JP2002032564A - Dealing system and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a dealing system 100 which has a Boltzmann model calculation engine 103 applying the nuclear reactor logic to an financial field and can flexibly supply the logical prices and risk indexes which are significant to the dealers or traders via an interactive screen interface 105 of a computer system on an option market that is adaptive to large price fluctuation of the original assets as that the inactive transactions. SOLUTION: In this dealing system 100, the calculation engine 103 of financial engineering is applied to an option price evaluation method, and the features of Leptokurcity and Fat-Tail are expressed in linear Boltzmann equations for defining the probability measure that is unique with neutral risk. As a result, the unique option price can be evaluated with neutral risk under consideration of Leptokurcity and Fat-tail of price fluctuation distribution.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a dealing system in the financial field and a computer-readable recording medium on which a dealing program is recorded.

[0002]

2. Description of the Related Art In a dealing system that supports the operations of dealers and traders in banks and securities companies, it has been conventionally assumed that a probability distribution at an arbitrary future time such as a stock price is assumed to be normal.
Sholes Model (Black, F. & M. Sholes, "The Prici
ng of Options and Corporate Liabilities ”, Journal
of Political Economy, 81 (May-June 1973), pp. 637
-59) Calculate the theoretical price of financial products or derivatives (hereinafter referred to as options) based on general theories such as -59) and extended models, and simulate risk assessment and position changes. Is common.

[0003]

However, the conventional method has the following problems.

(1) So-called Fat-Tail
Problems (eg Alan Greenspan, “Financial derivati
ves ”, March 19, 1999; http: //www.federalreserve.g
ov / boarddocs / speeches / 1999 / 19990319.htm) is serious in the financial sector. Conventionally, the assumption of normality, which is the premise of models that have been widely used, is based on the theoretical development of financial engineering and its implementation in computer systems when calculating the theoretical price of financial products or options, or simulating risk assessments and position changes. Is simply realized.
However, once a non-normality closer to the real financial market behavior is introduced, such as when there are large price fluctuations or when transactions are not very active, such theoretical development and implementation in a computer system are actually difficult. For this reason, dealers often have to rely on their experiences and intuitions for dealings. In dealing with such transactions, it is important for dealers to accurately grasp the volatility of the market.

(2) Among the volatility, there is a so-called historical volatility. this is,
Volatility based on certain past price movements. A general method of calculating this historical volatility is to regard the standard deviation of asset returns, that is, the past price movement of the closing price as asset returns, and obtain these standard deviations. On the other hand, there is also a well-known method of estimating from daily highs and lows, called the extreme value method, and a method of estimating considering the discontinuity of time in actual trading, called the modified Parkinson method. .

[0006] In applying these methods, when the trading is not active, not only is the price movement of the underlying asset itself not continuous, but also when the closing price is used, the settlement time varies. Calculation flaws are revealed.

[0007] On the other hand, even if the trading is active, these methods naturally assume normality as the market behavior distribution, so that there is naturally a limit in estimating taking into account large price fluctuations. Often used as a guide.

(3) In the option market, implied volatility (Implied Volatility: IV) is known in addition to historical volatility. This implied volatility is the volatility calculated backward from the option price observed in the market, and is often used as a material when calculating the theoretical price of an option.

However, for example, in the Japanese securities market, among options, in a market where transactions are not very active, such as an individual stock option market using stocks as underlying assets, observed option prices themselves are small, and such implied volatility is low. Not abundant. Therefore, in order to calculate the theoretical price of an option, it is necessary for the dealer itself to periodically change volatility parameters, etc., in order to reflect the latest market conditions, and rely on each experience and intuition We often deal.

[0010] (4) In the case of individual stock options, implied volatility is important information for knowing how the market perceives the volatility of a specific stock certificate, and in fact, the viewpoint of this market changes every moment. I do.

(5) In the option market, different implied volatility may be obtained from a plurality of options having the same underlying asset (hereinafter referred to as “smile effect”). In such a case, an approximate curve on the two-dimensional coordinates, called the smile curve, with the horizontal axis representing the option strike price and the vertical axis representing the corresponding implied volatility, is drawn as the option theory. Often used as material for calculating prices.

In order to examine how implied volatility changes in accordance with the period up to option expiration in light of (4) above, a volatility matrix and a generalized volatility matrix in which a time dimension up to expiration is added to the smile curve In many cases, a table of data is prepared, and points that cannot be observed from the market are compensated for by theoretical linear interpolation on the desk, and are often used as material for calculating the theoretical price of options.

(6) However, to obtain a meaningful smile curve or volatility matrix, abundant option prices must be observed in the market.
On the other hand, if trading is active, the observed option prices vary widely, making it difficult to grasp the overall trend.

(7) Generally, there is a trade-off between the amount of information observed in such a market and the assumption of a model serving as a base for calculating a theoretical price. That is, if the observed option prices are not abundant, stronger assumptions are needed for the model to obtain the dynamics of the expected probability distribution of the underlying asset price. A well-known advanced model in such cases is the stochastic volatility model SVM (Hull, John C. & Al
lan White, “The Pricing of Options on Assets with
Stochastic Volatilities ”, Journal of Finance, 4
2, June, 1987, pp. 281-300) and the GARCH model. However, these models assume normality,
Inability to adequately adapt to the fat-tail problem.

Conversely, a method that extends the grid method that does not assume normality (for example, Rubinstein, Mark, “Implied Bino
mial Trees ”, Journal of Finance, 49, July 1994, p
p. 771-818) can form a flexible distribution type that incorporates the smile effect, but on the other hand, to determine the distribution, it is necessary to observe a fairly large number of option prices. for that reason,
It is not fully adaptable in the less active options markets.

In addition, a jump model in which a fat tail (Fat-Tail) independently generates a stochastic process completely different from a normal distribution is also famous. However, the jump model assumes a discontinuous price change, and the stochastic volatility model S
VM is essentially a non-linear problem. Therefore, there is a defect that the risk-neutral probability measure cannot be uniquely obtained, and the option price cannot be uniquely defined.

(8) As described above, conventionally, even in a market where trading is not so active, the above information such as a smile curve and a volatility matrix that is significant for dealers and traders is applied to the fat tail problem. For dealers and traders in real time according to the changing market,
At the same time as providing it through the display screen of the computer system, it interactively takes in the data required for the calculation according to their request, and the appropriate model is automatically selected to flexibly analyze and deepen the analysis. It has been difficult to provide detailed information in real time.

The present invention has been made in order to solve the above-mentioned problem, and is based on a conventional general theory in an option market of a type that is adapted to a large price fluctuation of an underlying asset and is not actively traded. In place of the limited method, a calculation engine (Boltzmann model calculation engine) that applies nuclear reactor theory to the financial field is provided, and theoretical prices and risk indicators that are meaningful to dealers and traders can be displayed on an interactive screen interface of a computer system ( It is an object of the present invention to provide a dealing system that can be flexibly provided through a dealing terminal and a computer-readable recording medium recording a dealing program.

[0019]

According to a first aspect of the present invention, there is provided a dealing system, comprising: an implied volatility calculating section for calculating an implied volatility based on market data; A Boltzmann model calculation engine that calculates the option price of the option product; a filter that converts the option price calculated by the Boltzmann model calculation engine into black-Scholes volatility; The result of the conversion into the Sholes-type volatility and the implied volatility calculated from the market data, or the option price calculated by the Boltzmann model calculation engine, and the market It is that a dealing terminal to compare display and an optional price.

In the dealing system according to the first aspect of the present invention, a Boltzmann model in financial engineering is used for an option price evaluation method, and a Leptokurcity equation is calculated using a linear Boltzmann equation.
And Fat-Tail features to define a risk-neutral and unique probability measure. As a result, a risk-neutral and unique option price evaluation that considers Leptokurcity and Fat-Tail of the price fluctuation distribution is enabled. In addition, by applying the Boltzmann model to the option price evaluation of a predetermined option product, the overall tendency of the volatility matrix can be grasped from the transaction results that vary widely.

According to a second aspect of the present invention, in the dealing system according to the first aspect, the predetermined option product is a stock price index option. Understand the overall trend of the volatility matrix.

According to a third aspect of the present invention, in the dealing system according to the first aspect, the predetermined option product is an individual stock option. By determining the parameters of the Boltzmann model and confirming the consistency with the daily rate of return of the relevant stock, the overall volatility matrix of individual stock option prices can be obtained even if implied volatility due to trading performance is hardly obtained. Understand trends.

According to a fourth aspect of the present invention, in the dealing system of the first to third aspects, the Boltzmann model calculation engine has a function of calculating an option price while maintaining consistency with historical information.

In the dealing system according to the fourth aspect of the present invention, an option price that maintains consistency with historical information can be calculated by the Boltzmann model calculation engine and presented to the user through the dealing terminal.

According to a fifth aspect of the present invention, in the dealing system of the first to fourth aspects, the Boltzmann model calculation engine converts an option price based on a Boltzmann model obtained discretely with respect to an exercise price into a Black-Scholes volatility. It has a function of obtaining option prices and risk parameters by converting and interpolating by the Black-Scholes formula.

In the dealing system according to the fifth aspect of the present invention, the Boltzmann model calculation engine converts the option price according to the Boltzmann model, which is discretely determined with respect to the strike price, into a Black-Scholes volatility, and converts the option price into a Black-Scholes volatility. By inserting, the option price and the risk parameter can be obtained and presented to the user through the dealing terminal.

According to a sixth aspect of the present invention, in the dealing system of the first to fourth aspects, the Boltzmann model calculation engine converts a probability density function evaluated by the Boltzmann model into a table, and obtains an option price by a product-sum calculation of vectors. It has a function.

In the dealing system according to the invention of claim 6, the Boltzmann model calculation engine converts the probability density function evaluated by the Boltzmann model into a table, and obtains an option price by a product-sum calculation of a vector, thereby increasing a calculation speed. A more responsive system can be provided.

According to a seventh aspect of the present invention, there is provided a dealing system comprising: a dealing terminal as a graphical user interface;
Index calculation, theoretical price / index calculation engine capable of switching between detailed theoretical price / index calculation based on Boltzmann model at the time of user designation, interpolation theoretical calculation processing unit, and market data capture interface Is to display the market condition on the dealing terminal using the coarse calculation result, execute a detailed theoretical price / index calculation for the corresponding price range when the user specifies, and display the detailed evaluation result on the dealing terminal. It is.

[0030] In the dealing system according to the seventh aspect of the present invention, the display speed is increased by displaying the market condition on the dealing terminal usually using a rough calculation result, and the Boltzmann in the corresponding price range is designated when the user designates. Calculate detailed theoretical prices and indices based on the model, and display the detailed evaluation results so that users can quickly recognize changes in market conditions.

The dealing system according to the invention of claim 8 comprises a dealing terminal as a graphical user interface, an ordinary rough theoretical price / index calculation engine, and an option theoretical price / index based on an arbitrary multi-period Boltzmann model. A calculation engine, an interpolation theory calculation processing unit, and a market data capture interface are provided, and the market condition is normally displayed on the dealing terminal using a rough calculation result, and the volatility of any corresponding multi-period is specified at the time of user designation. It is displayed on the dealing terminal.

[0032] In the dealing system according to the eighth aspect of the present invention, the display speed is increased by displaying the market conditions on the dealing terminal usually using coarse calculation results. Find and display volatility based on the model. As a result, the term structure of volatility that does not exist in the market can be evaluated, and the development efficiency of structured bonds or exotic options can be improved.

The dealing system according to the ninth aspect of the present invention provides a dealing terminal as a graphical user interface, an ordinary rough theoretical price / index calculation engine, and a detailed theoretical price / index calculation based on the Boltzmann model.
Equipped with an index calculation engine, an interpolation theory calculation processing unit, a position setting processing unit, an automatic order processing unit, and a market data capture interface, and the stock index option price or individual stock option price can be set to a preset automatic order price range. An automatic order signal is output when the vehicle arrives, and the user can visually refer to the appropriate level of the advanced model, set a position, and automatically order in a timely manner.

According to a tenth aspect of the present invention, in the dealing system of the eighth or ninth aspect, a fading processing unit is provided, and a behavior animation of a period structure of implied volatility in an ATM (at the many) is displayed in a fading display. It has a function of fading and displaying the behavioral animation of the structure. By displaying the behavioral animation of the period structure of the implied volatility at the ATM in a fading manner, it is possible to make mistakes due to responsiveness to market fluctuations. Pricing can be prevented.

According to an eleventh aspect of the present invention, in the dealing system of the eighth to tenth aspects, a warning range setting processing unit for setting a warning range is provided, and a warning is output when a market condition enters the warning range. By setting a warning range by the user, a warning is issued if the market condition enters the warning range, thereby enabling the risk manager to perform appropriate risk management.

According to a twelfth aspect of the present invention, in the dealing system of the eleventh aspect, an alternative position extracting unit is provided to output the warning and extract and display the alternative position.

According to a twelfth aspect of the present invention, in the dealing system of the eleventh aspect, the dealing terminal has a function of outputting the warning and extracting and displaying an alternative position. Can be automatically extracted to prevent the occurrence of a loss due to a sensitive response to market fluctuations.

A computer-readable recording medium according to a thirteenth aspect of the present invention calculates implied volatility on the input market data, and performs a predetermined option on the input market data based on the Boltzmann model. Calculate the option price of the product,
The option price calculated by the Boltzmann model calculation engine was converted to black-Scholes volatility, the option price calculated by the Boltzmann model calculation engine was converted to black-Scholes volatility, and the result was calculated from the market data. It records an implied volatility or a dealing program for displaying option prices calculated by the Boltzmann model calculation engine and option prices in the market.

A computer-readable recording medium that records the dealing program of the invention of claim 13 can be built into a computer system to construct the dealing system of the invention of claim 1.

According to a fourteenth aspect of the present invention, in the computer readable recording medium storing the dealing program of the thirteenth aspect, the predetermined option product is a stock index option. The dealing system according to the second aspect of the present invention can be constructed by incorporating the system into a computer system.

According to a fifteenth aspect of the present invention, in the computer readable recording medium storing the dealing program of the thirteenth aspect, the predetermined option product is an individual stock option. The dealing system according to the third aspect of the present invention can be constructed by incorporating the system into a computer system.

[0042]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the present invention will be described below in detail with reference to the drawings. First, the theory and practice of option price evaluation will be described. Among the rights (options) that determine the future trading price of underlying assets (typically stocks or stock indices) traded in the free market, the price of a European option (exercise only on maturity date) Risk-neutral probability measure (probability density) P of the underlying asset price
By using (S, τ), the evaluation can be made by integrating Equations 1 and 2.

[0043]

(Equation 1)

(Equation 2) Here, S is the underlying asset price, τ is the period up to maturity, r is the non-risk interest rate (interest rate fixed by maturity), and K is the strike price.

Equation 1 is the price of the right (call option) to purchase the underlying asset at the strike price K on the maturity date, and Equation 2 is the price of the right to sell the underlying asset at the strike price K on the maturity date (put option). Price. The purchaser of these options can exercise at the strike price K, independent of the price of the underlying asset at maturity. That is, the call option purchaser can purchase at the price K even if the underlying asset price on the maturity date is larger than K. The seller of the call option has a price K
However, by repeating the buying and selling of these underlying assets according to price changes by the expiration date, the option can be sold to the option purchaser at the price K at least at the cost of equation (1).

A formula often used for option price evaluation is the Black-Scholes formula (BS formula). Using the following log-normal distribution of Equation 3 for the risk-neutral probability measures of Equations 1 and 2,

(Equation 3) The equations (1) and (2) are the following equations (4) and (5), which are BS equations.

[0046]

(Equation 4)

(Equation 5) Here, d ₁ and d ₂ are represented by the following equation (6).

[0047]

(Equation 6) The parameter σ in Equations (3), (4), and (5) is a price volatility (volatility), which is a diffusion coefficient of a geometric Brownian motion model of the underlying asset price (a model in which the underlying asset price is spread with respect to the logarithm of the price). It is.

The BS equation is derived on the assumption that the volatility σ is constant with respect to τ and S.
Thus, the BS formula assumes a static market where the market behaves consistently regardless of time and price.

However, it is recognized that the real market will change with time and price. FIG. 1 shows a price fluctuation rate C1 of the underlying asset and a typical price fluctuation rate (daily rate of return) C2 of the closing price predicted by the geometric Brownian model. Although they have the same volatility, price fluctuations are very different. In the geometric Brownian motion model C1, a large price fluctuation is hardly observed, whereas the actual price fluctuates greatly like a curve C2. Therefore, it is difficult to evaluate the option price using the BS formula when the stock price of the individual stock is used as the underlying asset, and there are currently few transactions of individual stock options.

The stock price index, such as the average stock price of multiple stocks such as Nikkei 225, is slower than the movement of stock prices of individual stocks. Therefore, the option price of the stock index becomes a problem that can be easily evaluated by the BS formula, and many trades are currently being made. However, even if the average of 225 brands is taken, as shown in FIG. 2, it can be seen that the fluctuation of the daily rate of return C3 is different from the geometric Brownian motion model (curve C1 in FIG. 1). Comparing this with the daily rate of return C2 of the individual issue of FIG. 1, it is essentially the same as the individual issue except that the fluctuation is small. Therefore, stock index option traders evaluate the option price by correcting the BS formula.

FIG. 3 shows an example of the correction. Implied volatility (IV) is the volatility where the option price traded in the market matches the valuation value of the BS formula
That. A mark 51 in FIG. 3 is a typical implied volatility of the Nikkei 225 stock index put option closing price.

The horizontal line C4 of 30% marked as historical volatility in FIG. 3 is the underlying asset Nikkei 22
Historical volatility calculated from the movement of the 5-stock index. If the market completely follows the geometric Brownian motion model based on the BS equation, the ■ mark 51 in the figure should be distributed on 30% of the line C4. However, in reality, the implied volatility tends to increase as the strike price moves away from the underlying asset price. The tendency that the implied volatility increases centering on the point where the strike price and the underlying asset price are equal (exercise price / underlying asset price = 1.00) is called a smile curve C5. It is also known that the smile curve C5 shows a period structure in which the curvature of the curve becomes gentler as the period until the expiration increases.

Usually, an option trader grasps a volatility matrix that summarizes a smile curve and a term structure of implied volatility based on a market transaction price, and corrects the option price by using the BS formula to correct the option price. Is determined.

Although the volatility matrix is the most successful option price evaluation method, it has disadvantages. The shortcomings can be summarized in the following two points.

1. If there are no or very few transactions, implied volatility cannot be obtained.

2. Actual transaction prices vary widely,
It is difficult to identify representative transactions that are a good representation of reality.

The above 1. The disadvantage of this is the inherent problem of implied volatility, which cannot be solved by implied volatility. On the other hand, 2. Is a filtering method that extracts significant information from information with large variations.
It may be possible to identify representative transactions that are well-presented in reality.

Before applying the filtering technique,
In order to understand the average behavior, it is necessary to clarify the mechanism by which the implied volatility smile and period structure occur. Although the mechanism of smile and term structure has not yet been elucidated, many empirical studies have shown that the actual probability of price fluctuations is sharper in areas where price fluctuations are smaller than the normal distribution assumed by the BS equation. (Leptokurcity), and it is considered that the main factor is that the skirt spreads (Fat-Tail) in areas where price fluctuations are large.

FIG. 4 shows an example. In FIG. 4, the □ mark 52 indicating the actual daily rate of return is sharper at the center and wider at the center than the normal distribution C6. According to such a price distribution, as indicated by a mark 53 in FIG. 5, the spread of the probability density (volatility) when the relative price is around 1.0 as compared with the lognormal distribution C7 used in the BS formula. It can be easily understood that the volatility of the probability density when the relative price is 2.0 or more and 2.5 or less becomes larger than that of the lognormal distribution C7. As the time elapses, the price distribution from the central limit theorem (in the figure,
Since the □ mark 54) is considered to approach a normal distribution,
The central portion and the spread of the tail of the price distribution become equal to the normal distribution C8 as time passes. This is considered to be the cause of the smile curve and period structure. A similar discussion can be found in John C. Hull, “OPTIONS, FUTURES & OTH
ER DERIVATIVES, Fourth Edition ”, Prentice-Hall In
It is also developed in ternational Inc., 2000, chapter 17.

The Fat-Tail of the price fluctuation distribution corresponds to a large price fluctuation that sometimes occurs in the actual price fluctuations C2 and C3 shown in FIGS. Two models are considered in consideration of these: a jump model in which a Fat-Tail is generated independently in a stochastic process completely different from a normal distribution, and a stochastic volatility model in which the standard deviation of a normal distribution, that is, volatility fluctuates with time. However, the jump model
Assuming discontinuous price changes, stochastic volatility models are essentially nonlinear problems. Therefore, a risk-neutral probability measure cannot be uniquely obtained. As a result, Equation 1 and Equation 2
There was a defect that the option price evaluation formula of the formula could not be applied to these models.

In contrast to these models, the recently proposed Boltzmann model is included in the stochastic volatility model in a broad sense, but the Leptokur equation is expressed by a linear Boltzmann equation.
The characteristics of city and Fat-Tail can be expressed. If the angle distribution is an isotropic distribution in the linear Boltzmann equation, its solution is risk-neutral and unique. Therefore, the basic trend of the volatility matrix can be evaluated by applying the Boltzmann model to option price evaluation.

As a feature of the Boltzmann model, consideration is given to the market dependence of price fluctuations. Market dependency is a large fluctuation in prices. Original paper on Boltzmann model "Yuji Uenohara and Ritsuo Yoshi
oka, ”Boltzmann Model in Financial Technology” Pr
oc. of 5th International Conference of JAFEE, Augu
st 28, 1999, Japan, pp.18-37 '' and Japanese Patent Application No. 11-242152
In "Price risk evaluation system and storage medium for financial products or their derivatives", in order to take into account Leptokurcity, we recommend the evaporation spectrum formula of Formula 7 which is a modification of Maxwell distribution to price distribution f (v). I have.

[0063]

(Equation 7) The Boltzmann model allows for the correlation between the price change of the underlying asset and the previous change. The Boltzmann model asserts that in the case of the closing price, there is a clear market dependence between the daily rate of return v 'on the previous day and the daily rate of return v on the day via the temperature T. I have. A typical example is shown in FIG.
In FIG. 6, a mark 55 indicates the temperature obtained from the actual closing price of the stock price, and a curve C9 is obtained by fitting these with a quadratic function. From FIG. 6, it can be seen that the temperature T shows a quadratic function tendency shown in the equation 8 with respect to the previous day's daily rate of return v '.

[0064]

(Equation 8) In the original paper, the quadratic change is a system that receives positive feedback that the specific heat increases as the temperature increases.
It alleges that it is an indication of the instability of the stock market.

The curve C5 which coincides with the actual value (５１ mark 51) in FIG. 3 showing the volatility smile is obtained by evaluating the option prices of the equations (1) and (2) using the Boltzmann model and obtaining the BS equation which is equal to the result. Is a plot of the volatility of FIG. 7 shows the daily rate of return C10 evaluated by the Boltzmann model in the course of the price evaluation simulation by the Boltzmann model. It can be seen from FIG. 7 that the daily rate of return (■ mark 56 in the figure) of the Nikkei Stock Average at the same time as the option trading has been almost reproduced.

The daily rate of return shown in FIG. 7 is a typical Fat-Tail
Is shown. When a random number 発 生 is generated in accordance with the daily rate of return distribution obtained by the Boltzmann distribution and the locus of the underlying asset price S is simulated according to the following equation 9, a jump model equivalent to the Boltzmann model is obtained. However, since the jump model ignores market dependence, large price changes are discontinuous, unlike the Boltzmann model.

[0067]

(Equation 9) A jump model equivalent to the Boltzmann model seems to give the same results as the Boltzmann model, but the results are quite different. FIG. 8 shows the implied volatility of the Boltzmann model and the jump model in comparison. The solid line C11 and the dashed-dotted line C12 in FIG. 8 are the results of the Boltzmann model.
This is the case on day 0. The dashed line C13 and the dotted line C14 are the results of the jump model.
This is the case on day 0.

From the comparison of FIG. 8, the jump model C1
3 and C14 show that the volatility is larger than that of the Boltzmann models C11 and C12, and the curvature of the smile curve is smaller. It can be seen that the implied volatility by the jump model is large even when compared with the actual value. In the jump model, the central limit theorem appears early because the magnitude of price fluctuation is completely uncorrelated, and the price spreads quickly. Therefore, in order to obtain the same result as the Boltzmann model in the jump model, it is necessary to use a distribution that takes a large probability density in a portion where the rate of return is lower than the daily rate of return C10 shown in FIG. Becomes However, as a result, the daily rate of return distribution is significantly different from that of the underlying asset. Thus, it can be seen that the Boltzmann model and the jump model are fundamentally different.

The Boltzmann model is not particularly complicated as compared with the jump model. For example, compare with the simplest Merton compound jump model. Merton's jump model uses a random number に よ る based on a normal distribution and a random number η based on a Poisson distribution, using the standard deviation σ of the normal distribution, the average jump size k of the Poisson distribution, and the probability λ of a jump to occur per unit time, Underlying asset price S
Is represented by the following equation (10).

[0070]

(Equation 10) In Merton's composite jump model, the probability density function has two normal distributions and Poisson distributions, and has three parameters. The Boltzmann model has one probability density function of Maxwell distribution and three parameters, and the Boltzmann model is simpler because the number of types of the probability density function is small.

Up to this point, the theory and practice of option price evaluation have been described. Next, a dealing system for evaluating option prices based on the Boltzmann model will be described.

FIGS. 9 and 10 show the configuration of the dealing system 100 of the present embodiment. The system 100 includes an implied volatility calculation unit 102 that communicates with an external market database 101 to fetch market data and calculates implied volatility, and a configuration shown in FIG. 10. A model calculation engine (BMM) 103 and an option price output from the BMM 103 are referred to as implied volatility (I
V) and an dealing terminal 1 as a graphical user interface (GUI) for displaying necessary information, printing out, and performing data entry.
05.

The Boltzmann model calculation engine (B
The MM) 103 has the configuration shown in FIG. 10 and includes an initial value input unit 3 for price, fluctuation rate, and fluctuation direction, an evaluation condition input unit 4, a Boltzmann model analysis unit 5, and a GUI 1 as an input / output device.
05 (common to FIG. 9), total cross section / stochastic process input unit 7, velocity distribution / direction distribution input unit 8, random number generation unit 9
And is connected to the market database 101 to capture necessary market data.

The Boltzmann model analysis unit 5 further includes an initialization unit 12, an initial value setting unit 13, a sampling unit 14, a price fluctuation simulation unit 15 using a Boltzmann model, a probability density calculation unit 16, and a trial end determination unit 1.
7, an end-of-trial-end determining unit 18, a probability density editing unit 19, a price distribution calculating unit 20, and a price converting unit 21.

Note that the present system does not mean that it is included in one computer in a physical sense.
For example, a system that performs distributed processing, such as a client-server system, can be adopted as the system 100. In addition, each element corresponds to each program that executes the processing indicated by the name, and these elements are not physically incorporated in the present system. Therefore, the present invention can be basically realized by incorporating a dealing program for executing these processing functions into one computer having a communication function.

The initial value input unit 3 receives the stock price to be evaluated or
Equation 8 T for the underlying asset of the stock index ₀, C₀, G₀A
It is input to the Rutzmann model analysis unit 5. This parameter is
Obtained from actual data. Preferably, the initial value input unit 3
Information about the stock or index
Relevant stock searched from the ket database 101
Price of the formula or stock index, price volatility,
Obtain initial values and output to Boltzmann model analysis unit 5
You.

The evaluation condition input section 4 is an element for inputting the evaluation conditions of the Boltzmann model analysis section 5. The evaluation conditions of the Boltzmann analysis unit 5 are conditions for the Boltzmann model analysis unit 5 to analyze the number of trials, an evaluation time zone, an evaluation price zone, and the like. By this evaluation condition input unit 4,
Evaluation conditions under which significant analysis can be performed can be set in the Boltzmann model analysis unit 5.

The Boltzmann model analysis means 5 is a central component of the present invention. Boltzmann model analysis means 5
For details, see Japanese Patent Application No. 11-24, which is a prior application of the present inventors.
This is described in detail in No. 2152. It is redundant here to refer again, so please refer to this. FIG. 10 is substantially the same as FIG. 1 of Japanese Patent Application No. 11-242152, except that a price distribution calculating section 20 and a price converting section 2 are newly added.
1 will be described.

The price distribution calculation unit 20 of the Boltzmann model analysis unit 5 is an element for calculating the price distribution based on the probability density of the price change of the underlying asset edited by the probability density editing unit 19.

The price conversion unit 2 of the Boltzmann model analysis unit 5
Reference numeral 1 denotes an element for calculating and outputting an option price to be evaluated based on the price distribution calculated by the price distribution calculation unit 20.

The dealing terminal 105 as a GUI
Is an element that outputs the progress of the processing of the system and the final processing result, and outputs the price distribution of the option to be evaluated. The terminal 105 has an input function using a pointing device such as a keyboard and a mouse. The terminal 105 can display the information on a display, print out the data using a printer, transmit the data to another system via a network, and write the data to a storage device. It has an output function in a broad sense, including.

The market database 101 is a database that stores information related to optional products to be evaluated. Here, "database" means
It includes data systematically managed in the database, means for searching for data, and hardware for storing and managing them.

The market database 101 contains:
It may be provided uniquely to this system, but if there is an existing database outside, it may be used.

A method for evaluating the stock price index option price by the option price evaluation system having the above system configuration will be described below.

FIG. 11 shows six procedures from A1 to A6. In stock index option price valuation, usually, a lot of transaction performance data can be obtained. These performance data are accumulated in the market database 101, and the total cross section / probability process input unit 7 calculates the implied volatility using the performance data of the database 101 in the processing step of A1.

Next, the processing steps A2 and A3 on the left side of FIG. 11 are conventional procedures. In the processing step of A2,
The overall tendency of the volatility matrix is determined from the implied volatility obtained in the processing step of A1, based on experience and intuition or a simple moving average or a regression model, and the volatility matrix is determined in the processing step of A3. Conventionally, arbitrary judgment has been required in the processing step of A2.

The Dealing System 10 of the Present Embodiment
At 0, in the processing step of A4, the implied volatility is fetched by the Boltzmann model analysis unit 5 and the temperature parameters of the Boltzmann model (three coefficients T ₀ , c ₀ , g of equation 8) are set to match the implied volatility. ₀ ) is determined.

If they match, the process proceeds to the processing step of A5, and the matching with the daily rate of return of the underlying asset is confirmed. Here, if the daily rates of return of the underlying assets do not match, the process returns to the processing step of A4, and the parameters are reviewed. If they match, A
In the processing step 6, consistency with the market dependence of the underlying asset is confirmed.

In the processing step of A6, if the market value coincides with the market dependency of the underlying asset, the result of the Boltzmann model is used to determine the volatility matrix in the processing step of A3. Actually, since it is rare that a clear market dependence can be observed, the flow from A5 to A6 (broken line with an arrow in FIG. 11) is often the final decision. If a clear market dependence is obtained, but does not match the actual situation, the process returns to the processing step of A4 and the parameters are reviewed.

The actual market cannot always be explained well by the Boltzmann model. The processing step of A4 can explain the volatility matrix well,
It can be inconsistent with the daily rate of return. In that case,
It gives up ensuring the consistency with the daily rate of return, and shifts to the processing step of A3. If the value does not match the implied volatility in the processing step of A4, the market exceeds the limit of the Boltzmann model.
Returning to the processing step (1), the same method as in the past is used, and the judgment is left to the judgment of a dealer or the like.

Next, a method for evaluating the price of an individual stock option by the dealing system 100 will be described. The fact that the daily rate of return evaluated by the Boltzmann model can be equal to the daily rate of return of the underlying asset means that the option price can be evaluated from the behavior of the underlying asset even if there is no record of option trading. Therefore, it can be said that this is the most effective method for valuing individual stock option prices, which has little trading experience at present.

In the Boltzmann model, the method is exactly the same for stock price index option price evaluation and individual stock option price evaluation. For each stock, the three coefficients T in equation 8
_0, c _0, by determining the g _0, can be evaluated the option price.

FIG. 12 shows whether the tendency of Formula 8 is actually observed for individual brands. FIG. 12 shows the temperature T obtained for a part of listed stocks on the Tokyo Stock Exchange. The horizontal axis is by industry, in this case, construction, food,
This is a list in which the historical volatility of stock prices is small for chemical, steel, electric, financial, and service.
The solid lines C21, C22,..., C27 in FIG. 12 are obtained by converting the historical volatility into the temperature T. In the figure, filled circles indicate the temperature of the day's profit rate distribution when the previous day's daily rate of return is within 5%, and crosses indicate the temperature when the previous day's daily rate of return is 5% to 10%. And □
The mark indicates the temperature when the previous day's daily rate of return is 10% to 15%.

FIG. 12 shows that these three types of temperatures are roughly proportional to the historical volatility C21, C22,... Also, it can be seen that the temperature T increases as the daily rate of return on the previous day increases. Further, looking at the distribution of the filled-in ○ mark, □ mark, and × mark, the difference between the × mark group and the □ mark group is larger than the difference between the □ mark group and the filled ○ mark group. In other words, as the previous day's daily rate of return increases,
It can be seen that not only the temperature but also the rate of temperature rise is large. This suggests a quadratic dependence of equation (8).

FIGS. 13 and 14 show examples of individual stock option price evaluation. FIG. 13 is an example of a call option price evaluation. The horizontal axis shows the ratio between the strike price and the underlying asset price, and the vertical axis shows the ratio between the call option price and the underlying asset price. FIG. 14 is an example of put option price evaluation, and the vertical axis is the ratio between the put option price and the underlying asset price. 13 and 14
The solid lines C31 and C41 and the dashed-dotted lines C32 and C42 are evaluated by the Boltzmann model, and the periods until the maturity are 20 days and 40 days, respectively. The broken lines C33 and C43 and the dotted lines C34 and C44 are based on the BS formula.

Here, it is assumed that the brand has a historical volatility of about 70%, and from FIG. 12, the temperature of equation (11) is used.

[0097]

[Equation 11] The historical volatility of about 70% is about twice the volatility of the stock index, which is a somewhat large but realistic value for the historical volatility of individual stocks.

FIGS. 15 and 16 show the implied volatility of the call option and the put option. Like the implied volatility of the stock index in Figure 8,
It can be seen that the smile curve and period structure are reflected.

FIG. 17 shows the flow of processing when the above-described individual stock option price evaluation is performed by the dealing system 100. As in FIG. 11, the left side shows the flow of the conventional method.

In the individual stock option trading, usually, the trading performance is small. Since the one with the most transaction results is the same as the stock index option, here, the one with little transaction result will be described using FIG.

Conventionally, based on the historical volatility of the relevant stock in the processing step of B1, the smile and term structure of the volatility are estimated from the experience of valuation of stock index options and the like, and the volatility matrix is determined in the processing step B2. Reach.

However, in the dealing system 100 of this embodiment, the temperature parameter of the Boltzmann model of the brand is determined in the processing step B3. Then, in processing step B4, the consistency with the daily rate of return of the relevant issue is confirmed. If the daily returns do not match, the process returns to processing step B3, and the parameters are reviewed. If they match, processing step B
In 5, confirm the consistency with the market dependence. If they match, the determination of the volatility matrix in the processing step B2 of the conventional method is performed. If the market dependence does not match, the process returns to the processing step B3, the temperature parameter is reviewed, and the above processing is repeated. In this case, too, it is rare that a clear market dependence is actually observed. Therefore, the flow from the processing steps B4 to B5 (broken line with an arrow in the figure) is often the final decision.

Next, the above dealing system 100
An option price valuation method that maintains consistency with historical information based on the Boltzmann model will be described. He stated that the Boltzmann model can evaluate the smile and term structure of implied volatility while maintaining consistency with the historical information of the underlying assets. This feature has the advantage that the basis for offering option prices can be clarified when trading. Pricing in real markets does not necessarily require a rational explanation.
In particular, if the transaction is carried out entirely at your own risk, large losses due to mispricing are matters of the parties only. However, in business trade and option pricing consultations, the impact of price valuation goes beyond just the party who priced it. Therefore, a long-term experience and intuition are not enough, and a reasonable basis for pricing is required.

The markets are so uncertain that arbitrary judgments relying on experience and intuition are not completely eliminated. However, if these judgments are supported by other information, it is not just an arbitrary judgment but an action based on rational evidence. Given that the basics of current financial engineering are such that the price of a derivative is determined from the behavior of the underlying asset price, the Boltzmann model's ability to maintain consistency with historical information of the underlying asset implies the rationality of price valuation. It can be a great basis for claiming.

It is difficult to clearly explain the basis of the deviation, assuming that the deviation from the historical information of the underlying asset is assumed, as in the above-described jump model and volatility matrix. Of course, the model is not perfect, so in some cases a price evaluation that deviates from the historical information of the underlying asset is also required. However, in a model such as the Boltzmann model that maintains the consistency of the underlying asset with the lithographic information in principle, the deviation is small and there is relatively little opportunity to deviate. Therefore,
In the event of a deviation, more time is available for consultation with stakeholders, and the likelihood of a particular dealer or consultant misjudgment resulting in a huge loss is reduced.

Now, the above-described dealing system 10
When executing the option price evaluation using 0, it is necessary to evaluate the risk parameters shown in Expressions 12 to 16 for risk hedging.

[0107]

(Equation 12)

(Equation 13)

[Equation 14]

(Equation 15)

(Equation 16) Here, C is the option price, S is the underlying asset price, r is the non-risk interest rate, τ is the period to maturity, and σ is the volatility. It is known that if the underlying asset is bought and sold in proportion to these risk parameters, the price fluctuation of the underlying asset can be basically canceled out.

It can be seen that these risk parameters are the derivative of the option price. The Boltzmann model presupposes the Monte Carlo method as a solution, but a disadvantage of the Monte Carlo method is that it takes a long calculation time to evaluate the differential amount. For example, a procedure for exactly obtaining Θ of the call option price C by the Monte Carlo method will be described. By setting the minute change amount δτ of the period τ until the expiration and calculating Equation 17, Θ can be evaluated.

[0109]

[Equation 17] Here, the numerator of Expression 17 is converted from Expression 1 into Expression 18 below.

[0110]

(Equation 18) Although the integral on the right side of Expression 18 is obtained by the Monte Carlo method, the change of τ as an input variable is small. Therefore,
The difference between the integral of the first term and the integral of the second term on the right side of Expression 18 also becomes small.

In the Monte Carlo method, the calculation results vary within the range of the statistical error. Therefore, when the difference is small, it is necessary to increase the amount of calculation in order to reduce the total error. Normal,
The statistical error is inversely proportional to the square of the calculation amount. Therefore, when the amount of change is small, a significant difference cannot be detected without spending an enormous amount of calculation time.

This problem involves not only the financial Monte Carlo method but also the Monte Carlo method in general, and no fundamental solution has been found yet. Although there is a method of simulating only a small amount of variation, such as a perturbation Monte Carlo method used in the radiation transport Monte Carlo method, a slight approximation is required, and the strictness which is a feature of the Monte Carlo method may be lost.

At present, it is not realistic to stick to the exactness of the solution, because the Monte Carlo method cannot strictly simulate the minute fluctuation amount. In situations where option prices can be explained by implied volatility,
The difference between the Boltzmann model and the BS model is small. Since the first-order to second-order derivatives such as risk parameters generally have a weak model dependence, substitute implied volatility back calculated from option prices evaluated by the Boltzmann model into the risk parameter evaluation formula based on the BS formula. The risk parameter can be evaluated with sufficient accuracy for practical use.

Specifically, by replacing the volatility σ of the risk parameter evaluation formula based on the BS formula shown in Formulas 19 to 23 below with an implied volatility matching the option price of the Boltzmann model,
Can be used as risk parameters for Boltzmann model.

[0115]

[Equation 19]

(Equation 20)

(Equation 21)

(Equation 22)

(Equation 23) Here, Erf (x) is an expression defined as follows.

[0116]

(Equation 24) Next, a method of tabulating the probability density function evaluated by the Boltzmann model using the present dealing system 100 and calculating the option price not by the recalculation of the Monte Carlo method but by the product-sum calculation of the vector will be described. .

The implied volatility is a Black-Scholes volatility calculated by backcalculating the option price evaluated by the Boltzmann model and the option price according to the Black-Scholes (BS) formula. In the Boltzmann model, the option price is expressed by the above-mentioned equations (1) and (2), and the numerical integration of these equations (1) and (2) is obtained by the Monte Carlo method.

When the probability density function P (S, τ) does not change significantly with respect to S, that is, when a normal price distribution can be applied, the probability density function is tabulated with respect to S, and the following equation (25) is used. By approximation by the series of Equation 26, a value very close to the result strictly evaluated by the Monte Carlo method can be obtained.

[0119]

(Equation 25)

(Equation 26) Here, the probability density function P (Si, τ) can be obtained by using the following Expression 27 by the Monte Carlo method and evaluating the Expression 27.

[0120]

[Equation 27] Here, if ΔSi is sufficiently small for practical use and the probability density functions of Equation 27 are stored as a table, Equations 25 and 26 are simple product-sum operations of vectors, and can be calculated at high speed.

Next, the dealing system 10 of the present invention will be described.
A specific processing function using 0 will be described. FIG.
Is a sub-screen on the dealing terminal 105 that displays the history of the stock index. FIG. 19 is a sub-screen showing, in the dealing terminal 105, the implied volatility and the market price of each stock price option using the stock price index as the underlying asset by strike price and contract month in a table format.

FIGS. 20A and 20B are sub-screens showing the information in the table format of FIG. 19 in the same manner in the dealing terminal 105 in the form of a graph. The graph with the vertical axis of the implied volatility in FIG. 3A is a so-called smile curve, and the graph in FIG. 3B is a graph of option price-strike price for each contract month.

The dealing system 100 executes the processing shown in the flowchart of FIG. 21 in more detail. During normal market conditions, the market data 101 is fetched (step S05), and the sub screen shown in FIG.
The display speed is improved using the coarse calculation results (steps S10 and S15).

On the other hand, when there is a large change in the underlying asset, as in the part a of the graph displayed on the sub-screen of FIG. 18, the user can use the sub-screen of FIG. 20 and FIG. The area 110 on which the detailed evaluation is to be performed (here, the area of K4-K5) is diagonally dragged with a mouse (or a similar pointing device) to designate the screen enlargement (steps S20 and S2).
5), necessary additional input data, specifically, FIG.
As shown in (b), the virtual strike price a corresponding to K451, K452, and K453 is automatically passed to the BMM 103 to execute the interpolation calculation (step S30; S30-1, S30-1).
S30-2).

Based on the calculation result, specifically, the implied volatility and option strike price b corresponding to a are received from the BMM 103 (step S30-3), and the dealing terminal 105 is shown in FIG. 19 and FIG. The screen and the scales of the sub-screens of FIGS. 20 and 23A are refreshed (step S35-1), and the results of the detailed evaluation are linked and shown (step S35-2; step S3).
5). The illustrated graph is shown in FIG.

Next, the theoretical calculation server BMM103
The calculation processing performed in will be specifically described with reference to FIG.

As described above, the implied volatility (IV) is the black-Scholes volatility calculated backward so that the option price evaluated by the Boltzmann model and the option price by the Black-Scholes formula (BS formula) match. is there. In the Boltzmann model, the option price is expressed by the above-mentioned equations (1) and (2), and the numerical integration of these is obtained by the Monte Carlo method. In these equations 1 and 2, the probability density function P (S,
When τ) does not change significantly with respect to S, that is, when a normal price distribution can be applied, the probability density function P (S, τ) is tabulated for S, and
By approximating with the series of Equations 5 and 26, a value very close to the result strictly evaluated by the Monte Carlo method can be obtained.

Here, the probability density function P (Si, τ) can be determined by the Monte Carlo method using the above-mentioned equation (27) and evaluating the equation (27). Then, if ΔSi is sufficiently small for practical use and the probability density functions of Equation 27 are stored as a table, Equations 25 and 26 are simply vector-sum operations of vectors, and can be calculated at high speed.

The series of Equation 25 is schematically shown in FIG. The smooth curve C61 in FIG.
(S, τ). The histogram C62 is a tabulated probability density P (Si, τ). The strict evaluation result of Equation 1 is obtained by numerically integrating the product of P (S, τ) and the straight line C63 having a slope 1 starting from S = K by Monte Carlo method. When the details are evaluated by the user's designation in step S20 in FIG. 21, this process is applied (branch to YES in step S20). On the other hand, a product obtained by integrating the product of the straight line C63 and the histogram C62 is an approximation expressed by Expression 25, and this process is applied during normal market conditions (step S20).
Branch to NO).

In this way, when a detailed evaluation is performed, more precise results can be obtained. FIG. 22 (b)
In the graph of the above, the code C is a normal coarse calculation result C6
4 shows the deviation from the result C65 of the detailed evaluation.

According to this processing, usually, the display speed is improved by using a coarse calculation result, and the detailed evaluation result is displayed by enlarging the screen when the user designates it. Be able to detect quickly.

Next, by calculating and displaying volatility of an arbitrary multi-period by the dealing system 100 shown in FIG. 9, the term structure of volatility that does not exist in the market is evaluated, and the development of structured bonds or exotic options is performed. A method for providing the information will be described. FIG.
The flowchart of FIG. This FIG.
In the flowchart of FIG. 21, the same reference numerals are given to the processing steps common to the flowchart of FIG.

Normally, by using the rough calculation results, FIGS.
As shown in FIG. 20, the market condition is transmitted on the sub-screen of the dealing terminal 105. Here, when the user wants to evaluate volatility for an arbitrary multi-period, the “start date” 201 and “maturity date” are set on the period setting screen 200 in FIG. The user inputs a date 202 and an evaluation interval 203, or performs a necessary selection operation.

It is not necessary that these are set in the market. For example, on the screen for displaying implied volatility and market prices shown in FIG. 27, options for the first and second contract months indicated by the symbol a are traded, but options for the m contract month indicated by the symbol b are traded in the market. Suppose not.

Here, the user performs an interrupt operation (FIG. 2).
In step S20 'in FIG. 5, on the period setting screen 200 in FIG. 26, enter the last day of this m-month in "Expiration Date" 202, select "monthly" as "Evaluation Interval" 203, and press the execute button (step). S25 '). Then, the additional input information a is automatically passed to the BMM 103 (step S30 ';S30-1', S30-2 ').

Then, the BMM 103 executes an operation based on the Boltzmann model described above, and receives the calculation result, specifically, the implied volatility and option price b of the m contract month (step S30-3 '), and The scale is refreshed on the sub-screen of FIG. 19 and the sub-screen of FIG. 20 at 105, and the results are connected and displayed (steps S35-1, S35-2; S35).

The graph shown in FIG. 28 is shown in FIG.
Is exemplified. In FIG. 28, curves C71 and C72
Indicates the volatility of the option existing in the market, and the curve C73 indicates the volatility of the option not existing in the market.

In this way, by obtaining and displaying volatility of an arbitrary multi-period, it is possible to evaluate the term structure of volatility that does not exist in the market,
This can improve the development efficiency of structured bonds or exotic options.

Next, ATM (At the Manny) executed by the dealing system 100 of the present embodiment.
29 and 30 show a method of fading and displaying a behavior animation of a period structure of an IV (implied volatility) in FIG.
This will be described with reference to FIG.

The flowchart of FIG. 29 shows a processing procedure when a fading function is added to the flowchart of FIG. In FIG. 29, FIG.
The processing steps common to 1 are denoted by the same reference numerals. The different process is the process of screen display in step S150.

In the flowchart of FIG. 29, usually, the market condition is reported on the dealing terminal sub-screen of FIGS. 18 to 20 using the rough calculation result (step S1).
0). Here, for example, when there is a large change in the underlying asset on the sub-screen of FIG. 18 (the portion indicated by reference numeral a in FIG. 18), the user can use the sub-screen of FIG.
As shown in (2), the area 110 for which detailed evaluation is to be performed is designated by a mouse to enlarge the screen (YES in step S20).

By this operation, in addition to the display of the market condition at the normal time, when a user interrupt occurs, necessary input data is automatically passed to the BMM engine 103, and the data shown in FIG. 31 is returned as a calculation result. . Here, FIG.
KR is a real-time ATM imagined between the exercise price bands (discrete values) set in the market.
This is an ATM imagined to be equal to the real-time underlying asset price.

Since the risk index and the option price change most greatly in the vicinity of the ATM, it is extremely important for dealers and traders to know the changes in market conditions and the period structure in this vicinity.

Therefore, depending on market conditions, even if the underlying asset price moves between the discrete exercise price bands set in the market on the sub-screen of FIG. 18, the ATM is virtualized as shown by KR in FIG. By doing so, the term structure of the implied volatility can be flexibly evaluated.

However, by this operation, FIG.
The information to be displayed as the graph shown in (b) increases (in this case, for example, there are six graphs up to six contract months). Therefore, it is necessary to display them accurately, quickly and intuitively for the user.

Therefore, in the present processing, the behavior animation of the period structure of the implied volatility is subjected to the fading display as shown in FIG. 33 by the processing based on the flowchart of FIG. In FIG. 33 (a), only the a1 contract month is displayed as a solid line (step S150-4), and after the elapsed time of the weight level value w, the a1 contract month is displayed as a broken line as shown in FIG. , A2 contract month is displayed as a solid line (steps S150-5, S150-6). Hereinafter, as shown in FIG. 33D, the display is repeated until the ae contract month (steps S150-7, S150-8,..., S15).
0-e, S150- (e + 1)).

Here, as shown in the detailed processing flowchart of FIG. 30, the interrupt processing is started at any time by inputting the "+" and "-" keys from the keyboard as shown in the detailed processing flowchart of FIG. 30, and the display processing of FIG. 33 is immediately started. This is reflected (steps S150-1 to S150-3). It should be noted that the interrupt processing can be accepted by using a pointing device such as a mouse instead of the key input.

The calculation result received from the BMM engine 103 shown in FIG. 31 is displayed as a graph as shown in FIG. In FIG. 32, KR is a virtual ATM, and Δ mark is B
The output data of the MM engine 103 and the x mark represent market condition data.

According to this processing, by displaying the animation of the behavior of the period structure of the IV in the ATM in a fading manner, it is possible to prevent mispricing due to an excessive response to the market fluctuation.

Similarly, the flowchart of FIG.
5 shows a processing procedure when a fading function is added to the flowchart of FIG. In FIG. 34, processing steps common to those in FIG. 25 are denoted by the same reference numerals. Then, the different processing is performed in step S15.
This is the process of screen display of 0 '.

In the flowchart of FIG. 34, usually, the market condition is reported on the dealing terminal sub-screen of FIGS. 18 to 20 using the rough calculation result (step S1).
0). Here, if the user wants to evaluate volatility of arbitrary multi-period at the same time, on the period setting screen 200 of FIG. 26, in order to set the period of the option to be evaluated, “start date” 201, “maturity year” Date 20
2 is input, and the "evaluation interval" 203 is selected (step S20 ').

When such a user interrupt process occurs, necessary input data is automatically passed to the BMM engine 103, and data as shown in FIG. 27 is returned as a calculation result (steps S25 'and S30'). . Then, by displaying this calculation result as a graph, a graph as shown in FIG. 28 is displayed (step S35).

Here, when fading display is designated on the screen display, multi-period volatility is displayed by the processing shown in the flowchart of FIG. 30 in the same manner as described above.

According to the present processing, by displaying the behavior animation of the period structure of the implied volatility of an arbitrary multi-period in a fading manner, it is possible to prevent mispricing due to an excessive response to market fluctuation.

Next, the processing function in which the dealer sets a position and automatically places an order in a timely manner by the dealing system 100 shown in FIG. 9 will be described with reference to the flowcharts of FIGS. 35 to 37. In the flowchart of FIG. 35, the same process steps as those of the flowchart of FIG. 21 are denoted by the same step numbers.

In this processing function, the market condition is usually reported on the dealing terminal sub-screen shown in FIGS. 18 to 20 using coarse calculation results (steps S05 to S15), and the user can determine the appropriate level of the altitude model. Visually referencing.

If the user wants to order a sales order, an interrupt request is made in step S40, and areas L, M, and N shown in FIG. 36 are sequentially designated by dragging with the mouse (steps S40 and S45). When the area L is specified first, the transaction condition input screen 210 of FIG.
The attributes of the designated position, such as strike price, call / put, implied volatility, or quote, are automatically inserted in the appropriate fields. By further inputting the sell / buy and the number of copies and operating the “execute order” button from this screen, the order specified here is stored in the order data 130 of FIG. 35 (step S50).
The same applies to the remaining areas M and N.

After the execution of the order, a change in market conditions is checked in real time at intervals of t seconds as to whether the market has returned to the target area (steps S60, S10, S10).
S15, S20, S40).

When the market returns to the target area, the flow branches to YES in step S60, and an automatic order is immediately placed in the market (steps S65 and S7).
0), at the time of execution (step S76), when the position of the target area, for example, area N is executed, area N of FIG. 36 is released from the screen (step S76).
75).

With such a processing method, the dealer can visually refer to the appropriate level of the advanced model, set a position, and automatically place an order in a timely manner.

Even in such a processing function in which the dealer sets a position and automatically places an order in a timely manner, the behavior animation of the term structure of the implied volatility of the ATM is displayed fading on the dealer terminal 105. Can be. 38 to 42 show a flowchart of such fading display processing, and FIG. 43 shows a display mode of the dealer terminal 105. In the flowcharts of FIGS. 38 to 42, the same reference numerals are given to the processing steps common to the processing steps of the flowcharts of the other drawings.

Normally, the market situation is reported on the dealing terminal sub-screen shown in FIGS. 18 to 20 using the rough calculation results (steps S05 and S10).

Here, since the risk index and the option price change most greatly near the ATM, it is extremely important for dealers and traders to perceive changes in market conditions and the period structure in the vicinity. Therefore, depending on market conditions, even if the underlying asset price moves between the discrete exercise price bands set in the market on the sub-screen in FIG.
By imagining the ATM as shown by (1), the period structure of the implied volatility can be easily displayed by fading display (steps S150-1 to S150- (e + 1)).

On the basis of this information, the user designates the position of the area L in FIG. 43 with the mouse (steps S40, S45, S50), and thereby the step S60 is performed.
Is automatically checked at intervals of t seconds as to whether the market has returned to the target area, and when the market returns to the target area, an automatic order is immediately placed in the market (steps S65 and S70).

As described above, in the dealing system 100 of the present embodiment, when the dealer visually refers to the appropriate level of the advanced model, sets a position, and executes a process of automatically ordering in a timely manner,
By fading and displaying the behavior animation of the period structure of the implied volatility (IV) in the TM, mispricing due to excessive response to market fluctuations can be prevented, and the dealer can set an appropriate position.

Next, the automatic warning function by the dealing system 100 of this embodiment will be described with reference to the flowchart of FIG. 44 and the explanatory diagram of FIG. FIG.
In the flowchart of FIG. 4, processing steps common to the flowcharts of FIGS. 38 to 42 are denoted by the same reference numerals.

In the flowchart of FIG. 44, the market condition is usually transmitted on the dealing terminal sub-screen of FIGS. 18 to 20 using the rough calculation result (step S).
05, S10, S150), the user visually refers to the appropriate level of the altitude model.

Here, in FIG. 45, in FIG. 45, the output of the Boltzmann model engine 103 by this system is a curve C101, the regression of the market is predicted by the curve C102, and the implied volatility of the market is the curve C103. If it is desired to place a buy / sell order at position a, the position is designated with the mouse in step S80 and the order is placed.

Here, a setting is made for automatically issuing a warning to the position ordered by the user (position a in the graph of FIG. 45) according to a change in market conditions. Specifically, an interrupt request is issued in step S80, and the range of the watched market, for example, the watch area b in FIG. 45, is designated by a mouse (step S85). This designated information is stored in the alert area data 131.

When setting a guard range for each of a plurality of positions, the interrupt request is similarly issued a plurality of times.

Further, as shown in the guard area b in FIG. 45, the ordered position a is an option of the strike price K2, but the guard area b straddles the area of the strike price K3. Exercise prices other than the strike price of the position undertaken in this way, that is, indicators of other option stocks, can be flexibly included as alert conditions.

After setting the alert range, in step S90, the alert area data 131 and the market data 101 are checked in real time at intervals of t seconds to see if a market has entered the alert area b. Then, the prediction of the market is deviated, and the actual market becomes a curve C104. If the market enters the caution area b, the position a where the order is issued is immediately flickered (d) and the user is notified (step S95). .

With this processing function, the dealer sets a caution range, issues a warning if the market enters the caution range, and enables the risk manager to perform appropriate risk management.

It should be noted that, in addition to the above processing functions, the processing function of FIG. 46 can be added to the portion D in the flowchart of FIG. That is, when the prediction of the existing order position is incorrect and the actual market enters the alert area b as shown by the curve C104, not only the warning output but also a new alternative position area e as shown in FIG. Is added.

In order to realize this, usually, FIG.
In the flowchart of FIG.
Market conditions are reported on the dealing terminal sub-screens of FIGS. 8 to 20, and as shown in FIG. 47, the user has set a guard area b for the position a for which an order has been placed.

Here, it is assumed that the market condition has changed and the actual market index C104 has entered the alert area b. In such a case, the position a is flickered immediately to notify the user of this state. Subsequently, in step S86 in the flowchart of FIG. 46, an alternative position area e for the existing position a in FIG. 47 is calculated based on the order data 131 and the market data 101. This is based on the market movement that was initially assumed (Fig. 4
Curve C102 in FIG. 7 unexpectedly changes to curve C10.
This corresponds to the opposite position, which compensates for the transition to the state indicated by 4.

Subsequently, the calculated alternative position area e is immediately shown to the dealing terminal 105 in the screen display process of step S88 as shown in FIG.

The user can place an order again at the position f that he considers appropriate from the illustrated alternative position area e.

If such a substitute position proposal function is added, in the dealing system 100 which issues a warning for a prediction deviation from the actual market, the substitute position is automatically extracted and the response to the market fluctuation can be performed. The occurrence of a huge loss can be prevented.

Although the above embodiment has been described with reference to the stock index option, the present invention is not limited to the stock index option, but may be any option product in which the underlying asset exhibits the behavior of a geometric Brownian motion, such as an individual stock option, currency, etc. The same applies to options and the like.

[0181]

As described above, according to the present invention, in the option market, including those that are not actively traded, which adapts to large price fluctuations of the underlying asset, based on the conventional theory of financial engineering. Equipped with a Boltzmann model calculation engine that applies reactor theory to the financial field instead of the limited method, and provides flexible theoretical prices and risk indicators for dealers and traders through the interactive screen interface of computer systems. be able to.

[Brief description of the drawings]

Fig. 1 Price fluctuation rate C1 of the underlying asset predicted by the geometric Brownian model and the fluctuation rate of the closing price of a typical stock price (daily rate of return)
Graph of C2.

FIG. 2 is a graph showing a change in a daily rate of return C3 of the Nikkei 225 average stock price.

FIG. 3 is a graph showing the implied volatility and smile curve of a typical Nikkei 225 stock index put option.

FIG. 4 is a graph showing a comparison between an actual price fluctuation probability and a normal distribution assumed by a BS formula.

FIG. 5 is a graph showing a comparison between an actual price fluctuation probability and a lognormal distribution used in the BS equation.

FIG. 6 is a graph showing a relationship between a daily return rate v ′ and a temperature T on the previous day.

FIG. 7 is a graph showing the relationship between the daily rate of return and the probability evaluated by the Boltzmann model in the course of the price evaluation simulation by the Boltzmann model.

FIG. 8 is a graph showing the implied volatility of a Boltzmann model and a jump model in comparison.

FIG. 9 is a block diagram showing a system configuration of one embodiment of a dealing system of the present invention.

FIG. 10 is a block diagram showing a functional configuration of a Boltzmann model calculation model in the above dealing system.

FIG. 11 is a flowchart showing theoretical calculation processing by the above-mentioned dealing system.

FIG. 12 is a graph showing a temperature T obtained for a part of stocks listed on the Tokyo Stock Exchange by the above dealing system.

FIG. 13 is obtained by the above dealing system.
9 is a graph showing an example of a call option price evaluation of an individual stock option, showing a relationship between an exercise price / underlying asset price and a call option price / underlying asset price.

FIG. 14 is an example of a put option price evaluation of an individual stock option obtained by the above-mentioned dealing system, in which an exercise price / underlying asset price and a put option price /
Graph showing the relationship with the underlying asset price.

FIG. 15 obtained by the above dealing system;
7 is a graph showing the relationship between the exercise price / underlying asset price of a call option and implied volatility.

FIG. 16 is obtained by the above dealing system.
13 is a graph showing the relationship between the exercise price / underlying asset price of a put option and implied volatility.

FIG. 17 is a flowchart showing another example of the theoretical calculation process by the above-mentioned dealing system.

FIG. 18 is an explanatory diagram of a sub-screen for displaying a stock price index history displayed by the dealing terminal in the dealing system.

FIG. 19 is a sub-screen showing, in the form of a table, implied volatility and market price by strike price, contract month, of a stock index option using the stock index displayed by the dealing terminal as an underlying asset in the above-mentioned dealing system. FIG.

FIG. 20 is a sub-screen showing, in a graph form, implied volatility and market price by strike price, contract month, of a stock index option using the stock index displayed by the dealing terminal as an underlying asset in the above-mentioned dealing system. FIG.

FIG. 21 is a flowchart showing a detailed price evaluation process executed by the above-mentioned dealing system.

FIG. 22 is an explanatory diagram showing a change in a display screen in a graph format at the dealing terminal in the detailed price evaluation process.

FIG. 23 is an explanatory diagram showing a change in a display screen in a table format at the dealing terminal in the above detailed price evaluation processing.

FIG. 24 is a graph illustrating a theoretical calculation process performed by the Boltzmann model calculation engine in the above dealing system.

FIG. 25 is a flowchart showing an arbitrary multi-period volatility evaluation process executed by the dealing system.

FIG. 26 is an explanatory diagram showing a period setting screen displayed on the dealing terminal in the above-described arbitrary multi-period volatility evaluation processing.

FIG. 27 is a market price table for explaining the above-described arbitrary multi-period volatility evaluation processing.

FIG. 28 is a graph of arbitrary multi-period volatility displayed on the dealing terminal as a result of the above-described arbitrary multi-period volatility evaluation processing.

FIG. 29 is a flowchart of a processing procedure when a fading function is added to the detailed price evaluation processing executed by the above-mentioned dealing system.

FIG. 30 is a detailed flowchart of the above fading processing step.

FIG. 31 is an implied volatility and option price table including real-time ATM implied volatility imagined between exercise price bands set in the market in the detailed price evaluation process executed by the above-mentioned dealing system.

FIG. 32 In the detailed price evaluation processing executed by the above-mentioned dealing system, the implied volatility of a multi-period including the real-time implied volatility of an ATM imagined between the exercise price bands set in the market is calculated. The graph shown.

FIG. 33 is an explanatory diagram of the fading display process.

FIG. 34 is a flowchart of a processing procedure when a fading function is added to an arbitrary multi-period volatility evaluation processing executed by the above-described dealing system.

FIG. 35 is a flowchart of processing in which the dealer sets a position and automatically places an order in a timely manner by the above-mentioned dealing system.

FIG. 36 is a graph showing a relationship between calculation engine output and implied volatility when performing the above-described position setting operation.

FIG. 37 is an explanatory diagram showing an input screen displayed on the dealing terminal when performing the above-described position setting operation.

FIG. 38 is a first part of a flowchart of a process for fading and displaying the behavior animation of the period structure of the implied volatility of the ATM by the above-mentioned dealing system.

FIG. 39 is a second part of the flowchart of the processing for fading and displaying the behavior animation of the period structure of the implied volatility of the ATM.

FIG. 40 is a third part of the flowchart of the processing for fading and displaying the behavior animation of the period structure of the implied volatility of the ATM.

FIG. 41: Step S in the flowchart of FIG. 39
30 is a flowchart showing the detailed processing of 30.

FIG. 42 is step S in the flowchart of FIG. 39;
The flowchart which shows the detailed process of 30 '.

FIG. 43 is a graph illustrating automatic order processing.

FIG. 44 is a flowchart showing an automatic warning process for a market condition in the above-mentioned dealing system.

FIG. 45 is a graph illustrating an automatic alert process for market conditions.

FIG. 46 is a flowchart showing a function of automatically calculating an alternative position added to the automatic warning processing function for market conditions in the above-mentioned dealing system.

FIG. 47 is a graph for explaining automatic alert processing for market conditions and processing for presenting an alternative position.

[Explanation of symbols]

 3 Initial value input unit 4 Evaluation condition input unit 5 Boltzmann model analysis unit 7 Total cross section / stochastic process input unit 8 Speed distribution / direction distribution input unit 9 Random number generation unit 12 Initialization unit 13 Initial value setting unit 14 Sampling unit 15 Simulation Unit 16 Probability density calculation unit 17 One trial end determination unit 18 All trial end determination unit 19 Probability density editing unit 20 Price distribution calculation unit 21 Price conversion unit 100 Dealing system 101 Market database 103 Boltzmann model calculation engine 104 Implied volatility filter 105 Dealing terminal

────────────────────────────────────────────────── ───

[Procedure amendment]

[Submission Date] October 2, 2000 (2000.10.
2)

[Procedure amendment 1]

[Document name to be amended] Statement

[Correction target item name] 0009

[Correction method] Change

[Correction contents]

However, in a market where transactions are not so active (for example, in the Japanese securities market, among the options, an individual stock option market in which stocks are underlying assets), observed option prices themselves are small,
Such implied volatility cannot be obtained abundantly. So to calculate the theoretical price of an option,
In order to reflect the latest market conditions, dealers themselves need to periodically perform operations such as changing volatility parameters, and often engage in transactions based on their experience and intuition.

[Procedure amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0014

[Correction method] Change

[Correction contents]

(7) Generally, there is a trade-off between the amount of information observed in such a market and the assumption of a model serving as a base for calculating a theoretical price. That is, if the observed option prices are not abundant, stronger assumptions are needed for the model to obtain the dynamics of the expected probability distribution of the underlying asset price. A well-known advanced model in such cases is the stochastic volatility model SVM (eg, Hull, John
C. & Allan White, “The Pricing of Options on Ass
ets with Stochastic Volatilities ”, Journal of Fin
ance, 42, June, 1987, pp. 281-300) and GARCH models (see, for example, T. Bollerslev, “Generalized Autoregre
ssive Conditional Heteroskedasticity, ”Journal of
Econometrics, Vol. 31, 1986, pp. 307-327). However, these models assume normality,
Inability to adequately adapt to the fat-tail problem.

[Procedure amendment 3]

[Document name to be amended] Statement

[Correction target item name] 0016

[Correction method] Change

[Correction contents]

[0016] In addition, a jump model (for example, RC Merton, “Option Pricing Whe”) that generates a fat tail independently of a stochastic process completely different from a normal distribution.
n Underlying Stock Returns Are Discontinuous, ”Jo
urnal of Financial Economics, vol. 3, March 1976,
pp. 125-144) are also famous. However, the jump model assumes discontinuous price changes, and the stochastic volatility model SVM is essentially a nonlinear problem. Therefore, there is a defect that the risk-neutral probability measure cannot be uniquely obtained, and the option price cannot be uniquely defined.

[Procedure amendment 4]

[Document name to be amended] Statement

[Correction target item name] 0044

[Correction method] Change

[Correction contents]

Equation 1 is the theoretical price of the right to buy the underlying asset at the expiry price K on the maturity date (call option), and Equation 2 is the right to sell the underlying asset at the expiration price K on the maturity date (put option). Is the theoretical price. The purchaser of these options will have a strike price K regardless of the price of the underlying asset at maturity.
To exercise your rights. That is, even if the underlying asset price on the maturity date is greater than K,
Can be purchased at The call option seller is obliged to sell at the price K on the maturity date, but by repeating the buying and selling of these underlying assets according to price changes by the maturity date, the option purchase can be made at least at the cost of formula 1. Can be sold to the price K.

[Procedure amendment 5]

[Document name to be amended] Statement

[Correction target item name] 0061

[Correction method] Change

[Correction contents]

In contrast to these models, the recently proposed Boltzmann model is included in the stochastic volatility model in a broad sense.
It can express the characteristics of urcity and Fat-Tail. If the angle distribution is an isotropic distribution in the linear Boltzmann equation, its solution is risk-neutral and unique. Therefore, the basic trend of the volatility matrix can be evaluated by applying the Boltzmann model to option price evaluation.

[Procedure amendment 6]

[Document name to be amended] Statement

[Correction target item name] 0066

[Correction method] Change

[Correction contents]

The daily rate of return shown in FIG. 7 is a typical Fat-Tail
Is shown. A random number 発 生 is generated according to the daily rate of return distribution obtained by the Boltzmann distribution, and the locus of the underlying asset price S is simulated according to the following equation (9). However, since the jump model ignores market dependence, large price changes are discontinuous, unlike the Boltzmann model.

[Procedure amendment 7]

[Document name to be amended] Statement

[Correction target item name] 0067

[Correction method] Change

[Correction contents]

[0067]

(Equation 9) This jump model seems to give the same results as the Boltzmann model, but the results are quite different. FIG. 8 shows the implied volatility of the Boltzmann model and the jump model in comparison. Solid line C in FIG.
11 and the dashed-dotted line C12 are the results of the Boltzmann model, in which the periods until the maturity are 40 days and 80 days, respectively.
The dashed line C13 and the dotted line C14 are the results of the jump model, and the cases until the maturity are 40 days and 80 days, respectively.

[Procedure amendment 8]

[Document name to be amended] Statement

[Correction target item name]

[Correction method] Change

[Correction contents]

From the comparison of FIG. 8, the jump model C1
3 and C14 show that the volatility is larger than that of the Boltzmann models C11 and C12, and the curvature of the smile curve is smaller. It can be seen that the implied volatility by the jump model is large even when compared with the actual value. In the jump model, the central limit theorem appears early because the magnitude of price fluctuation is completely uncorrelated. This is because in a discontinuous model such as a jump model, the price spreads faster. Therefore, in order to obtain the same result as the Boltzmann model in the jump model, it is necessary to use a distribution that takes a large probability density in a portion where the rate of return is lower than the daily rate of return C10 shown in FIG. Becomes However, as a result, the daily rate of return distribution is significantly different from that of the underlying asset. Thus, it can be seen that the Boltzmann model and the jump model are fundamentally different.

[Procedure amendment 9]

[Document name to be amended] Statement

[Correction target item name]

[Correction method] Change

[Correction contents]

FIG. 12 shows that these three types of temperatures are roughly proportional to the historical volatility C21, C22,..., C27. Also, it can be seen that the temperature T increases as the daily rate of return on the previous day increases. Further, looking at the distribution of the filled-in ○ mark, □ mark, and × mark, the difference between the × mark group and the □ mark group is larger than the difference between the □ mark group and the filled ○ mark group. That is, it can be seen that as the daily rate of return on the previous day increases, not only the temperature but also the rate of temperature rise increases. This suggests a quadratic dependence of equation (8).

[Procedure amendment 10]

[Document name to be amended] Statement

[Correction target item name] Brief description of drawings

[Correction method] Change

[Correction contents]

[Brief description of the drawings]

Fig. 1 Price fluctuation rate C1 of the underlying asset predicted by the geometric Brownian model and the fluctuation rate of the closing price of a typical stock price (daily rate of return)
Graph of C2.

FIG. 2 is a graph showing a change in a daily rate of return C3 of the Nikkei 225 average stock price.

FIG. 3 is a graph showing the implied volatility and smile curve of a typical Nikkei 225 stock index put option.

FIG. 4 is a graph showing a comparison between the probability of an actual daily rate of return and a normal distribution assumed by a BS formula.

FIG. 5 is a graph showing a comparison between a probability of a time change of a price evaluated by a Boltzmann model and a lognormal distribution used in a BS formula.

FIG. 6 is a graph showing a relationship between a daily return rate v ′ and a temperature T on the previous day.

FIG. 7 is a graph showing the relationship between the daily rate of return and the probability evaluated by the Boltzmann model in the course of the price evaluation simulation by the Boltzmann model.

FIG. 8 is a graph showing the implied volatility of a Boltzmann model and a jump model in comparison.

FIG. 9 is a block diagram showing a system configuration of one embodiment of a dealing system of the present invention.

FIG. 10 is a block diagram showing a functional configuration of a Boltzmann model calculation model in the above dealing system.

FIG. 11 is a flowchart showing theoretical calculation processing by the above-mentioned dealing system.

FIG. 12 is a graph showing a temperature T obtained for a part of stocks listed on the Tokyo Stock Exchange by the above dealing system.

FIG. 13 is obtained by the above dealing system.
9 is a graph showing an example of a call option price evaluation of an individual stock option, showing a relationship between an exercise price / underlying asset price and a call option price / underlying asset price.

FIG. 14 obtained by the above dealing system;
9 is a graph showing an example of a put option price evaluation of an individual stock option, showing a relationship between an exercise price / underlying asset price and a put option price / underlying asset price.

FIG. 15 obtained by the above dealing system;
7 is a graph showing the relationship between the exercise price / underlying asset price of a call option and implied volatility.

FIG. 16 is obtained by the above dealing system.
13 is a graph showing the relationship between the exercise price / underlying asset price of a put option and implied volatility.

FIG. 17 is a flowchart showing another example of the theoretical calculation process by the above-mentioned dealing system.

FIG. 18 is an explanatory diagram of a sub-screen for displaying a stock price index history displayed by the dealing terminal in the dealing system.

FIG. 19 is a sub-screen showing, in the form of a table, implied volatility and market price by strike price, contract month, of a stock index option using the stock index displayed by the dealing terminal as an underlying asset in the above-mentioned dealing system. FIG.

FIG. 20 is a sub-screen showing, in a graph form, implied volatility and market price by strike price, contract month, of a stock index option using the stock index displayed by the dealing terminal as an underlying asset in the above-mentioned dealing system. FIG.

FIG. 21 is a flowchart showing a detailed price evaluation process executed by the above-mentioned dealing system.

FIG. 22 is an explanatory diagram showing a change in a display screen in a graph format at the dealing terminal in the detailed price evaluation process.

FIG. 23 is an explanatory diagram showing a change in a display screen in a table format at the dealing terminal in the above detailed price evaluation processing.

FIG. 24 is a graph illustrating a theoretical calculation process performed by the Boltzmann model calculation engine in the above dealing system.

FIG. 25 is a flowchart showing an arbitrary multi-period volatility evaluation process executed by the dealing system.

FIG. 26 is an explanatory diagram showing a period setting screen displayed on the dealing terminal in the above-described arbitrary multi-period volatility evaluation processing.

FIG. 27 is a market price table for explaining the above-described arbitrary multi-period volatility evaluation processing.

FIG. 28 is a graph of arbitrary multi-period volatility displayed on the dealing terminal as a result of the above-described arbitrary multi-period volatility evaluation processing.

FIG. 29 is a flowchart of a processing procedure when a fading function is added to the detailed price evaluation processing executed by the above-mentioned dealing system.

FIG. 30 is a detailed flowchart of the above fading processing step.

FIG. 31 is an implied volatility and option price table including real-time ATM implied volatility imagined between exercise price bands set in the market in the detailed price evaluation process executed by the above-mentioned dealing system.

FIG. 32 In the detailed price evaluation processing executed by the above-mentioned dealing system, the implied volatility of a multi-period including the real-time implied volatility of an ATM imagined between the exercise price bands set in the market is calculated. The graph shown.

FIG. 33 is an explanatory diagram of the fading display process.

FIG. 34 is a flowchart of a processing procedure when a fading function is added to an arbitrary multi-period volatility evaluation processing executed by the above-described dealing system.

FIG. 35 is a flowchart of processing in which the dealer sets a position and automatically places an order in a timely manner by the above-mentioned dealing system.

FIG. 36 is a graph showing a relationship between calculation engine output and implied volatility when performing the above-described position setting operation.

FIG. 37 is an explanatory diagram showing an input screen displayed on the dealing terminal when performing the above-described position setting operation.

FIG. 38 is a first part of a flowchart of a process for fading and displaying the behavior animation of the period structure of the implied volatility of the ATM by the above-mentioned dealing system.

FIG. 39 is a second part of the flowchart of the processing for fading and displaying the behavior animation of the period structure of the implied volatility of the ATM.

FIG. 40 is a third part of the flowchart of the processing for fading and displaying the behavior animation of the period structure of the implied volatility of the ATM.

FIG. 41: Step S in the flowchart of FIG. 39
30 is a flowchart showing the detailed processing of 30.

FIG. 42 is step S in the flowchart of FIG. 39;
The flowchart which shows the detailed process of 30 '.

FIG. 43 is a graph illustrating automatic order processing.

FIG. 44 is a flowchart showing an automatic warning process for a market condition in the above-mentioned dealing system.

FIG. 45 is a graph illustrating an automatic alert process for market conditions.

FIG. 46 is a flowchart showing a function of automatically calculating an alternative position added to the automatic warning processing function for market conditions in the above-mentioned dealing system.

FIG. 47 is a graph for explaining automatic alert processing for market conditions and processing for presenting an alternative position.

[Description of Signs] 3 Initial value input unit 4 Evaluation condition input unit 5 Boltzmann model analysis unit 7 Total cross section / stochastic process input unit 8 Speed distribution / direction distribution input unit 9 Random number generation unit 12 Initialization unit 13 Initial value setting unit 14 Sampling unit 15 Simulation unit 16 Probability density calculation unit 17 One trial end determination unit 18 All trial end determination unit 19 Probability density editing unit 20 Price distribution calculation unit 21 Price conversion unit 100 Dealing system 101 Market database 103 Boltzmann model calculation engine 104 Implied volatility filter 105 Dealing terminal

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Takahiro Tachimi 1-9-11 Kaigan, Minato-ku, Tokyo Inside RIC Corporation (72) Inventor Tadahiro Ohashi 1-1-1, Shibaura, Minato-ku, Tokyo No. Toshiba Corporation Head Office (72) Inventor Masatoshi Kawashima 2-1 Ukishima-cho, Kawasaki-ku, Kawasaki-shi, Kanagawa Prefecture Inside the Toshiba Hamakawasaki Plant (72) Inventor Hiroaki Okuda 1-Toshiba-cho, Fuchu-shi, Tokyo F-term in Toshiba Fuchu Office (reference) 5B055 CC00

Claims (15)

[Claims] An implied volatility calculating unit that calculates an implied volatility based on market data; a Boltzmann model calculation engine that calculates an option price of a predetermined option product based on a Boltzmann model with respect to the market data; A filter that converts the option price calculated by the Boltzmann model calculation engine into black-Scholes volatility; a result obtained by converting the option price calculated by the Boltzmann model calculation engine into black-Scholes volatility; and calculation from the market data. The implied volatility, or the option price calculated by the Boltzmann model calculation engine, and the option price of the market, the dealing terminal that displays the comparison. Dealing system provided. 2. The dealing system according to claim 1, wherein the predetermined option product is a stock index option. 3. The dealing system according to claim 1, wherein the predetermined option product is an individual stock option. 4. The Boltzmann model calculation engine,
The dealing system according to any one of claims 1 to 3, further comprising a function of calculating an option price while maintaining consistency with historical information. 5. The Boltzmann model calculation engine,
It has a function to convert the option price obtained by the Boltzmann model, which is discretely calculated with respect to the exercise price, into the volatility of the Black-Scholes formula, and obtain the option price and the risk parameter by interpolating with the Black-Scholes formula. The dealing system according to any one of claims 1 to 4, wherein 6. The Boltzmann model calculation engine,
The dealing system according to any one of claims 1 to 4, further comprising a function of tabulating a probability density function evaluated by the Boltzmann model and calculating an option price by a product-sum calculation of a vector. 7. A dealing terminal as a graphical user interface, a strike price set in the market under normal market conditions, and a contract month (hereinafter, “coarse”
Theoretical price / index calculation based on the Boltzmann model at the time of user designation, including the exercise price and contract month not set in the market (hereinafter referred to as “details”) A theoretical price / index calculation engine capable of switching between, an interpolation theory calculation processing unit, and a market data capture interface are provided, and usually the market condition is displayed on the dealing terminal using a rough calculation result, and when specified by a user, A dealing system, wherein a detailed theoretical calculation / index calculation of a corresponding price range is performed, and a detailed evaluation result is displayed on the dealing terminal. 8. A dealing terminal as a graphical user interface, an exercise price set in the market, a rough theoretical price / index calculation engine for each contract month, and an option theoretical price / index based on an arbitrary multi-period Boltzmann model. An index calculation engine, an interpolation theory calculation processing unit,
A market data acquisition interface is provided, and at normal times, the market condition is displayed on the dealing terminal using a rough calculation result. Characteristic dealing system. 9. A dealing terminal as a graphical user interface, an exercise price set in the market, a rough theoretical price / index calculation engine for each contract month, and an exercise price not set in the market based on the Boltzmann model. A detailed theoretical price / index calculation engine including a contract month and a contract month, an interpolation theoretical calculation processing unit, a position setting processing unit, an automatic order processing unit, and a market data capture interface are provided. A dealing system characterized by outputting an automatic order signal when a price reaches a preset automatic order price range. 10. An ATM having a fading processing unit,
10. The dealing system according to claim 8 or 9, wherein a behavior animation of a volatility term structure obtained by converting an option price by the Boltzmann model in (At the Manny) is faded and displayed. 11. The dealing system according to claim 8, further comprising a warning range setting processing unit for setting a warning range, and outputting a warning when a market condition enters the warning range. . 12. The dealing system according to claim 11, further comprising an alternative position extraction processing section, which outputs the warning and extracts and displays the alternative position. 13. An implied volatility is calculated with respect to the input market data, an option price of a predetermined option product is calculated with respect to the input market data based on a Boltzmann model, and based on the Boltzmann model. Converting the calculated option price to Black-Scholes volatility, the result of converting the option price calculated by the Boltzmann model calculation engine to Black-Scholes volatility, and the implied volatility calculated from the market data, Alternatively, a computer-readable recording medium recording a dealing program for displaying the option price calculated by the Boltzmann model calculation engine and the option price in the market in a comparative manner. 14. The computer-readable recording medium according to claim 13, wherein the predetermined option product is a stock index option. 15. The computer-readable recording medium according to claim 13, wherein the predetermined option product is an individual stock option.