Domain truncation error analysis for a multidimensional system of PDEs of option prices

Abstract

This paper examines a multidimensional system of parabolic partial differential equations arising in European option pricing within a Markov-switching market model. To solve this numerically, the domain must be truncated, and artificial boundary conditions should be imposed. By deriving an estimate for the domain truncation error at all points in the truncated domain, we generalize existing results that address option pricing equations solely under no-switching scenarios. Unlike previous approaches, our method provides a sharper error estimate in specific regions of the domain. Combining the proposed estimate with the existing one yields a strictly improved result. Numerical examples are presented to provide a thorough comparison with the existing literature.