Pricing European and American options under Heston's stochastic volatility model with accelerated explicit finite differencing methods

We present an acceleration technique, effective for explicit finite difference schemes
describing diffusive processes with nearly symmetric operators, called Super-Time-
Stepping (STS). The technique is applied to the two-factor problem of option pricing
under stochastic volatility. It is shown to significantly reduce the severity of the stability
constraint known as the Courant-Friedrichs-Lewy condition whilst retaining the
simplicity of the chosen underlying explicit method.
For European and American put options under Heston’s stochastic volatility model
we demonstrate degrees of acceleration over standard explicit methods sufficient to
achieve comparable, or superior, efficiencies to a benchmark implicit scheme. We conclude
that STS is a powerful tool for the numerical pricing of options and propose them
as the method-of-choice for exotic financial instruments in two and multi-factor models.