Abstract

The purpose of this paper was to investigate the dynamics of the option pricing in the market through the two-dimensional time fractional-order Black–Scholes equation for a European put option. The Liouville–Caputo derivative was used to improve the ordinary Black–Scholes equation. The analytic solution is a powerful tool for describing the behavior of the option price in the European style market. In this study, analytic solution is carried out by the Laplace homotopy perturbation method. Moreover, the obtained solution showed that the Laplace homotopy perturbation method was an efficient method for finding an analytic solution of two-dimensional fractional-order differential equation.

中文翻译：

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关于欧洲看跌期权的二维分数阶Black-Scholes方程的解

摘要

本文的目的是通过针对欧洲看跌期权的二维时间分数阶布莱克-斯科尔斯方程来研究市场中期权定价的动态。Liouville–Caputo导数用于改进普通的Black–Scholes方程。解析解决方案是描述欧式市场期权价格行为的强大工具。在这项研究中，解析解是通过拉普拉斯同伦摄动法进行的。此外，所获得的解表明，拉普拉斯同伦摄动法是寻找二维分数阶微分方程解析解的有效方法。