Simultaneous Two-Dimensional Continuous-Time Markov Chain Approximation of Two-Dimensional Fully Coupled Markov Diffusion Processes

Abstract

In this paper, we propose a novel simultaneous two-dimensional continuous-time Markov chain (CTMC) approximation method, in contrast to the existing double-layer approach, to approximate the general fully coupled Markov diffusion processes which cover all the classical models. Extensive simulation studies on different kinds of financial option pricing problems in the European, American, and barrier settings, confirm that the proposed methodology has superior accuracy and outperforms the widely applicable Monte Carlo (MC) simulation approach consistently.

Keywords: Finance, Option Pricing, Two-Dimensional Fully Coupled Markov Diffusion Processes, Continuous-Time Markov Chains

JEL Classification: 91G80, 93E11, 60J20