Stability of central finite difference schemes for the Heston PDE

TL;DR

This paper investigates the stability of central finite difference schemes for the Heston PDE, providing rigorous bounds and numerical validation for their stability in financial modeling.

Contribution

It offers the first rigorous stability bounds for central second-order finite difference discretizations of the Heston PDE using the logarithmic spectral norm.

Findings

Stability bounds are established for the discretization scheme.

Numerical experiments confirm the theoretical stability results.

The approach applies to large semi-discrete systems with non-normal matrices.

Abstract

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments.