High-Order Convergent Numerical Method for Pricing Asian Options Under Regime-Switching Model

In this paper, we study the fourth-order convergent finite difference method for solving a moving boundary partial differential equation (PDE) system of regime-switching Asian option pricing and conduct the convergence analysis in the discrete L∞-norm. First, the finite difference method is proposed for solving the PDE system and combined with the Richardson extrapolation scheme for improving the computational accuracy. Then the fourth-order convergence rates in both time and space are rigorously proved in the discrete L∞-norm. Numerical examples are presented to demonstrate the convergence results and show the effectiveness of the studied scheme.