L^∞-norm convergence rates of an IMEX scheme for solving a partial integro-differential equation system arising from regime-switching jump-diffusion Asian option pricing

Abstract

The purpose of this paper is to rigorously prove $L^{\mathrm{\infty }}$-norm convergence rates of an implicit-explicit (IMEX) difference method called Crank-Nicolson-Leap-Frog (CN-LF) scheme for solving a partial integro-differential equation (PIDE) system with moving boundaries from the regime-switching jump-diffusion Asian option pricing. The IMEX scheme is employed to discretize the PIDE system. Then the unconditional stability, unique solvability and convergence of second-order rates in both time and space are rigorously proved in the sense of $L^{\mathrm{\infty }}$-norm. Finally, several numerical examples are conducted to verify the theory.

Keywords:

• Asian option pricing
• partial integro-differential equations
• regime-switching jump-diffusion models
• implicit-explicit finite difference methods
• $L^{\mathrm{\infty }}$-norm convergence rates

2020 Mathematics subject classifications:

• 45K05
• 65N12
• 91G60
• 91G20

Acknowledgments

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

Data availability statement

Not applicable as no datasets were used during the current study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by Technology and Venture Finance Research Center of Sichuan Key Research Base for Social Sciences [grant number KJJR2019-003].