Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models
نویسندگان
چکیده
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. AMS subject classifications: 91B28, 62P05, 35K15, 65F10, 65M06, 91B70, 47B35
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