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

Anindya Goswami and Kuldip Singh Patel

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 236, issue C, 354-378

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.

Keywords: Markov-switching market model; Existence and uniqueness of solution; Theory of system of PDEs; Domain truncation error estimates (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:236:y:2025:i:c:p:354-378

DOI: 10.1016/j.matcom.2025.04.002

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