Numerical methods for solving PIDEs arising in swing option pricing under a two-factor mean-reverting model with jumps

TL;DR

This paper develops and analyzes second-order numerical methods for solving complex two-dimensional PIDEs with jumps, arising in swing option pricing under a two-factor mean-reverting model, ensuring stability and convergence.

Contribution

It introduces robust second-order numerical schemes tailored for convection-dominated PIDEs with nonlocal terms and nonsmooth initial data in swing option valuation.

Findings

Numerical methods exhibit second-order convergence.

Methods are stable under challenging conditions.

Effective handling of jumps and nonsmooth data demonstrated.

Abstract

This paper concerns the numerical valuation of swing options with discrete action times under a linear two-factor mean-reverting model with jumps. The resulting sequence of two-dimensional partial integro-differential equations (PIDEs) are convection-dominated and possess a nonlocal integral term due to the presence of jumps. Further, the initial function is nonsmooth. We propose various second-order numerical methods that can adequately handle these challenging features. The stability and convergence of these numerical methods are analysed theoretically. By ample numerical experiments, we confirm their second-order convergence behaviour.