Stability of numerical methods under the regime-switching jump-diffusion model with variable coefficients

Abstract

In this paper we introduce three numerical methods to evaluate the prices of European, American, and barrier options under a regime-switching jump-diffusion model (RSJD model) where the volatility and other parameters are considered as variable coefficients. The prices of the European option, which is one of the financial derivatives, are given by a partial integro-differential equation (PIDE) problem and those of the American option are evaluated by solving a linear complementarity problem (LCP). The proposed methods are constructed to avoid the use of any fixed point iteration techniques at each state of the economy and time step. We analyze the stability of the proposed methods with respect to the discrete l2-norm in the time and spatial variables. A variety of numerical experiments are carried out to show the second-order convergence of the three numerical methods under the regime-switching jump-diffusion model with variable coefficients.