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 - <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>