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Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models

Published online by Cambridge University Press:  28 May 2015

Hong-Kui Pang  and
Hai-Wei Sun
Hong-Kui Pang*
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, China
Hai-Wei Sun*
Affiliation:
Department of Mathematics, University of Macau, Macao, China
*
Corresponding author. Email: [email protected]
Corresponding author. Email: [email protected]
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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 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.

Keywords

91B2862P0535K1565F1065M0691B7047B35Stochastic volatility jump diffusionEuropean optionbarrier optionpartial integro-differential equationmatrix exponentialshift-invert Arnoldimatrix splittingmultigrid method
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 1 , February 2014 , pp. 52 - 68
Copyright
Copyright © Global-Science Press 2014

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