JP3504194B2 - Price risk assessment system and storage medium for financial products or their derivatives - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a system for evaluating the price distribution or risk distribution of financial products or their derivatives, and more particularly, more strictly including the probability of large price fluctuations by introducing the Boltzmann model. A financial system that evaluates the price distribution and risk value distribution of financial instruments and their derivatives, and applies the Boltzmann model to analyze price fluctuation events of financial instruments and its derivatives that could not be analyzed in the past. It relates to a price risk assessment system for products or their derivatives.

[0002]

2. Description of the Related Art A technique for analyzing the price fluctuation data of a financial product or a derivative product and probabilistically obtaining the price distribution or risk value distribution of the financial product or the derivative product is generally called financial engineering.

In conventional financial engineering, it is common to use the Wiener process when modeling stock price fluctuations. This Wiener process is one of the Markov stochastic processes that assumes that future states do not depend on past processes, and is used to represent the Brownian motion of molecules in the physical world. .

The Wiener process has a characteristic that the following equation holds between the minute changes Δt between Δt and Δt, where t is time and z is a variable dependent on the Wiener process.

[Equation 1]

Ε is a random sampling from the standard normal distribution.

As described above, in the Wiener process, the change occurring in the variable is evaluated based on the standard normal distribution.

In the conventional risk evaluation of financial products or derivative products, it is common to use the Ito process which is a further development of the above Wiener process.

The Ito process is based on the assumption that fluctuations in stock prices follow the Wiener process, and a drift term is added to this.
Furthermore, it introduces a parameter function of time and variables.

The evaluation formula for the price fluctuation of the stock price by the Ito process is as shown in Formula 1.

[Equation 2] Here, S is a stock price, r is a non-risk interest rate, σ is volatility (expected volatility), and W is a normal distribution with an expected value of 0 and a standard deviation of 1.

The simplest example of the Ito process is the geometric Brownian motion model of stock prices. In the geometric Brownian motion model, Equation 1 becomes Equation 2 below.

[Equation 3] It is known that not only is the feature of Equation 4 simple, but the price fluctuations of financial derivative products derived from financial products are also the same type (Ito's theorem), so the price fluctuation of any financial derivative product is easy. There is a point that can be evaluated. As a result, many financial derivatives have emerged.

[0011]

However, the above-described conventional risk evaluation method for financial products or derivatives thereof, or the evaluation system for executing the risk evaluation method cannot perform sufficiently reliable evaluation. .

This is because, in the conventional risk evaluation method for financial products and the like, since the price distribution of financial products and the like is evaluated based on the normal distribution as described above, the probability of a particularly large price fluctuation is underestimated. Because it was done.

Although such a large price fluctuation has a low probability of occurrence, it has a large effect on investment risk that cannot be compared with a normal price fluctuation. If you can't evaluate
It is not a reliable risk assessment system or method for financial products.

Therefore, one of the problems to be solved by the present invention is to develop a system that can accurately evaluate the price distribution and risk distribution of financial instruments or their derivatives by introducing a probability density function with higher accuracy than the normal distribution. To do.

Further, in the conventional risk evaluation method for financial instruments, a heterogeneous problem in which the probability density function used for evaluation changes depending on the price, or a nonlinear problem in which the probability density function is nonlinear, etc. However, we had to deal with it by making corrections based on experience or know-how. In this respect, the objective evaluation was insufficient.

[0016] Therefore, another object of the present invention is to provide a price risk evaluation system for a financial product or a derivative product thereof which can theoretically evaluate these non-homogeneous and nonlinear problems. .

Further, in the conventional risk evaluation method for financial instruments, the degree of freedom in describing, defining and evaluating variables of price fluctuation is not sufficient.

That is, conventionally, when the distribution of price fluctuations of financial instruments, etc. has a distribution other than the standard normal distribution, or when the price fluctuation rate is affected by the price fluctuation rate before the fluctuation, or the price fluctuation If there is a correlation between the probability that the price increases and the probability that the price decreases, or if there is a correlation between the price fluctuation rate and the price fluctuation direction, etc. Could not be described in. In addition, the probability distribution in the direction of price fluctuations of financial products could not be evaluated in connection with the inability to describe the probability density function in the direction of price fluctuations of financial products.

Therefore, another problem to be solved by the present invention is to introduce a probability density function for newly evaluating the price distribution and risk value distribution of financial instruments, etc. It is an object of the present invention to provide a price risk evaluation system for a financial product or a derivative product thereof, in which the definition, description method, and evaluation method of variables that could not be sufficiently expressed in the above are established.

Further, in the conventional risk evaluation method for financial instruments and the like, a numerical analysis method such as Monte Carlo method is used when it is executed, but the flexibility of the sampling method is low and the variance reduction cannot be achieved. It was

Therefore, another problem to be solved by the present invention is to introduce a probability density function for newly evaluating the price distribution and risk value distribution of financial instruments, etc. , By providing a sampling method that improves calculation efficiency, it is to provide a price risk evaluation system for financial products or their derivatives that can be calculated with high efficiency.

Further, the invention is intended to be applied to a parallel computer, and thereby to provide a price risk evaluation system for a financial product or a derivative product thereof that can be calculated with high efficiency as described above.

[0023]

A price risk evaluation system for a financial product or a derivative thereof according to claim 1 of the present invention is a financial product or a derivative thereof for evaluating a price distribution or a risk distribution of a financial product or a derivative thereof. In the price risk evaluation system, the initial value input means for inputting the initial value of at least one of the price, the price fluctuation rate, and the price fluctuation direction of the financial product or the derivative product to be evaluated, and at least the evaluation time and the number of trials Evaluation condition input means for inputting the evaluation conditions including, and the finance to be evaluated
Price, price change rate, price change of a product or its derivative products
Velocity distribution / direction distribution input procedure to input the probability distribution in the moving direction
And the random numbers used in the Boltzmann model analysis.
Boltzma by means of random number generating means and Monte Carlo method
Price simulation
Boltzmann model analysis for distribution or risk distribution
Means and an output means, and the Boltzmann model solution
Analysis means are sampling means and price fluctuation simulation
Means for calculating probability density and means for calculating the initial value.
Of financial instruments or their derivatives
At least one of price, price change rate, and price change direction
After inputting two initial values, the sampling means
The sampling width is determined by
The required price, price fluctuation rate, price fluctuation direction
Enter the probability distribution and enter the random numbers generated by the random number generator.
Enter and use the price fluctuation simulation means
The Tuman model is used to determine the immediately preceding price or price fluctuation rate.
Rui is the price after the sampling width from the price fluctuation direction
Is the price fluctuation rate or price fluctuation direction
Evaluation input by the evaluation condition inputting means
Repeated within the range of conditions, by the probability density calculation means
The price fluctuation simulation was simulated
Integrate the price or the price change rate or the price change direction
It is characterized in that the probability density is calculated by

A price risk evaluation system for a financial product or a derivative product according to claim 2 of the present application is the system according to claim 1, wherein the initial value input means is a corporate database storing information about the financial product or the derivative product. The price of the financial instrument or its derivative products to be evaluated,
The price fluctuation rate and the initial value of the price fluctuation direction are acquired and input to the Boltzmann model analysis means, and the velocity distribution / direction distribution input means obtains actual data on a predetermined financial product or a derivative product from the company database. It is characterized in that a probability density function having variables of price, price fluctuation rate, price fluctuation direction, and time of the financial product or a derivative product thereof is inputted and inputted to the Boltzmann model analysis means.

The price risk evaluation system for a financial product or a derivative product thereof according to claim 3 of the present application sets the sampling time width during the price fluctuation simulation for the Boltzmann model analysis means in the system of claim 1. Has a cross-sectional area / stochastic process input means for inputting information on the financial product or its derivative from a corporate database that stores information on financial products or derivative products. It is characterized in that the price fluctuation frequency and the price fluctuation rate of a product are acquired, and the value obtained by dividing the price fluctuation frequency by the price fluctuation rate is input to the total cross-sectional area in the Boltzmann equation.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 4 of the present application is the system according to claim 1, wherein the velocity distribution / direction distribution input means stores information about the financial product or derivative product. Acquiring actual data on a predetermined financial instrument or its derivative from a database, estimating the distribution of the price fluctuation rate of the financial instrument or its derivative from the actual data using a sigmoid function and its approximate form, and calculating the Boltzmann It is characterized in that it is inputted to the model analysis means.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 5 of the present application is the system according to claim 1, wherein the velocity distribution / direction distribution input means stores information about the financial product or derivative product. From the database, obtain actual data on a predetermined financial product or a derivative product thereof, determine the sigmoid function of the price change rate distribution after the price change using the price change rate before the price change as a parameter from the actual data, and calculate the Boltzmann model. It is characterized in that it is inputted to the analyzing means.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 6 of the present application is the system according to claim 1, wherein the velocity distribution / direction distribution input means stores information about the financial product or derivative product. Acquiring actual data on a predetermined financial product or its derivative from a database, estimating a probability distribution in the price fluctuation direction of the financial product or its derivative from the actual data, and inputting it to the Boltzmann model analysis means. It is a feature.

In the price risk evaluation system for a financial product or a derivative product thereof according to claim 7 of the present application, in the system of claim 6, the velocity distribution / direction distribution input means is a price fluctuation direction of the financial product or a derivative product thereof. When estimating the probability distribution of, the probability distribution in the price fluctuation direction is estimated by adding the correlation between the probability of price increase and the probability of price decrease.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 8 of the present application is the system according to claim 1, wherein the velocity distribution / direction distribution input means stores information about the financial product or derivative product. From the database, input the actual data on a predetermined financial product or its derivative products, generate a probability distribution by adding the correlation between the distribution of the price fluctuation rate of the financial product or its derivative products and the distribution in the price fluctuation direction, The data is input to the Boltzmann model analysis means.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 9 of the present application is the system of claim 1, wherein the velocity distribution / direction distribution input means is a velocity distribution or direction input to the Boltzmann model analysis means. Regarding the probability distribution of the distribution, a uniform probability distribution that does not depend on price or a non-homogeneous probability distribution that depends on price is generated and input to the Boltzmann model analysis means.

A price risk evaluation system for a financial product or a derivative thereof according to claim 10 of the present application is the system according to claim 1, wherein the Boltzmann model analyzing means has a probability that a cross section in a Boltzmann equation is a financial product or a derivative thereof. Calculate the price distribution or risk distribution of a financial instrument or its derivative using a linear Boltzmann model that does not depend on density or flux, or a nonlinear Boltzmann model whose cross section depends on the probability density or flux of a financial instrument or its derivative It is characterized by that.

A price risk evaluation system for a financial product or a derivative thereof according to claim 11 of the present application is the system according to claim 1, wherein the Boltzmann model analyzing means is a probability density function of the financial product or a derivative thereof and per unit time. It is characterized by finding the price distribution or risk distribution of a financial instrument or its derivative by using the product of the price fluctuation rate of and as the flux in the Boltzmann equation.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 12 of the present application is the system according to claim 1, wherein the Boltzmann model analysis means obtains a track obtained by using a flux of the financial product or a derivative product thereof. The feature is that the variance is reduced by evaluating the probability density at an arbitrary time from the estimated amount.

A price risk evaluation system for a financial product or a derivative product according to claim 13 of the present application is the system according to claim 1, wherein the Boltzmann model analysis means applies a point detector in a radiation transport Monte Carlo simulation to obtain a financial product. Alternatively, by using all or part of the price fluctuation event of the derivative product, by evaluating the probability of the price or risk value of the financial product or the derivative product in any minute price band or time zone,
It is characterized by reducing dispersion.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 14 of the present application is the system according to claim 1, wherein the Boltzmann model analysis means is
It is characterized in that the variance is reduced by obtaining the adjoint probability density or the adjoint flux in the adjoint Boltzmann equation of the price fluctuation of the financial instrument or its derivative, and weighting the sampling proportional to the adjoint probability density or the adjoint flux. It is a thing.

According to a fifteenth aspect of the present invention, in the price risk evaluation system for a financial product or a derivative product thereof, in the system according to the first aspect, the velocity distribution / direction distribution input means is:
When estimating the velocity distribution or direction distribution of an arbitrary financial product or its derivative products among a plurality of financial products or its derivative products, a probability distribution is generated by taking into account the correlation between the financial products or its derivative products, It is characterized in that it is inputted to the model analysis means.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 16 of the present application is the system of claim 1, wherein the Boltzmann model analysis means evaluates a price distribution or a risk value distribution of a predetermined financial product. Later, it is characterized by applying Ito's theorem to evaluate the price distribution or risk value distribution of derivative products of the financial product.

A price risk evaluation system for a financial product or a derivative product thereof according to claim 17 of the present application is the system of claim 1.
In the system, the Boltzmann model analysis means has a plurality of means for performing price fluctuation simulation by the Boltzmann model, and evaluates the probability density by aggregating each trial price fluctuation simulation.

The storage medium storing the program for evaluating the price risk of the financial product or its derivative according to claim 18 controls the computer, and the price and the price fluctuation rate of the financial product or its derivative to be evaluated. , An initial value input means for inputting an initial value of at least one of price fluctuation directions, an evaluation condition input means for inputting an evaluation condition including at least an evaluation time and the number of trials, and an evaluation target
Price, price volatility, price of financial instruments or their derivatives
Velocity distribution / direction distribution input
Force means and random numbers used in Boltzmann model analysis
Random number generating means and the Monte Carlo method
Performing price fluctuation simulation using the Tuman model
Boltzmann model for price or risk distribution
The Boltzmann model is provided with an analysis unit and an output unit.
The means for analyzing
And a probability density calculation means,
From the value input means, the financial product to be evaluated or its derivative
At least the product price, price change rate, or price change direction
Also, after inputting one initial value, the sampling means
Sampling width is determined by
Required price, price change rate, price change method from distribution input means
The random distribution generated by the random number generator.
Enter the number and use the price fluctuation simulation means
Previous price or price change using Boltzmann model
From the rate or the direction of price fluctuations, the price
Simulates price fluctuation rate or price fluctuation direction
Input by the evaluation condition input means.
Repeatedly within the range of the evaluation conditions, the probability density calculation means
More from the price fluctuation simulation
Product price or price change rate or price change direction
It stores a program for performing processing so as to calculate the probability density by dividing.

[0041]

BEST MODE FOR CARRYING OUT THE INVENTION Next, an embodiment of the "price risk evaluation system for financial products or derivatives thereof" according to the present invention will be described below with reference to the drawings attached to the application.

FIG. 1 shows the configuration of an embodiment of a price risk evaluation system for financial products and the like according to the present invention and the flow of processing between each component.

The price risk evaluation system 1 for financial products and the like according to the present embodiment includes a portfolio input means 2 and a price / price.
Variation rate / variation direction initial value input means 3, evaluation condition input means 4, Boltzmann model analysis means 5, and output means 6
It has a total cross section / stochastic process input means 7, a velocity distribution / direction distribution input means 8, a random number generation means 9, a VaR evaluation device 10, and a company database 11.

The Boltzmann model analysis unit 5 further includes an initialization unit 12, an initial value setting unit 13, a sampling unit 14, a Boltzmann model price fluctuation simulation unit 15, a probability density calculation unit 16, and a trial end determination. It has a means 17, an all trial end determination means 18, and a probability density editing means 19.

The alternate long and short dash line in FIG. 1 indicates the range included in the system of this embodiment. Corporate database 11
The fact that the VaR evaluation device 10 and the VaR evaluation device 10 straddle the line indicating the range of the present system indicates that the device can be connected by data communication as a device external to the present system.

The range surrounded by the one-dot chain line does not mean that the range is physically included in one computer. For example, when the system of the present invention performs distributed processing like a client server system, each of the above means can be appropriately distributed to the processing elements of the distributed processing system.

The portfolio input means 2 is means for inputting a portfolio and outputting a financial product or derivative product to be evaluated.

In normal asset management, the assets to be managed are allocated to a plurality of financial products or their derivative products to reduce risks and enable the most advantageous asset management as a whole. This combination of multiple financial products or their derivatives is called a portfolio. The portfolio input means 2 is a means for inputting a predetermined portfolio to cut out a financial product or derivative product to be evaluated from the relevant portfolio and output it.

Preferably, the portfolio input means 2
Has a table or database of portfolios inside so that the user can enter the identification code of the specified portfolio to indicate the composition of the portfolio and select the financial product or derivative product to be evaluated. To

The portfolio input means 2 is not an essential component of the present invention, and can be omitted if the data for evaluation of the financial product or derivative product to be evaluated is known.

The initial value input means 3 is means for inputting at least one initial value of the price, price change rate, or price change direction of the financial product or derivative product to be evaluated to the Boltzmann model analysis means 5.

The initial values of the price, fluctuation rate, and fluctuation direction of the financial product or derivative product to be evaluated are obtained from the actual data of the financial product or derivative product. Preferably initial value input means 3
Inputs the financial product or derivative product to be evaluated from the portfolio input means 2, searches the corporate database 11 for information about the financial product or derivative product, and based on the actual data of the searched financial product or derivative product, The price of the product or the derivative product, the price fluctuation rate, and the initial value in the price fluctuation direction are acquired and output to the Boltzmann model analysis unit 5.

The initial value input means 3 is an essential component of the price risk evaluation system 1 for financial products and the like.

The evaluation condition input means 4 is means for inputting the evaluation conditions of the Boltzmann model analysis means 5. The evaluation conditions of the Boltzmann model analysis means 5 are conditions for analysis of the number of trials by the Boltzmann model analysis means 5, the evaluation time zone, the evaluation price range, and the like. The evaluation condition input means 4 allows the Boltzmann model analysis means 5 to be set with an evaluation condition that enables significant analysis.

The evaluation condition input means 4 is also an essential component of the price risk evaluation system 1 for financial products in the sense of enabling significant analysis.

The Boltzmann model analysis means 5 is a central component of the price risk evaluation system 1 for financial products and the like.

The Boltzmann model analysis means 5 inputs the price, the price change rate, and the initial value of the price change direction of the financial product or the derivative product to be evaluated from the initial value input means 3,
By inputting the evaluation condition from the evaluation condition input means 4, the price fluctuation simulation by the Boltzmann model is repeated within the range of the evaluation condition by the Monte Carlo method for the financial product or the derivative product to be evaluated, and the price of the financial product or the derivative product. It is a means to obtain the distribution or risk distribution.

The Monte Carlo method is a numerical analysis method for obtaining an exact solution of the Boltzmann equation.

The initialization means 12 of the Boltzmann model analysis means 5 is means for initializing the price, price change rate, and price change direction of the financial product or derivative product to be evaluated when starting the evaluation.

The initial value setting means 13 of the Boltzmann model analysis means 5 sets the price, the price change rate, and the initial value of the price change direction of the financial product or derivative product to be evaluated based on the output of the initial value input means 3. Is a means to do.

The sampling means 14 of the Boltzmann model analyzing means 5 is means for determining the sampling width of the price fluctuation simulation. In the present invention, the sampling means 14 can set the fluctuation probability of the unit time of the price fluctuation by the input of the total cross section / stochastic process input means 7. Therefore, it is possible to omit the setting of the time grid for the price fluctuation simulation, which has been considered difficult in the past.
This will be described further below.

The price fluctuation simulation means 15 of the Boltzmann model analysis means 5 is means for simulating the next price from the immediately preceding price by the Monte Carlo method based on the probability distribution of the velocity distribution and the direction distribution.

The price fluctuation simulation means 15 uses the Borman model to simulate price fluctuations, and the price fluctuation rate of the financial product or the like corresponding to the speed distribution or the direction distribution of the variables in the Boltzmann equation is calculated from the speed distribution / direction distribution input means 8. , Enter the price fluctuation direction.

The price fluctuation simulation means 15 inputs the random number generated by the random number generation means 9 in order to obtain the solution of the Boltzmann equation by the Monte Carlo method.

The probability density calculation means 16 of the Boltzmann model analysis means 5 is the price fluctuation simulation means 15 described above.
Is a means for calculating the probability density by integrating the price distribution simulated by.

The one-trial end judging means 17 of the Boltzmann model analyzing means 5 is a means for judging whether one trial has ended.

Here, "one trial" is one price fluctuation simulation from the evaluation start time to the evaluation end time. The one trial end determination means 17 can determine whether one trial has ended by comparing the currently calculated time point with the evaluation time zone. The condition for ending one trial is input from the evaluation condition input means 4.

If one trial has not ended, the one trial end determination means 17 returns the processing to the sampling means 14 again, and the next price and probability density are calculated from the immediately preceding price and the velocity distribution / direction distribution.

The all trial end judging means 18 of the Boltzmann model analyzing means 5 is means for judging whether or not the total number of trials set by the evaluation condition inputting means 4 has been reached.

The total number of trials is input to the total trial end determination means 18 by the initial value input means 3.

The probability density editing means 19 of the Boltzmann model analysis means 5 aggregates the probability densities of all trials and edits the probability density of the price fluctuation of the financial product or derivative product to be evaluated, or as described later, Boltzmann. When there are a plurality of means for performing price fluctuation simulation by a model, it is means for editing the probability density of price fluctuations that each price fluctuation simulation means has tried.

The above is the internal components of the Boltzmann model analyzing means 5, but the specific processing of the Boltzmann model analyzing means 5 will be described later.

The output means 6 is means for outputting the processing result of this system. That is, the output means 6 outputs the price distribution of a predetermined financial product or the like obtained by this system, the risk value distribution, and the integrated risk value as a risk index.

The output means 6 can take the form of any known output means as long as it outputs the processing result in some form. For example, a printer for outputting on paper, a monitor for outputting as an image, a communication means for outputting to an external data file, etc. are all included in the output means 6.

Further, the output means 6 can output an intermediate result of the processing of the Boltzmann model analysis means 5, for example, a price fluctuation simulation by a certain trial, its probability density distribution and the like. In addition, the case of physically having a plurality of output means is included.

As described in relation to the sampling means 14 of the Boltzmann model analysis means 5, the total cross-section / stochastic process input means 7 gives the sampling means 14 a variation probability (variation frequency) in a unit time. ,
It is a means for setting the time width for sampling.

The total cross-sectional area / stochastic process input means 7 obtains the price fluctuation frequency and the price fluctuation rate of the financial product to be evaluated or its derivative product from the company database 11, and divides the price fluctuation frequency by the price fluctuation rate. Enter the result as the total cross section in the Boltzmann equation.

It will be described later that the total cross-sectional area in the Boltzmann equation corresponds to the price fluctuation frequency of financial products or derivative products.

The total cross section / stochastic process input means 7 is
This can be omitted when the sampling time grid is conventionally set instead of the price fluctuation frequency.

The speed distribution / direction distribution input means 8 is means for inputting the price fluctuation rate or the distribution in the price fluctuation direction to the price fluctuation simulation means 15, as described in relation to the price fluctuation simulation means 15.

The velocity distribution / direction distribution input means 8 inputs the actual result data of the financial product or the like to be evaluated from the company database 11, and inputs the price fluctuation rate or the price fluctuation direction from the actual data to the price fluctuation simulation means 15. .

The velocity distribution / direction distribution input means 8 is
It has a numerical analysis function itself and estimates the distribution of the price fluctuation rate from the actual data of financial instruments using the sigmoid function and its approximate form, or after the price fluctuation using the price fluctuation rate before the price fluctuation as a parameter. The sigmoid function of the price fluctuation rate distribution is determined, or the distribution in the price fluctuation direction is estimated by adding the correlation between the probability that the price increases and the probability that the price decreases, or the correlation between the price fluctuation rate and the price fluctuation direction is calculated. In consideration of this, the price fluctuation rate or the distribution in the price fluctuation direction is estimated, or when the price fluctuation rate or the distribution in the price fluctuation direction depends on the price, a probability distribution corresponding to the price is generated.

The random number generation means 9 is means for the Boltzmann model analysis means 5 to generate a random number for simulating the price fluctuation by the Monte Carlo method. The random number generated by the random number generation means 9 is input to the price fluctuation simulation means 15 as described above. The method of using the random number will be described later.

The velocity distribution / direction distribution input means 8 and the random number generation means 9 are essential components as long as the analysis by the Boltzmann model is performed.

The VaR evaluation device 10 is a device for calculating a risk value or a risk value distribution from the price distribution of a predetermined financial product or derivative product.

Conventionally, there is an apparatus for calculating the risk value or risk value distribution of a financial product or derivative product from the price distribution of the financial product or derivative product. V
As the aR evaluation device 10, the existing VaR evaluation device can be applied as it is.

That is, the probability density calculated by the Boltzmann model of the present invention is directly output to the VaR evaluation device 10 of the existing price risk evaluation system, and the existing VaR evaluation device 10 outputs the price distribution, the risk value distribution, and the index. The integrated risk value can be output.

The VaR evaluation device 10 is not an essential element of the present invention in the sense that any existing device can be used as the VaR evaluation device 10.

The corporate database 11 is a database that stores information about financial products or derivative products.

The term "database" used in this specification includes data systematically managed in the database, means for searching the data, and hardware for storing and managing them.

The corporate database 11 is an essential element for carrying out the present invention, but it is also possible to use an existing external database. If the corporate database 11 is an existing external database, a system using such a database is included in the invention, provided that it comprises the other components of the invention.

The above is the constituent means of the price risk evaluation system 1 for financial products and the like, which is an embodiment of the present invention. Of the above-mentioned constituent means, the means for performing data processing is preferably one in which the CPU of the computer activates a predetermined program and performs the respective processing under the control thereof.
Therefore, different processing means may be physically the same hardware. Further, among the above-mentioned constituent means, the input means may be an ordinary keyboard or pointing device, and when inputting from another data file by data communication, it means the data communication means.

Next, it is theoretical that the Boltzmann model introduced for the risk analysis of financial products by the present invention has a high degree of freedom and can correctly evaluate the probability distribution of price fluctuations of financial products. The background will be described below.

According to the present invention, the initial price, the price fluctuation rate distribution, the price fluctuation direction distribution, and the prediction target time of financial instruments or financial derivatives, which are parameters of the Boltzmann equation, are input, and the Boltzmann equation is solved by the Monte Carlo method to make a prediction. It outputs the distribution of time price and risk value.

First, for financial products and financial derivatives, the time transition of prices is described by the Boltzmann equation. The present invention applies, among the Boltzmann equations, the neutron transport Boltzmann equation that has a proven record in reactor design in the existing industry.

The equation that describes the macroscopic behavior of neutrons is the Boltzmann equation for neutron transport. A model that explains a phenomenon based on the Boltzmann equation is called a Boltzmann model.

[0097]

[Equation 4] Product, called the double differential cross section. These mean the neutron collision probability per unit length.

The macroscopic cross section is the atomic number density (unit: 1 / c
m ³ ) and the microscopic cross section. The microscopic cross section is determined by the nuclides that make up the reactor (eg, uranium, oxygen, hydrogen, etc.). The microscopic cross section is the effective cross section of the nucleus (unit: cm ² ). Then, the collision probability of one nucleus and one neutron is given. The name cross-section comes from the area of the nucleus.

Since a concept similar to the atomic number density has not been found in finance, it is impossible to distinguish between a macroscopic cross section and a microscopic cross section. Therefore, when the neutron transport Boltzmann equation is applied to finance, the macroscopic cross section and the microscopic cross section are integrated, and all are called cross sections. In the physical world, the double differential cross section corresponds to the velocity and angular distribution of neutrons emitted from the reaction of atomic nuclei.

It is impossible to exactly solve any Boltzmann equation in a deterministic way. This is because the cross section changes intricately in phase space. On the other hand, it is known that the Monte Carlo method can solve the Boltzmann equation without approximation.

[0101]

[Equation 5]

Flux expressions are very convenient for neutron transport problems. The flux representation gives many advantages to Monte Carlo simulations. Neutron transport Monte Carlo simulations are characterized by a rich and powerful dispersion reduction technique. These techniques can be introduced by the flux expression. However, explaining the financial Monte Carlo with the flux expression can cause a lot of confusion, so we will temporarily return to the conventional density expression.

[0103]

[Equation 6]

[0104]

[Equation 7] It can be seen that the total cross-sectional area (Equation.14) is inversely proportional to the square of volatility. Here, we can obtain the equivalence between the volatility of financial engineering and the total cross section of the Boltzmann model.

[0105]

[Equation 8]

In financial engineering, the concept equivalent to the double differential cross section of neutrons has not been defined yet. However, in order to apply the Boltzmann model, a double differential cross section must be defined. Here, the neutron cross section evaluation method is directly applied to evaluate the double differential cross section of the stock price.

The cross section can be evaluated from experimental data of nuclear physics and theoretical calculation. At present, there is no theory for evaluating the cross section of stock prices, so the double differential cross section is evaluated from experimental data. An example of the experimental data is a stock price published on newspapers or on the Internet.

As these evaluation methods, the distribution of the price fluctuation rate v per unit time is estimated from the actual price data by using the sigmoid function and its approximate form.

In the Boltzmann model, the velocity distribution term of the double differential cross section of the Boltzmann equation must be determined, but the sigmoid of the price fluctuation rate v after the price fluctuation with the price fluctuation rate v ′ before the fluctuation as a parameter. The velocity distribution term of the double differential cross section of the Boltzmann equation can be determined by determining the function.

In solving the Boltzmann equation, the directional distribution term of the double differential cross section of the Boltzmann equation can be determined from the probability data of the fluctuation direction of the financial instrument or its derivative product from the actual price data of the financial instrument or its derivative product. .

Further, when there is a correlation between the probability that the price increases and the probability that the price decreases in the price fluctuation direction of financial instruments, etc., when determining the direction distribution term of the double differential cross section of the Boltzmann equation, , Probability drift can be evaluated in detail by considering the correlation between the probability of price increase and the probability of price decrease.

When the price distribution of a financial instrument or the like has a symmetrical distribution with respect to the expected value and an asymmetrical distribution, the symmetrical distribution has a variable velocity distribution term and a directional distribution term of the double differential cross section. It can be realized by separating, and the asymmetric distribution can be realized by considering the correlation between the distribution of the price fluctuation rate and the probability of the fluctuation direction.

Further, according to the Boltzmann model, it can be applied both when the cross-sectional area, which is the basic parameter of the Boltzmann equation, does not depend on price (homogeneous problem) and when it depends on price (heterogeneous problem).

That is, the homogeneity problem can be dealt with by making the price fluctuation rate and the distribution in the price fluctuation direction constant regardless of the price x of the financial product or the like. Heterogeneous problems can be dealt with by assuming that the price fluctuation rate and the distribution in the price fluctuation direction change.

Therefore, it is difficult to realize a general model in which the volatility depends on the price, whereas in the Boltzmann model, the volatility is reduced by applying the Boltzmann equation to the homogeneous problem and the inhomogeneous problem. Both the case that does not depend on the price and the case that depends on the price can be described in a unified manner.

According to the Boltzmann model, by applying the Boltzmann equation to a linear problem or a non-linear problem, both a linear problem whose cross-sectional area does not depend on the probability density or flux of a financial instrument, or a dependent linear problem. Can handle.

Therefore, it has been difficult to realize a model in which the volatility depends on the price distribution, but according to the present invention, the volatility depends on the price distribution by applying the Boltzmann equation to a linear problem or a non-linear problem. It is possible to describe in a unified manner both when it does not and when it depends on the price distribution.

Further, according to the present invention, by introducing the product (flux) of the probability density function of the financial product or its derivative product and the price fluctuation rate per unit time, the variance reduction effective for improving the calculation efficiency is reduced. Can adopt the law.

By introducing the concept of flux,
It is possible to simulate price fluctuations of financial products and the like at arbitrary times. That is, similar to the track estimator in the neutron diffusion equation, the track length estimator that evaluates the price probability from these track lengths based on the flux of the financial product or its derivative products reduces the variance of the Boltzmann model analysis by the Monte Carlo method. Can be measured.

Further, by introducing the concept of flux and introducing the concept of the point detector in the neutron diffusion evaluation into the evaluation of the price fluctuation of the financial product or the derivative product, it is possible to reduce the variance of the Boltzmann model analysis by the Monte Carlo method. You can

That is, the event of price fluctuation cannot occur during random sampling using all or part of the event of price fluctuation of a financial instrument or its derivative, and
It is possible to reduce the variance of Boltzmann model analysis by the Monte Carlo method by evaluating the probability in the minute time zone and price zone that cannot pass through as flux.

Further, by introducing the concept of flux, finding the adjoint probability density and the adjoint flux of the price fluctuation of the financial instrument or its derivative from the adjoint Boltzmann equation, and weighting the adjoint probability density and the sampling proportional to the adjoint flux. Thus, it is possible to reduce the variance of Boltzmann model analysis by the Monte Carlo method.

The Boltzmann model can also be applied to a financial product that considers the correlation between a plurality of financial products or their derivatives.

Accordingly, when evaluating a portfolio that is a financial derivative product that is a combination of a plurality of financial products, it is possible to consider the correlation between a plurality of financial products or their derivative products. Connection with the evaluation system is possible.

In the field of financial engineering, Ito's theorem is known that, if a financial product follows the above-mentioned Ito process, its derivative products also follow the Ito process. This Ito theorem can also be applied to the Boltzmann model. Therefore, in the Boltzmann model, when evaluating the price or risk of a financial derivative, the price distribution of the derivative financial instrument can be propagated based on Ito's theorem. This can be reflected in the price and risk assessment systems developed so far, and as a result, connection with conventional assessment systems is possible.

Finally, since the Boltzmann model of the present invention performs price fluctuation simulation and accumulates probability distributions by individual simulations to obtain price distribution and risk value distribution, the price fluctuation simulation means 15 and probability density By parallelly processing the price fluctuation simulation of the financial product etc. by the calculation means 16,
The calculation speed can be improved.

The above is the theoretical background of introducing the Boltzmann model for risk analysis of financial products, etc. Next, an example of analysis of price distribution and risk value distribution of financial products by the Boltzmann model will be given. It will be specifically described.

FIG. 2 shows the flow of processing in the Boltzmann model analysis means 5 of the present invention.

As shown in FIG. 2, the Boltzmann model analyzing means 5 carries out the processes A to I.

Process A is a process for initializing the Boltzmann equation. This processing A is performed by the initialization means 12.

[0131]

[Equation 9]

Process C is a process for setting the sampling method. Here, it is assumed that there is a price change once a day. It should be noted that the case of sampling according to the frequency of price change based on the total cross section will be described later.

This processing C is performed by the sampling means 14.

Process D is a part for simulating price fluctuations by the Monte Carlo method.

[0135]

[Equation 10]

The above process E is performed by the probability density calculating means 16.

The process F determines whether or not one trial is completed. The process F is performed by the one trial end determination means 17. If one trial is not completed, the process is C
Return to.

Processes G and H determine whether all the trials have been completed, and if all the trials have not been completed, the process returns to B. The processes G and H are performed by the all trial end determination means 18.

Process I is a process for editing the obtained probability density, which is performed by the probability density editing means 19.

Although FIG. 2 has been sampled assuming that the probability change occurs once a day, FIG. 3 shows a case where the sampling time width is set according to the frequency of price change.

FIG. 3 is the same as FIG. 2 except for the processes C'and E '.

[0142]

[Equation 11] I am trying. The stochastic process and the total cross-sectional area in the above equation are input by the total cross-sectional area / stochastic process input means 7.

In process D of FIG. 3, price fluctuations are simulated in accordance with the above sampling method. This price fluctuation simulation itself is completely the same as the processing of the price fluctuation simulation D of FIG.

[0144]

[Equation 12]

FIGS. 4 and 5 schematically show simulations in a predetermined observation region corresponding to FIGS. 2 and 3, respectively. In particular, in FIG. 5, it can be seen that the price fluctuation can be simulated in a predetermined time width according to the price fluctuation frequency regardless of the time grid.

In the price fluctuation simulation by the Boltzmann model of the present invention, as a function representing time T, direction M, and speed V,

[Equation 13] x. As shown in FIG. 7, it can be seen that the evaluation results 25 and 26 reproduce both the theoretical value 23 when there is a drift and the theoretical value 24 when there is no drift.

Since the velocity distribution direction distribution in the above simulation is a probability distribution similar to the standard normal distribution, it has a probability density equivalent to the diffusion model.

In order to realize the Boltzmann model, the velocity distribution and the direction distribution must be evaluated.

Next, an example of evaluation of velocity distribution will be shown.

[Equation 14]

The spectrum shown in FIG. 8 is required to obtain the velocity distribution of the stock price. The spectrum has the density p (x,
v, μ; t) x, μ, and t are integrated and expressed by Equation 15.

[Equation 15]

Since these are indicated by two lines (a steep slope 30 and a gentle slope 31), it can be seen that these spectra are composed of two components. The convex curve in FIG. 8 has a Gaussian distribution 18 (normal distribution). The Gaussian distribution approximately reproduces steep lines, but extremely underestimates gently sloping lines.

The dependence of the spectrum on the incident velocity is investigated. The results are shown in Fig. 9. In Figure 9, the filled symbol 3
3, points 34, and unfilled symbols 35
Show velocity distributions for incident velocities of about 1%, about 2%, and about 3%, respectively. These distributions are standardized to one.

[0153]

[Equation 16] Here, an example is shown in which the price fluctuation rate distribution after the price fluctuation is determined by a sigmoid function using the price fluctuation rate before the fluctuation as a parameter. From FIGS. 9 to 11, it can be seen that the spectrum deviates in the higher direction according to the incident velocity v, so that the concept of temperature can be introduced. The distributions in FIGS. 9 to 11 can also be described by the Maxwell distribution.

Since FIGS. 9-11 suggest an exponential distribution, the evaporation spectrum used to describe the neutrons emitted in the nuclear reaction, Equation 20, is used.

[Equation 17] Next, an example of estimating the probability of a financial product or its derivative in the direction of fluctuation from the actual price data of the financial product or its derivative is shown.

In this problem, the directions take only 1 and −1. 1
Means an increase in price. And -1 means a decrease in price. In financial engineering, the directional distribution is given by Equation 22.

[Equation 18] The correlation between the probability that a price will increase and the probability that a price will decrease with respect to the probability of a financial instrument or its derivative moving in the direction of change is
It is shown in FIG. In Fig. 14, the probability that the price will continue to rise (filled square 36 in the figure) and the probability that the price will continue to fall (□ 37 in the figure) will change in the direction of repulsion with each other over time. means.

By considering the correlation shown in FIG. 14 in the angular distribution of the double differential cross section, more accurate stochastic drift can be evaluated.

Next, the evaluation by the price risk evaluation system of the financial product of the present invention or a derivative product thereof will be shown in comparison with the evaluation by the prior art.

FIG. 15 shows the result of the Boltzmann model using the evaluated velocity distribution and direction distribution. The thin solid line 40 in FIG. 15 is the evaluation result of the Boltzmann model, and the thick solid line 4
1 is performance data. It can be seen that the Boltzmann model can simulate a price jump (large fluctuation).

FIG. 16 is an enlarged view of FIG. The filled-in squares 42 represent the actual data. The actual data shows a price change (jump) 43 of about 10% per day everywhere.

Unfilled □ 44 and □ 45 are parts of the simulation example by the Boltzmann model. These show jumps 46 similar to the actual data. It is important to be able to simulate this price jump in terms of risk assessment of financial products.

On the other hand, the conventional diffusion model (see FIG.
+47) cannot reproduce such a sudden jump and can only simulate continuous price changes.

The log distribution of the stock price after 200 days was simulated. Results are shown in FIG. In this simulation, deterministic drift terms (eg non-risk interest rate) are not considered. The conventional diffusion model is shown by the solid curve 48 (expected value is 0 and standard deviation is 0.29) in FIG. The Boltzmann model results in a slight drift (filled square 49). This is a purely stochastic process. Corrected the drift

[Formula 19]

The features of the Boltzmann model are shown by the results of this example. That is, the Boltzmann model can be used to evaluate the probability and the stochastic drift of a portion where the price change is large, which was impossible in the conventional technique.

Next, the case where there is a correlation between the speed v (rate of price change) and the angle μ (direction of price change) will be described. In the above-described analysis example, with respect to the double differential cross section, the velocity v and the angle μ are variable-separated as shown in Expression 19 and are assumed to be independent.

However, in the Boltzmann model, the correlation between the velocity v and the angle μ can be considered by introducing a function that does not separate variables. In an example that does not consider these correlations,
Only the symmetrical distribution around the average value is evaluated. On the other hand, by considering the correlation between the distribution of the price volatility and the probability of the fluctuation direction, it is possible to introduce a function that does not separate variables and evaluate an asymmetric distribution.

Next, the inhomogeneity problem will be described.

[Equation 20] For example, the volatility smile is used to correct the price dependence of volatility. However, these techniques rely heavily on experience and know-how.

In the Boltzmann model, the price dependency of volatility can be systematically considered by applying the non-homogeneous equation (5).

Next, the case where the heterogeneity changes due to the change in the price distribution will be described. Since conventional financial engineering cannot theoretically handle heterogeneous problems, they are often treated as stochastic volatility. However, this probability volatility also depends heavily on know-how and experience, so it cannot be denied that it lacks objectivity.

In the Boltzmann model, the stochastic volatility can be accurately handled by the following non-linear Boltzmann equation, Equation 25.

[Equation 21]

This technique has been realized as the calculation of combustion of nuclear fuel in the case of neutrons. In the case of financial engineering, it is a systematic evaluation method of stochastic volatility.

Next, the evaluation at any time within the observation area will be described. In the density expression in Equation 9, for example, 199 days
It is not possible to evaluate the probability density for any one hour during the 200 day period. This is because the event of price fluctuation cannot be detected here.

[0172]

[Equation 22] You can ask for it correctly. This is a track length estimator.

Next, an evaluation method for a point where significant sampling cannot be performed will be described.

Although the track length estimator can be evaluated at any time, it cannot be evaluated because significant sampling cannot be carried out even if enormous sampling is carried out in a very small price range and time range. Is.

In such a case, the concept can be applied by applying the concept of a point detector for evaluating neutrons at one point in the phase space to an event such as a financial product.

The concept of the point detector in the neutron evaluation is to evaluate the probability of starting from the point A, colliding with the point B, and passing through the point C when the neutron at a certain point C is evaluated. That is, the probability of passing the point C is estimated based on the information of the scattering that does not pass the point C. In the simplest example, the distance between points B and C is r, and neutrons are between points B and C.

[Equation 23]

By introducing the concept of this point detector into the evaluation of financial products and the like, and using all or part of the price fluctuation event of the financial products or their derivatives, the price or risk value of the target minute observation area The distribution can be evaluated.

That is, although the event in the minute area in the target phase space is not actually caused by sampling, the route that causes the event is automatically investigated, so that the price fluctuation during the random sampling can be suppressed. It is possible to evaluate the probability in a minute time zone and price zone that an event cannot occur and cannot pass as a flux in a realistic calculation time. In this way, it is possible to reduce the variance by evaluating the probability of the minute area in which the price fluctuation event does not occur and cannot pass as the flux.

Next, the case of introducing the adjoint probability density or the adjoint flux in the Boltzmann model will be described.

The Boltzmann equation adjoint equation shown in equation 6, equation 27

[Equation 24]

Next, description will be made regarding the application when there is a correlation between financial products and the like. Conventionally, a plurality, for example 2
The valuation of two financial instruments and their derivatives, if they correlate,

[Equation 25]

In the present invention, regarding the application to the portfolio, the Boltzmann equations are made simultaneous for a plurality of products by the Boltzmann model, as in the prior art,

[Equation 26]

Next, the application of Ito theorem in the Boltzmann model of the present invention will be described.

[Equation 27]

Therefore, according to the Boltzmann model, the price distribution can be obtained arbitrarily regardless of the normal distribution. When the variance of the distribution evaluated by the Boltzmann model is proportional to the square root of time, even in the conventional price evaluation system designed based on Ito's theorem, the random number x is replaced by the distribution obtained by the Boltzmann model from the normal distribution. Thus, the same effect as when the Boltzmann model is strictly applied can be realized.

Although the price distribution based on the Boltzmann model is not a normal distribution in a strict sense, the distribution form in which the price is standardized to the standard deviation is constant regardless of time as shown in FIG. The filled square 51 in FIG. 18 is 20 days later, the filled triangle 52 is 60 days later, and the filled diamond 53 is 1
00 days, □ 54 is 120 days later, △ 55 is 160 days later,
◇ 56 shows the price distribution after 200 days. They are,

[Equation 28] Within, it matches the normal distribution 57. The standard deviation of this normal distribution is proportional to the square root of time. Therefore, it means that the standard deviation of the probability distribution by the Boltzmann model is proportional to the square root of time. This example simulates the distribution of the stock prices of 60 Japanese electric machine manufacturers. If the conventional system for evaluating the price or risk value of financial instruments derived from these stock prices is based on Ito's theorem, the effects of the Boltzmann model can be incorporated simply by replacing the normal distribution with that of the Boltzmann model. You can

Finally, application of the present invention to a parallel processing system will be described. The present invention uses the Monte Carlo method as the basis of the analysis method. The Monte Carlo method is widely recognized as a numerical analysis method that can be speeded up by parallel processing. Especially, the neutron transport Monte Carlo method has many achievements in terms of speeding up by parallel processing. Since the present invention uses the method of the neutron transport Monte Carlo method to realize the Boltzmann model, it is inevitable to achieve high speed by parallel processing.

In FIG. 19, each processing of processing blocks A to I is the same as each processing of FIGS. As shown in FIG. 19, in the parallel processing system, each of the price fluctuation simulations B to F is parallelized, and each trial is shared by a plurality of CPUs, so that speedup is realized according to the number of CPUs used for parallel processing. it can.

The description of the embodiment of the present invention is completed above, but the system for realizing the present invention has been described above. In an actual embodiment, a program for controlling a computer to perform the above-described processing is stored in a storage medium, the storage medium is transferred, etc., and the program is started by a predetermined computer system using the storage medium. , Which realizes a price risk evaluation system for the above financial products.

[0189]

As is apparent from the above description, according to the "price risk evaluation system for financial products or derivatives thereof" of the present invention, particularly in financial products, large price fluctuations occur compared to the normal distribution. It is possible to provide a system in which the probability can be accurately evaluated and the price distribution and risk distribution of financial products or their derivative products can be evaluated correctly.

Further, the “price risk evaluation system for financial products or derivatives thereof” according to the present invention is a heterogeneous problem in which the probability density function used for evaluation changes depending on the price, or the probability density function is non-linear. It is possible to objectively evaluate such a non-linear problem without relying on experience and know-how as in the past.

Further, the "price risk evaluation system for financial products or derivatives thereof" according to the present invention can flexibly express the probability distribution, and cannot be expressed by the conventional risk evaluation method for financial products. A distribution other than the distribution, or when the price fluctuation rate is affected by the price fluctuation rate before the fluctuation, or when there is a correlation between the probability that the price increases and the probability that the price decreases, Alternatively, it is possible to describe a case where there is a correlation between the price fluctuation rate and the price fluctuation direction.

Further, according to the "price risk evaluation system for financial products or derivatives thereof" of the present invention, it is possible to omit the time grid setting for price fluctuation simulation, which has been difficult in the past.

Further, the evaluation at an arbitrary time point within the observation region, which could not be sampled conventionally, can be evaluated by introducing a flux.

Further, according to the present invention, by introducing the concept of a point detector used in neutron evaluation, price fluctuation does not occur, and for a minute observation area where flux does not pass, A path that causes an event in a target area is automatically investigated from all or part of a price fluctuation event, and by doing so, an event in an arbitrary minute observation area can be evaluated and dispersion can be reduced.

According to the present invention, the concept of the adjoint probability density or the adjoint flux is introduced into financial engineering to give the phase space a weight proportional to the adjoint flux, thereby reducing the variance associated with the Monte Carlo method. be able to.

Further, according to the present invention, when there is a correlation in the price fluctuation probability distribution among a plurality of financial instruments, it is possible to evaluate the distribution in consideration of the correlation. Further, by applying Ito's theorem, it is possible to evaluate the price fluctuation probability distribution of the derivative product from the probability distribution of the price fluctuation of the financial product.

The "financial product or its derivative product price risk evaluation system" according to the present invention can be easily applied to a parallel computer, and the parallel processing makes it possible to process the price risk of financial products and the like with extremely high efficiency. An evaluation system can be provided.

Finally, the present invention introduces the Boltzmann model instead of the diffusion model which assumes the standard normal distribution. Therefore, existing financial engineering-related systems such as risk value evaluation and portfolio analysis can be used and easily incorporated into a part of them. As a result, not only the conventional hardware assets but also various kinds of information obtained by the analysis can be used as they are, and an efficient price risk evaluation system for financial products or derivatives thereof can be obtained.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration and processing flow of a price risk evaluation system for financial products and the like according to the present invention.

FIG. 2 is a flowchart showing the flow of processing in the Boltzmann model analysis means of the present invention.

FIG. 3 is another flowchart showing the flow of processing in the Boltzmann model analysis means of the present invention in which the price fluctuation frequency is introduced.

FIG. 4 is a diagram schematically showing the behavior in the observation region in the evaluation of FIG.

5 is a diagram schematically showing the behavior in the observation region in the evaluation of FIG.

FIG. 6 is a graph showing a probability distribution simulating a diffusion model using the Boltzmann model of the present invention.

FIG. 7 is a graph showing price fluctuations simulating a diffusion model using the Boltzmann model of the present invention.

FIG. 8 is a graph showing a spectrum relating to the price fluctuation rate v.

FIG. 9 is a graph showing the dependence of the spectrum on the incident velocity v ′.

FIG. 10 is a graph showing the dependency of the price increase component of the spectrum on the incident velocity v ′.

FIG. 11 is a graph showing the dependence of the price falling component of the spectrum on the incident velocity v ′.

FIG. 12 is a diagram showing application of an evaporation spectrum.

FIG. 13 is a graph showing an empirical expression for the velocity term of the differential cross section.

FIG. 14 is a graph showing the average of the probability that the price will continue to rise and the probability that the price will continue to fall every 5 days.

FIG. 15 is a graph showing stock price fluctuation simulation results by the Boltzmann model.

FIG. 16 is an enlarged graph showing a stock price fluctuation simulation result by the Boltzmann model.

FIG. 17: 200 obtained by the Boltzmann model
A graph showing the stock price distribution after day.

FIG. 18 is a graph showing a stock price distribution every 20 days according to the Boltzmann model.

FIG. 19 is a configuration diagram of a price risk evaluation system for a financial product or a derivative product of the present invention which is a parallel processing system.

[Explanation of symbols]

1 Price risk evaluation system for financial products 2 Portfolio input means 3 Initial value input means 4 Evaluation condition input means 5 Boltzmann model analysis means 6 Output means 7 Total cross section / stochastic process input means 8 Velocity distribution / direction distribution input means 9 Random number generation means 10 VaR evaluation device 11 Corporate Database 12 Initialization means 13 Initial value setting means 14 Sampling means 15 Price fluctuation simulation means 16 Probability density calculation means 17 One trial end judging means 18 All trial end judgment means 19 Probability density editing means

─────────────────────────────────────────────────── ─── Continuation of the front page (56) References Hiroshi Kobayashi et al., Extension of SA method and application to investment problems including time series prediction, Research report of Information Processing Society of Japan, Japan, Information Processing Society of Japan , January 17, 1996, Vol. 96 No. 4, p37-42 (58) Fields investigated (Int.Cl. ⁷ , DB name) G06F 17/60 204 G06F 19/00 110

Claims (18)

(57) [Claims] 1. A price risk evaluation system for a financial product or a derivative thereof for evaluating the price distribution or risk distribution of a financial product or a derivative thereof, and the price of the financial product or the derivative product to be evaluated,
Initial value input means for inputting an initial value of at least one of price fluctuation rate and price fluctuation direction, evaluation condition input means for inputting evaluation conditions including at least evaluation time and number of trials, and a financial product to be evaluated or its Price of derivative products, price
Velocity distribution that inputs volatility and probability distribution in the direction of price fluctuation
Generates random numbers used in Boltzmann model analysis with direction distribution input means
Price fluctuation by Boltzmann model by random number generation means and Monte Carlo method
Price distribution or risk distribution by simulation
Boltzmann model analysis means for obtaining the value and output means, wherein the Boltzmann model analysis means is sampling means.
, Price fluctuation simulation means, probability density calculator
And a financial quotient to be evaluated from the initial value input means.
Price of products or their derivatives, price fluctuation rate, price fluctuation
After entering an initial value for at least one of the directions,
Determine the sampling width by the sampling means
However, the price required from the velocity distribution / direction distribution input means,
Enter the price change rate and the probability distribution
Enter the random number generated by the number
Immediately before using Boltzmann model
Price, price change rate, or price change direction
Price after price range or price fluctuation rate or price
Simulate the direction of fluctuation
Repeatedly within the range of evaluation conditions entered by force means,
The price fluctuation simulation is performed by the probability density calculation means.
Price or price fluctuation rate
A price risk evaluation system for financial products or derivatives thereof that integrates price fluctuation directions to calculate probability density . 2. The initial value input means uses a company database that stores information about financial products or derivative products to calculate the price of the financial product or the derivative product to be evaluated,
The price fluctuation rate and the initial value of the price fluctuation direction are acquired and input to the Boltzmann model analysis means, and the velocity distribution / direction distribution input means obtains actual data on a predetermined financial product or a derivative product from the company database. 2. The Boltzmann model analyzing means is inputted, generates a probability density function having a price, a price change rate, a price change direction, and a time of the financial product or a derivative product thereof as variables, and inputs the probability density function to the Boltzmann model analysis means. Price risk assessment system for the listed financial products or their derivatives. 3. A total cross section / stochastic process input means for inputting information for setting a sampling time width during price fluctuation simulation to the Boltzmann model analyzing means, wherein the total cross section / stochastic process is included. The input means obtains the price fluctuation frequency and the price fluctuation rate of the financial product to be evaluated or its derivative products from the corporate database that stores information about financial products or derivative products, and divides the frequency fluctuation frequency by the price fluctuation rate. 2. The price risk evaluation system for a financial product or a derivative product thereof according to claim 1, wherein is input to the total cross-sectional area in the Boltzmann equation. 4. The velocity distribution / direction distribution input means obtains performance data regarding a predetermined financial product or a derivative product from a corporate database that stores information regarding financial products or derivative products, and the financial data is obtained from the performance data. The distribution of the price fluctuation rate of a product or its derivative product is estimated by using a sigmoid function and its approximate form, and is input to the Boltzmann model analysis means.
Price risk assessment system for the listed financial products or their derivatives. 5. The velocity distribution / direction distribution input means obtains performance data regarding a predetermined financial product or a derivative product from a corporate database that stores information about financial products or derivative products, and price fluctuations from the performance data. The price risk of the financial product or its derivative product according to claim 1, wherein a sigmoid function of the price volatility distribution after price fluctuation is determined using the previous price volatility as a parameter and is input to the Boltzmann model analysis means. Evaluation system. 6. The velocity distribution / direction distribution input means obtains performance data regarding a predetermined financial product or a derivative product from a corporate database that stores information about financial products or derivative products, and the financial data is obtained from the performance data. The price risk evaluation system for a financial product or a derivative product thereof according to claim 1, wherein a probability distribution in the price fluctuation direction of the product or a derivative product thereof is estimated and input to the Boltzmann model analysis means. 7. When the velocity distribution / direction distribution input means estimates a probability distribution in the price fluctuation direction of the financial product or its derivative product, the correlation between the probability of price increase and the probability of price decrease is taken into consideration. 7. The price risk evaluation system for a financial product or a derivative product thereof according to claim 6, wherein the probability distribution in the price fluctuation direction is estimated. 8. The velocity distribution / direction distribution input means inputs performance data on a predetermined financial product or a derivative product from a corporate database that stores information about the financial product or a derivative product, and inputs the financial product or the derivative product. The financial product according to claim 1, or a derivative thereof, wherein a probability distribution is generated by taking into account the correlation between the distribution of the price fluctuation rate of the product and the distribution in the price fluctuation direction, and the probability distribution is input to the Boltzmann model analysis means. Product price risk assessment system. 9. The velocity distribution / direction distribution input means relates to the probability distribution of the velocity distribution or direction distribution input to the Boltzmann model analysis means, and is a price-independent homogeneous probability distribution or a price-dependent inhomogeneous probability distribution. The price risk evaluation system for a financial product or a derivative product thereof according to claim 1, wherein the financial product or a derivative product thereof is generated and input to the Boltzmann model analysis means. 10. The Boltzmann model analysis means is a linear Boltzmann model in which the cross-sectional area in the Boltzmann equation does not depend on the probability density or flux of a financial product or its derivative, or the cross-section is the probability of a financial product or its derivative. The price risk evaluation system for a financial product or a derivative thereof according to claim 1, wherein the price distribution or risk distribution of the financial product or a derivative thereof is obtained by using a non-linear Boltzmann model depending on density or flux. 11. The Boltzmann model analysis means uses the product of the probability density function of a financial instrument or its derivative and the price fluctuation rate per unit time as a flux in the Boltzmann equation, and the price distribution of the financial instrument or its derivative. Alternatively, a price risk evaluation system for a financial product or a derivative product thereof according to claim 1, wherein a risk distribution is obtained. 12. The Boltzmann model analysis means reduces dispersion by evaluating a probability density at an arbitrary time from a track estimation amount obtained by using a flux of a financial product or a derivative product thereof. Claim 1
Price risk assessment system for the listed financial products or their derivatives. 13. The Boltzmann model analysis means applies a point detector in a radiation transport Monte Carlo simulation, and uses all or part of a price fluctuation event of a financial product or a derivative product thereof to detect a financial product or a derivative product thereof. The price risk evaluation system for a financial product or a derivative product thereof according to claim 1, wherein variance is reduced by evaluating the probability of the price or risk value in an arbitrary minute price band or time band. 14. The Boltzmann model analysis means obtains the adjoint probability density or the adjoint flux in the adjoint Boltzmann equation of the price fluctuation of the financial instrument or its derivative, and weights the adjoint probability density or the sampling proportional to the adjoint flux. The price risk evaluation system for a financial product or a derivative product thereof according to claim 1, wherein the variance is reduced. 15. The velocity distribution / direction distribution input means, when estimating the velocity distribution or direction distribution of an arbitrary financial product or its derivative products among a plurality of financial products or its derivative products, the financial product or its derivative products. The price risk evaluation system for a financial product or a derivative product thereof according to claim 1, wherein a probability distribution is generated in consideration of a correlation between them and is input to the Boltzmann model analysis means. 16. The Boltzmann model analysis means evaluates the price distribution or risk value distribution of a predetermined financial instrument, and then applies Ito's theorem to evaluate the price distribution or risk value distribution of a derivative product of the financial instrument. The price risk evaluation system for a financial product or a derivative product thereof according to claim 1. 17. The Boltzmann model analyzing means according to claim 1, characterized in that a plurality of means for performing the price fluctuation simulation by Boltzmann model to evaluate the probability density by aggregating the price fluctuations simulation trials
Price risk assessment system for financial instruments or derivatives thereof described in . 18. The price of a financial product or a derivative product to be evaluated, which is controlled by a computer,
Initial value input means for inputting an initial value of at least one of price fluctuation rate and price fluctuation direction, evaluation condition input means for inputting evaluation conditions including at least evaluation time and number of trials, and a financial product to be evaluated or its Price of derivative products, price
Velocity distribution that inputs volatility and probability distribution in the direction of price fluctuation
Generates random numbers used in Boltzmann model analysis with direction distribution input means
Price fluctuation by Boltzmann model by random number generation means and Monte Carlo method
Price distribution or risk distribution by simulation
Boltzmann model analysis means for obtaining the value and output means, wherein the Boltzmann model analysis means is sampling means.
, Price fluctuation simulation means, probability density calculator
And a financial quotient to be evaluated from the initial value input means.
Price of products or their derivatives, price fluctuation rate, price fluctuation
After entering an initial value for at least one of the directions,
Determine the sampling width by the sampling means
However, the price required from the velocity distribution / direction distribution input means,
Enter the price change rate and the probability distribution
Enter the random number generated by the number
Immediately before using Boltzmann model
Price, price change rate, or price change direction
Price after price range or price fluctuation rate or price
Simulate the direction of fluctuation
Repeatedly within the range of evaluation conditions entered by force means,
The price fluctuation simulation is performed by the probability density calculation means.
Price or price fluctuation rate
Integrate the price fluctuation direction to calculate the probability density
Storage medium storing a program which occupies perform processing.