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Compact IMEX scheme for a moving boundary PIDE system of the regime-switching jump-diffusion Asian option pricing

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Abstract

The aim of this paper is to develop a compact implicit-explicit (IMEX) difference scheme for solving a moving boundary partial integro-differential equation (PIDE) system of the regime-switching jump-diffusion Asian option pricing. First, the IMEX scheme is proposed for temporal discretization and combined with the compact difference scheme for spatial discretization. Then the unconditional stability, unique solvability, and convergence rates of second-order in time and fourth-order in space are proved in the discrete \(L^2\) and \(L^\infty \) norms. Numerical examples are given to demonstrate the theoretical results and show the effectiveness of the proposed scheme with respect to the efficiency and accuracy.

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Acknowledgements

The author is sincerely grateful to the editor and anonymous referees for their valuable comments that have led to a greatly improved paper.

Funding

The work was supported by Technology and Venture Finance Research Center of Sichuan Key Research Base for Social Sciences (Grant No. KJJR2019-003).

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  1. School of Economics, Xihua University, Chengdu, 610039, P.R. China

    Yong Chen

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  1. Yong Chen
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Chen, Y. Compact IMEX scheme for a moving boundary PIDE system of the regime-switching jump-diffusion Asian option pricing. Numer Algor 95, 1055–1077 (2024). https://doi.org/10.1007/s11075-023-01599-6

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