TY - JOUR T1 - Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models JO - East Asian Journal on Applied Mathematics VL - 1 SP - 52 EP - 68 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.280313.061013a UR - https://global-sci.org/intro/article_detail/eajam/10820.html KW - Stochastic volatility jump diffusion, European option, barrier option, partial integro-differential equation, matrix exponential, shift-invert Arnoldi, matrix splitting, multigrid method. AB -

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.