Finite Difference Method for the Multi-Asset Black–Scholes Equations

Abstract

In this paper, we briefly review the finite difference method (FDM) for the Black−Scholes (BS) equations for pricing derivative securities and provide the MATLAB codes in the Appendix for the one-, two-, and three-dimensional numerical implementation. The BS equation is discretized non-uniformly in space and implicitly in time. The two- and three-dimensional equations are solved using the operator splitting method. In the numerical tests, we show characteristic examples for option pricing. The computational results are in good agreement with the closed-form solutions to the BS equations.

Keywords

• operator splitting method
• black–scholes equations
• option pricing
• finite difference method