Convergence rates of moving mesh methods for moving boundary partial integro-differential equations from regime-switching jump-diffusion Asian option pricing

摘要

This paper studies the convergence rates of moving mesh methods for a system of moving boundary partial integro-differential equations (PIDEs) which arise in the Asian option pricing under the state-dependent regime-switching jump-diffusion models. The value function of the Asian option under the model is governed by a system of two-dimensional PIDEs. In this paper, the two-dimensional PIDEs are recast into a one-dimensional moving boundary problem of the PIDEs. A moving finite difference method (FDM) is proposed to solve the one-dimensional moving boundary problem and the convergence rates are proved. Numerical examples are provided to confirm the theoretical results. (C) 2019 Elsevier B.V. All rights reserved.