Pricing Options under Heston’s Stochastic Volatility Model via Accelerated Explicit Finite Differencing Methods

Conall O'Sullivan and Stephen O'Sullivan
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Conall O'Sullivan: University College Dublin
Stephen O'Sullivan: Dublin Institute of Technology

No 201031, Working Papers from Geary Institute, University College Dublin

Abstract: 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.

Pages: 41 pages
Date: 2010-06-29
New Economics Papers: this item is included in nep-cmp and nep-ore
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