Fourth‐order compact scheme with local mesh refinement for option pricing in jump‐diffusion model

The value of a contingent claim under a jump‐diffusion process satisfies a partial integro‐differential equation. A fourth‐order compact finite difference scheme is applied to discretize the spatial variable of this equation. It is discretized in time by an implicit‐explicit method. Meanwhile, a local mesh refinement strategy is used for handling the nonsmooth payoff condition. Moreover, the numerical quadrature method is exploited to evaluate the jump integral term. It guarantees a Toeplitz‐like structure of the integral operator such that a fast algorithm is feasible. Numerical results show that this approach gives fourth‐order accuracy in space. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011