Pricing european and american options in the Heston 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, efficiency to benchmark implicit schemes. We conclude that STS accelerated methods are powerful numerical tools for the pricing of options which inherit the simplicity of explicit methods whilst achieving high accuracy at low computational cost and offer a compelling alternative to conventional implicit techniques.