Volume 4, Issue 1
Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models

Hong-Kui Pang and Hai-Wei Sun

10.4208/eajam.280313.061013a

East Asian J. Appl. Math., 4 (2014), pp. 52-68.

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  • 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 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.

  • History

Published online: 2018-02

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