Option value calculation system based on time fractional order option pricing model

Abstract

The invention discloses an option value calculation system based on a time fractional order option pricing model, and relates to the technical field of option value evaluation. The system comprises aparameter initialization module, a stock price fluctuation ratio calculation module, an option type selection module, an option value calculation module, an adaptive grid generation module and a result output module. According to the system, a stable and effective differential discrete format is constructed on the adaptive grid, the singularity problem of an accurate solution is effectively solved, the problems of low numerical precision and inaccurate calculation result of a classical algorithm are solved, and the calculation precision of the option value is improved.

Description

technical field [0001] The invention relates to the technical field of option value evaluation, in particular to an option value calculation system based on a time fractional option pricing model. Background technique [0002] With the discovery of the fractal structure of the financial market, the standard Brownian motion in the traditional model is replaced by the Lévy process, combined with the generalization of other parameters, a series of fractional partial differential equation option pricing models are obtained. The fractional derivative terms in these models can well describe the memory characteristics of the market. Fractional partial differential equation option pricing models are difficult to obtain analytical solutions, and numerical methods are often used to solve them in practical applications. [0003] Fractional option pricing models have characteristics such as historical dependence and global correlation, exact solutions may contain singularities, and Ame...

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Problems solved by technology

[0003] Fractional option pricing models have characteristics such as historical dependence and global correlation, exact solutions may contain singularities, and American options are free boundary problems, which lead to some effective numerical calculation methods for integer order differential equations. For fractional order partial differential equations The option pricing model is no longer applicable, so the calculation difficulty of the fractional order option pricing model is much higher than the numerical calculation of the general integer order differential equation

[0004] Commonly used methods for solving fractional order partial differential equation option pricing models include finite difference method, finite element method and finite volume method, but none of the existing methods consider the singularity of the exact solution

Since the exact solution of fractional differential equations may have singularity, that is, the exact solution may change drastically in some areas, the existing algorithms cannot effectively deal with the singularity of the exact solution, resulting in low numerical accuracy of these algorithms, Calculations are inaccurate

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