An accurate and efficient numerical method for solving Black-Scholes equation in option pricing

Abstract

An efficient and accurate numerical method for solving the well-known Black-Scholes equation in option pricing is presented in this article. The method can be used for cases in which the coefficients in the Black-Scholes equation are time-dependent and no analytic solutions are available. It is an extension to the method by Liao, W. and Zhu, J. (2008 'A new method for solving convection-diffusion equations', Paper presented in the Proceedings of the 11th IEEE International Conference on Computational Science and Engineering, IEEE Computer Society, Los Alamitos, CA, USA, pp.107-114) for solving 1D convection-diffusion equations with constant diffusion and convection coefficients using the fourth-order Pade approximation on a 3-point stencil. The new method can handle equations with variable diffusion and convection coefficients that depend on x² and x, respectively, where x is the independent variable. Numerical examples are presented in the article to demonstrate the accuracy and efficiency of the method.