Operator splitting schemes for American options under the two-asset Merton jump-diffusion model

TL;DR

This paper develops and compares efficient operator splitting numerical schemes for pricing American options under a complex two-asset jump-diffusion model, focusing on convergence and performance in practical computations.

Contribution

It adapts and evaluates various operator splitting schemes, including IMEX and ADI types, for solving the two-dimensional PIDCP in American option pricing under jump-diffusion.

Findings

Schemes effectively handle nonlocal integral terms explicitly.

Numerical experiments demonstrate convergence and efficiency.

Performance varies with different splitting and penalty methods.

Abstract

This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model. We consider the adaptation of various operator splitting schemes of both the implicit-explicit (IMEX) and the alternating direction implicit (ADI) kind that have recently been studied for partial integro-differential equations (PIDEs) in [3]. Each of these schemes conveniently treats the nonlocal integral part in an explicit manner. Their adaptation to PIDCPs is achieved through a combination with the Ikonen-Toivanen splitting technique [14] as well as with the penalty method [32]. The convergence behaviour and relative performance of the acquired eight operator splitting methods is investigated in extensive numerical experiments for American put-on-the-min and put-on-the-average options.