Stability of central finite difference schemes for the Heston PDE

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 semidiscrete systems with nonnormal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments. We also apply the analysis to obtain useful stability bounds for time discretization methods.