East Asian J. Appl. Math., 4 (2014), pp. 52-68.
Published online: 2018-02
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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 shift-invert matrix-vector product in each inner iteration. Numerical results show that our proposed scheme is more robust and efficient than the existing high accurate implicit-explicit Euler-based extrapolation scheme.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280313.061013a}, url = {http://global-sci.org/intro/article_detail/eajam/10820.html} }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 shift-invert matrix-vector product in each inner iteration. Numerical results show that our proposed scheme is more robust and efficient than the existing high accurate implicit-explicit Euler-based extrapolation scheme.