Price and risk evaluation system for financial product or its derivatives, dealing system, recording medium storing a price and risk evaluation program, and recording medium storing a dealing program

• US 7,865,418 B2
• Filed: 04/09/2007
• Issued: 01/04/2011
• Est. Priority Date: 08/27/1999
• Status: Expired due to Fees

• Current Assignee: Kabushiki Kaisha Toshiba (Toshiba Corporation)
• Original Assignee: Kabushiki Kaisha Toshiba (Toshiba Corporation)
• Inventors: Ohashi, Tadahiro, Kawashima, Masatoshi, Uenohara, Yuji, Yoshioka, Ritsuo, Okuda, Hiroaki, Tatsumi, Takahiro, Onishi, Motohiko
• Primary Examiner(s): Akintola; Olabode
• Application Number:
  US11/733,057
• Publication Number:
  US 20070198387A1
• Time in Patent Office: 1,366 Days
• Field of Search: 705 36 R- 44
• US Class Current: 705/36.00R
• CPC Class Codes: G06Q 40/06 Asset management; Financial planning or analysis
• CPC Class Codes: G06Q 40/08 Insurance

Abstract

A system for correctly evaluating a price distribution and a risk distribution for a financial product or its derivatives introduces a probability density function generated with a Boltzmann model at a higher accuracy than the Gaussian distribution for a probability density. The system has an initial value setup unit and an evaluation condition setup unit. Initial values include at least one of price, price change rate, and the price change direction of a financial product. The evaluation conditions include at least time steps and the number of trials. The Boltzmann model analysis unit receives the initial values and the evaluation conditions, and repeats simulations of price fluctuation, based on the Boltzmann model using a Monte Carlo method. A velocity/direction distribution setup unit supplies the probability distributions of the price, price change rate, and the price change direction for the financial product to the Boltzmann model analysis unit. A random number generator for a Monte Carlo method employed in the analysis by the Boltzmann model, and an output unit displays the analysis result. A dealing system applies the financial Boltzmann model to option pricing, and reproduces the characteristics of Leptokurcity and Fat-tail by linear Boltzmann equation in order to define risk-neutral and unique probability measures. Consequently, option prices can be evaluated in a risk-neutral and unique manner, taking into account Leptokurcity and Fat-tail of a price change distribution.

Claims

1. A dealing system comprising:

an implied volatility computation engine configured to evaluate an implied volatility based on market data;

a Boltzmann model computation engine configured to evaluate an option price for a selected option product based on a Boltzmann model using the market data;

a filter configured to convert an option price obtained from the Boltzmann model computation engine into a volatility of a Black-Sholes equation; and

a dealing terminal configured to display volatility of the Black-Sholes equation in comparison with implied volatility calculated from the market data, or to display the option price calculated by the Boltzmann model computation engine in comparison with an option price in market.

2. The dealing system according to claim 1, wherein the selected option product is a stock price index option.

3. The dealing system according to claim 1, wherein the selected option product is an individual stock option.

4. The dealing system according to claim 1, wherein the Boltzmann model computation engine has a unit configured to calculate an option price consistent to historical information from the market data.

5. The dealing system according to claim 1, wherein the Boltzmann model computation engine has a converter configured to convert an option price, which was obtained in a discrete manner with respect to an exercise price based on the Boltzmann model, into a volatility obtained from the Black-Sholes equation in order to obtain the option price and risk parameter through interpolation with the Black-Sholes equation.

6. The dealing system according to claim 1, wherein the Boltzmann model computation engine has a table generator that generates a table of a probability density function evaluated by the Boltzmann model, and calculate an option price using a sum of inner products of vectors.

7. A computer-readable recording medium storing a dealing program for use in a dealing system, which when executed by a processor results in performance of steps comprising:

causing the dealing system to compute an implied volatility using market data supplied to the dealing system;

causing the dealing system to compute an option price based on a Boltzmann model using market data for selected derivatives;

causing the dealing system to convert the option price obtained from the Boltzmann model into a volatility of a Black-Sholes equation; and

causing the dealing system to display the volatility of the Black-Sholes equation in comparison with implied volatility calculated from the market data, or to display the option price based on the Boltzmann model in comparison with an option price in a market.