The stochastic volatility jump diffusion model with jumps in both return and
volatility leads to a two-dimensional partial integro-differential equation (PIDE). We
exploit a fast exponential time integration scheme to solve this PIDE. After spatial discretization and temporal integration, the solution of the PIDE can be formulated as
the action of an exponential of a block Toeplitz matrix on a vector. The shift-invert
Arnoldi method is employed to approximate this product. To reduce the computational
cost, matrix splitting is combined with the multigrid method to deal with the shiftinvert
matrix-vector product in each inner iteration. Numerical results show that our
proposed scheme is more robust and efficient than the existing high accurate implicitexplicit Euler-based extrapolation scheme.