Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 25, Issue 1, Pages 87-112Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drh011
Keywords
jump diffusion; implicit discretization; iterative solution
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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.
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