An Accurate and Efficient Numerical Method for Solving Black-Scholes Equation in Option Pricing

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Mathematics in Operational Research


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.

Original Citation

Liao, W. and Zhu, J. (2009), An accurate and efficient numerical method for solving Black-Scholes equation in option pricing, International Journal of Mathematics in Operational Research, 1:191 – 210.