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Abstract
An implicit–explicit Euler scheme in temporal direction is employed to discretize a partial integro-differential equation, which arises in pricing options under jump-diffusion process. Then the semi-discretized equation is approximated in space by the Sinc–Galerkin method with exponential accuracy. Meanwhile, the domain decomposition method is incorporated to handle the non-smoothness of the payoff function, and the improved fast Gauss transform is applied to accelerate the evaluation of the jump integral term. An effective preconditioner is proposed for solving the resulting dense Toeplitz-related systems by the preconditioned generalized minimum residual (GMRES) method. Numerical tests are performed to illustrate the efficiency of the proposed algorithm.
Acknowledgements
The authors would like to thanks Spike T. Lee for plenty of insightful discussions and constructive suggestions on polishing this paper. The authors are also grateful to the anonymous referees for their useful comments and suggestions. The research was partially supported by the research grants 033/2009/A and 005/2012/A1 from FDCT of Macao, and MYRG206(Y1-L4)-FST11-SHW from University of Macau.