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


  • Conall O'Sullivan

    (University College Dublin)

  • Stephen O'Sullivan

    (Dublin Institute of Technology)


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.

Suggested Citation

  • Conall O'Sullivan & Stephen O'Sullivan, 2010. "Pricing Options under Heston’s Stochastic Volatility Model via Accelerated Explicit Finite Differencing Methods," Working Papers 201031, Geary Institute, University College Dublin.
  • Handle: RePEc:ucd:wpaper:201031

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    1. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
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    3. Charles A.M. de Bartolome, 2007. "Tax competition and the creation of redundant products," Canadian Journal of Economics, Canadian Economics Association, vol. 40(4), pages 1213-1236, November.
    4. Joni Hersch, 2005. "Smoking Restrictions as a Self-Control Mechanism," Journal of Risk and Uncertainty, Springer, vol. 31(1), pages 5-21, July.
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