Robust Numerical Methods for Contingent Claims under Jump Diffusion Processes

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Robust Numerical Methods for Contingent Claims under Jump Diffusion Processes (2003)

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by Y. d'Halluin , P. A. Forsyth , K. R. Vetzal

Venue:	IMA Journal of Numerical Analysis
Citations:	52 - 15 self

BibTeX

@ARTICLE{d'Halluin03robustnumerical,
    author = {Y. d'Halluin and P. A. Forsyth and K. R. Vetzal},
    title = {Robust Numerical Methods for Contingent Claims under Jump Diffusion Processes},
    journal = {IMA Journal of Numerical Analysis},
    year = {2003},
    volume = {25},
    pages = {87--112}
}

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Abstract

An implicit method is developed for the numerical solution of option pricing models where it is assumed that the underlying process is a jump diffusion. This method can be applied to a variety of contingent claim valuations, including American options, various kinds of exotic options, and models with uncertain volatility or transaction costs. Proofs of timestepping stability and convergence of a fixed point iteration scheme are presented. For typical model parameters, it is shown that the fixed point iteration reduces the error by two orders of magnitude at each iteration. The correlation integral is computed using a fast Fourier transform (FFT) method. Techniques are developed for avoiding wrap-around effects. Numerical tests of convergence for a variety of options are presented.

Keyphrases

contingent claim jump diffusion process robust numerical method fixed point iteration numerical solution uncertain volatility wrap-around effect underlying process american option implicit method fast fourier transform transaction cost contingent claim valuation fixed point iteration scheme jump diffusion exotic option various kind correlation integral numerical test typical model parameter option pricing model

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