. The above-mentioned early performance boundary, the weight value of the European selling rights and the weight value of the European buying rights are solved to calculate the value of the above static safe investment portfolio.

Preferably, the failure boundary function is as follows:

Preferably, the value equivalence condition function is as follows:

Preferably, the smooth matching condition function is as follows: among them, For the difference in the European call, ( S , X , σ, r , q , τ)= e ^{-q τ} N ( d ₁ ), For the difference in the European selling rights, ( S , X , σ, r , q , τ) = -e ^{-q τ} N (- d ₁ ).

The invention further provides a computer readable recording medium, which stores a computer program, and can complete the above method when the computer loads the computer program and executes it.

The invention further provides an electronic device capable of loading a computer program stored in a computer readable recording medium for performing the above method.

〔this invention〕

1‧‧‧Electronic equipment

11‧‧‧ Processor

12‧‧‧Human Machine Interface

13‧‧‧Memory components

14‧‧‧Communication interface

S1‧‧‧Setting steps

S2‧‧‧ Estimation steps

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a system block diagram of an embodiment of a static hedging method for an American lower limit failure barrier type call of the present invention.

Figure 2 is a flow chart showing the operation of the embodiment of the static hedging method of the US-based lower limit failure type call of the present invention.

Figure 3 is a schematic diagram of the reverse procedure of the static hedging portfolio in which the US lower limit failure barrier type call is solved in the case where the barrier price is less than the strike price.

The above and other objects, features and advantages of the present invention will become more <RTIgt; American Down-and-Out Call (ADOC), one of the American Knock-Out Options, means that the buyer has the right to perform before the expiration date of the option contract. Call Option, and the buyer and the seller also agree on a lower limit price (Trigger Price). Once the spot price of the target touches the lower limit price within the right period, the contract of the purchase right is terminated immediately, which belongs to the technology of the present invention. Those with ordinary knowledge in the field can understand.

In the "Black-Scholes Model" as described in the full text of the present invention, the spot price of the indicator is a continuous logarithmic normal distribution, the price variation of the subject matter is fixed, and there is a risk-free name and a fixed value. The interest rate is understood by those of ordinary skill in the art to which the present invention pertains.

The "Static Hedge Portfolio" (SHP) as described in the full text of the present invention means that the hedging part of a financial product (eg, option, etc.) portfolio is no longer changed after it is established, and is held until maturity. It will be understood by those of ordinary skill in the art to which the present invention pertains.

The "Strike Price" as described in the full text of the present invention refers to the price at which the buyer of the option contract performs the selling right, which can be understood by those having ordinary knowledge in the technical field to which the present invention pertains.

The "barrier" as described throughout the present invention refers to the upper limit check price in the above-mentioned US lower limit failure type purchase right, which can be understood by those having ordinary knowledge in the technical field to which the present invention pertains.

The "European Call Options" as described in the full text of the present invention is one of the European Options, which means that the buyer has the right to demand the Call Option from the seller on the expiration date of the option contract. It will be understood by those of ordinary skill in the art to which the present invention pertains.

The "European Put Options" as described in the full text of the present invention is one of the European option rights, which means that the buyer has the right to request the seller to perform the sale option (Put Option) on the expiration date of the option contract, which belongs to the present invention. Those of ordinary skill in the art will understand.

Please refer to FIG. 1 , which is an American lower limit failure type call of the present invention. A system block diagram of an embodiment of a static hedging method. Wherein, an electronic device 1 can be used as an Execution Hardware to execute a computer software program to complete the static hedging method embodiment of the US lower limit failure type call. The electronic device 1 can be selected from devices including data output/input, storage, processing, and communication functions, such as a server, a notebook computer, an industrial computer, and a tablet computer. Tablet Computer), Smart Phone or Personal Digital Assistant (PDA), etc., but not limited to this. In this embodiment, the electronic device 1 includes a processor 11, a human interface 12, a memory component 13, and a communication interface 14. The processor 11 can be a microprocessor (MPU) or a digital signal processor ( DSP) or system single chip (SoC), etc., for executing the software program; the human interface 12 can be selected as a touch panel, a keyboard, a mouse or a handwriting tablet. And the human interface 12 is electrically connected to the processor 11 for the user to input data to the processor 11 or view the output of the processor 11; the memory component 13 can be selected as various memories. , the memory card (Memory Card), a hard disk (Hard-Disk), a compact disk (Compact-Disk) or a USB flash drive, etc., the memory component 13 is electrically connected to the processor 11 for storing the software program or its execution process Required information; the communication interface 14 can be selected as various wired transmitters or wireless communication transceivers, such as: USB, BlueTooth, GSM, 3G, 4G (LTE) and other communication protocol components, the communication interface 14 electrical connection The processor 11 is configured to communicate with the electronic device 1 and other devices.

Referring to FIG. 2, it is an operational flowchart of an embodiment of the static hedging method for the US-based lower limit failure type of the present invention, which includes a setting step S1 and an estimating step S2, respectively, as follows. Please refer to Figure 1 together.

The setting step S1 is to set a spot price, a strike price, a barrier price, a one-year risk-free interest rate, a one-year spot volatility, a spot interest rate, and a portfolio quantity, wherein the barrier price is less than The performance price. In detail, the user can input the spot price, the strike price, the obstacle price, the annualized risk-free rate, the annualized spot volatility, the spot interest rate, and the number of investment portfolios into the electronic device 1 to establish the lower limit of the US. American Down-and-Out Put (ADOC)'s static hedging portfolio and estimate its value. In this embodiment, the value of the US lower limit failure type call is estimated based on the Black-Scholes Model, and the subject matter of the sale is described by stock. And use the stock price as the spot price, but not limited to this; the spot price of the subject matter and the value of the above option will satisfy a partial differential equation (PDE), as shown in the following formula (1): Where σ is the annualized spot volatility; S is the spot price of the subject matter; F _ss is the second-order differential of the value function of the above option to the stock price; r is the annualized risk-free rate; q is the spot interest yield, and Set to a constant; F _s is a value function of the above-mentioned option weight to the stock price; F _t is the value function of the above-mentioned selling right to differentiate the time; F is the value of the above option. In addition, if the price of the obstacle is greater than or equal to the performance price, if there is “the spot interest rate is very high” or “the annualized risk-free rate and the performance price multiplied by the obstacle price, the quotient is less than the spot interest income. In the case of the rate, the US lower limit failure type call will be immediately executed, so it is not covered by the static hedging method of the present invention.

The estimating step S2 is based on the above-mentioned spot price, performance price, obstacle price, annualized risk-free interest rate, annualized spot volatility, spot interest rate of return and the number of investment portfolios to establish a static hedging of the above-mentioned US lower limit failure type call right. The portfolio can also estimate the value of the static hedge portfolio. In detail, the software program in the above electronic device 1 can establish the US lower limit failure obstacle type based on the above spot price, performance price, obstacle price, annualized risk-free interest rate, annualized spot volatility and spot interest rate. The right to hedge portfolio and estimate the value of the static hedge portfolio.

When the price of the above obstacle is less than the strike price, a portfolio quantity (ie, Static Hedge Portfolio, SHP) can be combined with two boundary conditions, one of which is the Knock-out boundary. The other is an early exercise boundary, which does not cross the barrier price (as shown in Figure 3). Wherein, the failure boundary means that when the quantity of the investment portfolio is 0, the obstacle price is equal to the performance price, and the early performance boundary condition can be defined as a value-matching and a smoothing-pasting. Condition, if the number of the portfolio is set to n, and the period T can be divided into n+1 time points t ₀ , t ₁ , . . . , t _n-1 , t _{n according to the value of n} , where the time point t ₀ =0 , time point t _n-1 = T - Δt, Δt = T / n, time point t _n = T.

In addition, in order to meet the above conditions, the static hedging portfolio may also be corresponding to an increase of 1 unit of European call options, the value of the new option must be within the failure boundary and early performance boundary of the next period. Zero, so as not to affect the result of the static hedging portfolio. For example, the static hedging portfolio can increase the w _{n -1} unit of European call rights at time t _n-1 and European put options of the unit, the European call right expires at the time point t _n =T and the strike price is equal to the early performance boundary B _{n -1} , the European sell right expires at the time point t _n =T and the strike price Equal to the barrier price. When the failure boundary condition is at the barrier price (ie, the spot price is equal to the barrier price), and the value equivalence condition and the smooth matching condition are at the early performance boundary (ie, the spot price is equal to the early performance boundary), The failure boundary function, the value equivalence condition function and the smooth matching condition function of the US lower limit failure barrier call can be estimated as shown in the following equations (2)~(4):

Where n is the number of the portfolio, and a period T can be divided into n+1 time points t ₀ , t ₁ , ..., t _n-1 , t _n according to the value of _n , time t ₀ =0, time point t _n-1 =T-Δt, Δt=T/n, time t _n =T; X is the performance price; H is the price of the obstacle; r is the annual risk-free interest rate; σ is the annualized spot volatility; for spot interest margin; B _{n -1} to time t _n-1 ahead of the compliance boundary; w _{n -1} at time t to the right of the right to sell the European weight value of _n-1; The weight of the European call for the time point t _n-1 ; C ^E (.) is the price of the European call, and P ^E (.) is the price of the European offer. and The difference between the European selling rights and the European buying rights (delta value) is based on the Blake-Hughes model, wherein the prices of the European and European selling rights are as shown in the following formulas (5a) and (5b), respectively. The difference between European call rights and European sell rights is shown in the following equations (5c) and (5d): C ^E ( S , X , σ, r , q , τ) = Se ^{-r τ} N ( d ₁ )- Xe ^{-r τ} N ( d ₂ ) (5a)

P ^E ( S , X , σ, r , q , τ) = Xe ^{-r τ} N (- d ₂ )- Se ^{-q τ} N (- d ₁ ) (5b)

Where S is the spot price; X is the performance price; σ is the annualized spot volatility; r is the annualized risk-free rate; q is the spot interest rate; τ is the expiration time; N(.) It is a cumulative distribution function of the standard normal distribution, which can be understood by those having ordinary knowledge in the technical field, and is not described here; d ₁ and d ₂ are respectively as follows (5e) and (5f):

Therefore, in order to understand the unknown variable w _{n -1 in} the above equations (2) to (4), And B _{n -1} , which can be solved by the above equations (3) and (4) to obtain w _{n -1} , The solution is a function of B _{n -1} , and then w _{n -1} , Substituting the above formula (2) to form a nonlinear function of B _{n -1} , and then obtaining the variable w _{n -1} by numerical solution, And the value of B _{n -1} , for example, is solved by the Newton-Raphson method, but not limited thereto.

And so on, when the time point t _i (i=n-1, n-2,..., 0), the static hedging portfolio can add the European call rights of the w _i unit and The European selling right of the unit, the European buying right expires at the time point t _i+1 and the performance price is equal to the early performance boundary B _i , the European selling right expires at the time point t _i+1 and the performance price is equal to the obstacle price H. In addition, the early-performance boundary of the time point t _i applies the knock-out boundary, value-matching, and smoothing-pasting conditions, similar to the above equations (2) to (4). .

Please refer to FIG. 3 , which is a schematic diagram of the reverse procedure of the static hedging investment portfolio of the present invention in which the US dollar lower limit failure type call right is solved in the case where the obstacle price is less than the performance price, wherein the static hedging investment portfolio is The failure boundary (dashed line as shown) and the early performance boundary (max(X, rX/q) curve as shown) match at n identical intervals. Therefore, w _{n -1} in the above formulas (2) to (4), , B _{n -1 is} changed to w _i , And B _i , to be all w _i , After the solution of B _{i is} solved, the value SHP _n of the US lower limit failure type call right of n static hedging portfolios at the time point of 0 (ie, the initial time) can be obtained, as shown in the following formula (6): Among them, SHP _{n is the value of} the US lower limit failure barrier type call; n is the number of the portfolio, and the period T is divided into n+1 time points t _i by the value of n (i=n-1, n-2,. ..,0)~t _n , time point t ₀ =0, time point t _n-1 =T-△t, △t=T/n, time point t _n =T; S ₀ is the spot price of time point t ₀ ; B ₀ ,..., B _{n -2} , B _{n -1} are the early performance boundaries of time points t ₀ ,..., t _n-2 , t _n-1 , respectively; w ₀ ,..., w _{n -2} , w _{n -1} respectively The weight value of the European call right for the time points t ₀ ,..., t _n-2 , t _n-1 ; ,..., , The weight value of the European selling rights for the time points t ₀ ,..., t _n-2 , t _n-1 respectively; X is the performance price; H is the price of the obstacle; σ is the annualized spot volatility; r is the year The risk-free interest rate; q is the spot interest rate; C ^E (.) is the price of the European seller, please refer to the above formula (5a); P ^E (.) is the price of the European seller, see above Formula (5b) is shown.

For example, if the number n of a one-year (T=1) US lower limit failure-type call is n, the relevant parameters are as follows: the spot price S ₀ =100 at the time point t ₀ (beginning), the performance The price X=100, the obstacle price H=90, the annual risk-free interest rate r=0.04, the spot interest rate q=0.04, the annualized spot volatility σ=0.2, and the conventional ternary tree method (the trinomial tree method) (taken from Ritchken, [1995]) performs 52,000 times/year as a standard inspection program, and the above parameters are evaluated by the standard inspection program as 6.237815. On the other hand, the present invention utilizes the above formula. (6) The value SHP _{i of} the American lower limit failure type purchase right can be obtained. As shown in the first list, the evaluation result (6.246) of the present invention is very close to the evaluation result of the standard inspection program (6.274), which proves the present invention. It has the effect of safe haven effect.

In addition, as can be seen from the above list 2, the present invention and the conventional Delta-Hedged are based on the Blake-Hughes model, and adopt the above parameters (S ₀ =100, X=100, H=110, r=0.04, q=0.04, σ =0.2), the safe-keeping performance of the invention using non-standard performance and standard performance is better than the conventional Delta-Hedged safe-haven combination, which proves that the invention has the effect of good risk-avoiding performance. Among them, the calculation method of each risk estimation factor can be found in "Siven, J., and R. Poulsen. "Auto-static for the People: Risk-Minimizing Hedges of Barrier Options." Review of Derivatives Research, 12 (2009), Pp.193-211." paper.

Further, as can be seen from the following Table 3, the present invention and the conventional Tree algorithm (Boyle, Tian, 1999) are based on the CEV model (β=4/3, X=45, H=40.5, r=0, q=0.0488, S). ₀ {40, 42.5, 45, 47.5, 50}, T {0.25, 0.5, 0.75, 1}, taking σ = 0.5 as an example) When evaluating 48 American lower limit failure type call rights (ADOC), the present invention only needs to calculate 24 o'clock when it is close to the evaluation result of the standard inspection program ( n=24), and the known Tree algorithm needs to calculate 200 hours (n=200), so the calculation times and calculation time of this case can be greatly reduced, which can achieve the effect of "significantly shortening the calculation time".

Embodiment of static avoidance method for American lower limit failure obstacle type call right of the present invention The program language (Program Language, such as C++, Java, etc.) can be used to compile a computer program product. The program code is written by the skilled person and can be understood. Alternatively, the computer program product may be stored in the computer-readable recording medium (eg, various types of memory, memory card, hard disk, optical disc or USB flash drive, etc.); and, by the above electronic device (eg: The method of the present invention can be implemented by a server, a notebook computer, an industrial computer, a tablet computer, a smart phone or a personal digital assistant, etc., and the electronic device can read a computer program product by using an external device or a built-in storage device. To perform the method of the invention.

The main features of the embodiment of the static hedging method for the US-based lower limit failure-type call of the present invention are as follows: First, the above-mentioned spot price, performance price, obstacle price, annualization are set via the above electronic device. Risk-free interest rate, annualized spot volatility and the number of portfolios, wherein the barrier price is less than the strike price (H<X); then, the electronic equipment is based on the above-mentioned spot price, strike price, barrier price, and annualized risk-free The interest rate, the annualized spot volatility and the number of portfolios establish a static hedging portfolio of the above-mentioned US lower limit failure barrier call, and estimate the value of the static hedge portfolio. The embodiment of the static hedging method for the US-based lower limit failure-type purchase right of the present invention can also be written into a computer program product, and can be stored in the computer-readable recording medium, or the computer can be read by the electronic device. Read the computer program product in the recording medium and execute it. Therefore, the present invention can effectively establish a static hedging investment portfolio of the US lower limit failure type call right, and estimate its value as a basis for the static hedging of the option. Compared with the conventional dynamic hedging method, the present invention can Reduce the number of estimates and time, and accurately estimate the value of the static hedge portfolio, reduce the risk of option issuance and investment, and achieve "good risk aversion", "high valuation accuracy" and "substantially shortened computing time" And other effects.

The embodiment of the static hedging method for the US-based lower limit failure-type call of the present invention can be written as a computer program product, or stored in the above-mentioned computer-readable recording medium, or can be read by the electronic device. Record and execute computer program products in the media, Therefore, it can achieve the effects of “helping users (such as option issuers, investors or investment consultants, etc.) to make the required decisions in a short period of time” and “reducing decision risks”.

While the invention has been described in connection with the preferred embodiments described above, it is not intended to limit the scope of the invention. The technical scope of the invention is protected, and therefore the scope of the invention is defined by the scope of the appended claims.

S1‧‧‧Setting steps

S2‧‧‧ Estimation steps

Claims (6)

A static hedging method for an American lower limit failure type call right, executed by a processor, comprising: setting a spot price, a strike price, a barrier price, a one-year risk-free interest rate, a one-year spot volatility, a spot interest rate and a portfolio quantity, wherein the price of the obstacle is less than the performance price; and based on the above spot price, performance price, barrier price, annualized risk-free rate, annualized spot volatility, spot interest rate and The number of portfolios establishes a static hedging portfolio of the above-mentioned US lower limit failure barriers, as shown in the following formula: Among them, SHP _{n is} the value of the static hedging portfolio; n is the number of the portfolio, and a period T can be divided into n+1 time points t _i according to the value of n (i=n-1, n-2, .. ., 0)~t _n , time t ₀ =0, time point t _n-1 =T-Δt, Δt=T/n, time point t _n =T; S _{0 is} the spot price; B ₀ ,..., B _{n -2} and B _{n -1} are the early performance boundaries of time points t ₀ ,..., t _n-2 , t _n-1 , respectively; w ₀ ,..., w _{n -2} , w _{n -1} are time points t ₀ Weights of European call rights for , ..., t _n-2 , t _n-1 ; ,..., , The weight value of the European selling rights for the time points t ₀ ,..., t _n-2 , t _n-1 respectively; X is the performance price; H is the price of the obstacle; σ is the annualized spot volatility; r is the year The risk-free interest rate; q is the spot interest rate; C ^E (.) is the price of the European call, C ^E ( S , X , σ, r , q , τ) = Se - ^{q τ} N ( d ₁ ) - Xe ^{-r τ} N ( d ₂ ), P ^E (.) is the price of the European selling rights, P ^E ( S , X , σ, r , q , τ) = Xe ^{-r τ} N (- d ₂ )- Se ^{-q τ} N (- d ₁ ), where , , S is the spot price, τ is the expiration time, N(.) is the cumulative distribution function of the standard normal distribution, the above spot price, performance price, obstacle price, annualized risk-free interest rate, annualized spot volatility, spot interest The rate of return and the number of portfolios are defined by a failure boundary function, a value equivalence condition function and a smooth matching condition function. The failure boundary function, the value equivalence condition function and the smooth matching condition function are based on Newton's approximation method. The above-mentioned early performance boundary, the weight value of the European selling rights and the weight value of the European buying rights are solved to calculate the value of the above static safe investment portfolio. According to the static hedging method of the US-type lower limit failure type call right described in Item 1 of the patent application scope, the failure boundary function is as follows: According to the static hedging method of the US-based lower limit failure type call right described in Item 1 of the patent application scope, the value equivalence condition function is as follows: According to the static hedging method of the US-based lower limit failure type call right described in the first item of the patent application scope, the smooth matching condition function is as follows: among them, For the difference in the European call, ( S , X , σ, r , q , τ)= e ^{- q τ} N ( d ₁ ), For the difference in the European selling rights, ( S , X , σ, r , q , τ)=- e ^{-q τ} N (- d ₁ ). A computer-readable recording medium storing a computer program capable of performing the method of any one of claims 1 to 4 when a computer is loaded into the computer program and executed. An electronic device is a computer program that can be loaded into a computer-readable recording medium for performing the method of any one of claims 1 to 4.