Robust numerical methods for contingent claims under jump diffusion processes

An implicit method is developed for the numerical solution ofoption pricing models where it is assumed that the underlyingprocess is a jump diffusion. This method can be applied to avariety of contingent claim valuations, including American options,various kinds of exotic options, and models with uncertain volatilityor transaction costs. Proofs of timestepping stability and convergenceof a fixed-point iteration scheme are presented. For typicalmodel parameters, it is shown the error is reduced by two ordersof magnitude at each iteration. The correlation integral iscomputed using a fast Fourier transform method. Numerical testsof convergence for a variety of options are presented.