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

Leif Andersen and Jesper Andreasen

Review of Derivatives Research, 2000, vol. 4, issue 3, 262 pages

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

Keywords: jump-diffusion process; local time; forward equation; volatility smile; ADI finite difference method; fast Fourier transform (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1011354913068

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