A numerical method for valuation of european option with regime-switching volatility and interest rate

Abstract

This paper develops a numerical method for pricing European options with regime-switching volatility and interest rate governed by the Black-Scholes equation. The method is based on a finite volume method with a spatial discretization and implicit time stepping technique. We show that the system matrix of the discretized system is an M-matrix and present an algorithm for solving the problem. Numerical experiment are implemented for some European option problems to illustrate the usefulness of this method.