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

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