Abstract

Abstract- In this paper, we develop a fast numerical scheme for computing the European option pricing problems governed by the Black-Scholes equation. We prove that the proposed scheme has second order accuracy in both time and space. Under some restrictions, the stability of the proposed method in the sense of Von Neumann analysis is presented. It is shown that the proposed scheme has a good performance in the sense of the computational cost compare to the Crank-Nicolson scheme. Also the accuracy of the proposed scheme is better than the semi-implicit scheme in most cases. Index Terms- Black-Scholes equation, European option pricing, asymmetric scheme, stability analysis, numerical example