@Article{IJNAM-6-110,
author = {K. Zhang and S. Wang},
title = {A Computational Scheme for Options Under Jump Diffusion Processes},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2009},
volume = {6},
number = {1},
pages = {110--123},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/758.html}
}