TY - JOUR
T1 - Fitted Finite Volume Method for Pricing American Options under Regime-Switching Jump-Diffusion Models Based on Penalty Method
AU - Gan , Xiaoting
AU - Yin , Jun-Feng
AU - Li , Rui
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 748
EP - 773
PY - 2020
DA - 2020/04
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0017
UR - https://global-sci.org/intro/article_detail/aamm/16422.html
KW - American option pricing, regime-switching jump-diffusion model, complementarity problem, fitted finite volume method, Penalty method.
AB - <p style="text-align: justify;">In this paper we develop a novel numerical method for pricing American options under regime-switching jump-diffusion models which are governed by a system of partial integro-differential complementarity problems (PIDCPs). Based on a penalty approach, the PIDCPs results in a set of coupled nonlinear partial integro-differential equations (PIDEs). To numerically solve these nonlinear penalized PIDEs, we introduce a fitted finite volume method for the spatial discretization, coupled with the backward Euler and Crank-Nicolson time stepping schemes. We show that these schemes are consistent, stable and monotone, hence it ensures the convergence to the solution of continuous problem. To solve the discretized nonlinear system effectively, an iterative method is designed. Numerical experiments are presented to demonstrate the accuracy, efficiency and robustness of the new numerical method.</p>