Comparison of some finite difference methods for the Black-Scholes equation

Abstract

In this work, we use two numerical methods in order to solve the Black-Scholes equation with specified initial and boundary conditions. We use a classical finite difference scheme and an unconditionally positive definite scheme. The stability region is obtained in terms of an inequality involving the temporal step size. We compare the results from both methods at some different values of temporal step size by computing L1, L2 and L∞ errors.