Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models
Year: 2014
East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 1 : pp. 52–68
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.280313.061013a
East Asian Journal on Applied Mathematics, Vol. 4 (2014), Iss. 1 : pp. 52–68
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Stochastic volatility jump diffusion European option barrier option partial integro-differential equation matrix exponential shift-invert Arnoldi matrix splitting multigrid method.
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