Numerical simulation of the Black-Scholes equation using the SPH method

Abstract

In this paper we present a numerical method for solving the European options (call and put) using the Black-Scholes model. The numerical method considered is based on the SPH method. SPH is one of the most popular and efficient numerical schemes used in the approximation of partial differential equations particularly in fluid dynamic. Before applying SPH method, the Black-Scholes equation needs to be written into the heat equation. With this form, the numerical resolution of the Black-Scholes equation is further simplified and ensures the stability of the scheme. Numerical experiments were performed for different financial parameters. We investigate the accuracy of the numerical method proposed by given some comparisons between analytical and numerical computation.