# Operator splitting schemes for the two-asset Merton jump-diffusion model

## TL;DR

This paper develops and compares seven operator splitting schemes for efficiently solving the complex two-asset Merton jump-diffusion PIDE, enabling accurate valuation of rainbow options with nonlocal and mixed derivative features.

## Contribution

It introduces and evaluates seven novel operator splitting schemes tailored for the two-asset Merton jump-diffusion PIDE, enhancing numerical stability and efficiency.

## Key findings

- Seven schemes exhibit stable convergence in numerical experiments.
- Explicit treatment of the integral part improves computational efficiency.
- Performance varies depending on option type and scheme choice.

## Abstract

This paper deals with the numerical solution of the two-dimensional time-dependent Merton partial integro-differential equation (PIDE) for the values of rainbow options under the two-asset Merton jump-diffusion model. Key features of this well-known equation are a two-dimensional nonlocal integral part and a mixed spatial derivative term. For its efficient and stable numerical solution, we study seven recent and novel operator splitting schemes of the implicit-explicit (IMEX) and the alternating direction implicit (ADI) kind. Here the integral part is always conveniently treated in an explicit fashion. The convergence behaviour and the relative performance of the seven schemes are investigated in ample numerical experiments for both European put-on-the-min and put-on-the-average options.