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Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing

  • Leif Andersen
  • Jesper Andreasen
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    This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (PartialIntegro-Differential Equation) and demonstrates how this equationcan be used to fit the model to European option prices. For numerical pricing of general contingent claims, we develop an ADI finite difference method that is shown to be unconditionally stable and, if combined with Fast Fourier Transform methods, computationally efficient. The paper contains several detailed examples fromthe S&P500 market. Copyright Kluwer Academic Publishers 2000

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    File URL: http://hdl.handle.net/10.1023/A:1011354913068
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    Article provided by Springer in its journal Review of Derivatives Research.

    Volume (Year): 4 (2000)
    Issue (Month): 3 (October)
    Pages: 231-262

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    Handle: RePEc:kap:revdev:v:4:y:2000:i:3:p:231-262
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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    2. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
    3. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    4. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
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