@Article{EAJAM-4-52,
author = {},
title = {Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {4},
number = {1},
pages = {52--68},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.280313.061013a},
url = {http://global-sci.org/intro/article_detail/eajam/10820.html}
}