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

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  • Leif Andersen
  • Jesper Andreasen

Abstract

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

Suggested Citation

  • Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    • Handle: RePEc:kap:revdev:v:4:y:2000:i:3:p:231-262
    DOI: 10.1023/A:1011354913068
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