A Laplace transform finite difference method for the Black-Scholes equation

Abstract

An efficient numerical method for solving the Black-Scholes equation is developed. Based on the adaptive numerical inverse Laplace transform and the finite difference method, the scheme computes the European option prices. The computational costs for the method are reduced significantly compared with those for the conventional time-marching schemes. The accuracy and the efficiency of the method are shown through the numerical simulations. (C) 2009 Elsevier Ltd. All rights reserved.