ADI schemes for valuing European options under the Bates model

TL;DR

This paper develops and analyzes three ADI schemes for numerically solving the Bates model's PIDEs in finance, focusing on stability and convergence through theoretical analysis and numerical experiments.

Contribution

It introduces three adapted ADI schemes for Bates model PIDEs and provides stability analysis and numerical validation of their effectiveness.

Findings

All three schemes are stable under certain conditions.

Numerical experiments confirm convergence and stability.

The schemes are effective for practical Bates model pricing.

Abstract

This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.