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Zbl 1134.91405
D'Halluin, Y.; Forsyth, P.A.; Vetzal, K.R.
Robust numerical methods for contingent claims under jump diffusion processes. (English)
[J] IMA J. Numer. Anal. 25, No. 1, 87-112 (2005). ISSN 0272-4979; ISSN 1464-3642/e

Summary: 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 the error is reduced by two orders of magnitude at each iteration. The correlation integral is computed using a fast Fourier transform method. Numerical tests of convergence for a variety of options are presented.

MSC 2000:: *91B28 Finance etc.
65M06 Finite difference methods (IVP of PDE)

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