TY - JOUR
T1 - A Computational Scheme for Options Under Jump Diffusion Processes
AU - K. Zhang & S. Wang
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 110
EP - 123
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/758.html
KW - Jump diffusion processes, option pricing, finite volume method, integral partial differential equation, FFT.
AB - <p style="text-align: justify;">In this paper we develop two novel numerical methods for the
partial integral differential equation arising from the valuation of an option
whose underlying asset is governed by a jump diffusion process. These methods
are based on a fitted finite volume method for the spatial discretization, an
implicit-explicit time stepping scheme and the Crank-Nicolson time stepping
method. We show that the discretization methods are unconditionally stable
in time and the system matrices of the resulting linear systems are M-matrices.
The resulting linear systems involve products of a dense matrix and vectors and
an Fast Fourier Transformation (FFT) technique is used for the evaluation of
these products. Furthermore, a splitting technique is proposed for the solution
of the discretized system arising from the Crank-Nicolson scheme. Numerical
results are presented to show the rates of convergence and the robustness of
the numerical method.</p>