Instabilities of Super-Time-Stepping Methods on the Heston Stochastic Volatility Model

TL;DR

This paper investigates the instabilities of explicit super-time-stepping methods, like Runge-Kutta-Chebyshev and Runge-Kutta-Legendre, when applied to the Heston stochastic volatility model, highlighting broader stability concerns.

Contribution

It provides a detailed analysis of the stability issues of super-time-stepping schemes on the Heston model, extending understanding beyond existing literature.

Findings

Identifies specific instability conditions for super-time-stepping methods

Highlights relevance of stability issues beyond super-time-stepping schemes

Provides insights for improving numerical stability in stochastic volatility models

Abstract

This note explores in more details instabilities of explicit super-time-stepping schemes, such as the Runge-Kutta-Chebyshev or Runge-Kutta-Legendre schemes, noticed in the litterature, when applied to the Heston stochastic volatility model. The stability remarks are relevant beyond the scope of super-time-stepping schemes.