L ∞-norm convergence rates of an IMEX scheme for solving a partial integro-differential equation system arising from regime-switching jump-diffusion Asian option pricing

Abstract

The purpose of this paper is to rigorously prove -norm convergence rates of an implicit-explicit (IMEX) difference method called Crank-Nicolson-Leap-Frog (CN-LF) scheme for solving a partial integro-differential equation (PIDE) system with moving boundaries from the regime-switching jump-diffusion Asian option pricing. The IMEX scheme is employed to discretize the PIDE system. Then the unconditional stability, unique solvability and convergence of second-order rates in both time and space are rigorously proved in the sense of -norm. Finally, several numerical examples are conducted to verify the theory.