TY - JOUR
T1 - Finite Volume Method for Pricing European and American Options under Jump-Diffusion Models
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 227
EP - 247
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.260316.061016a
UR - https://global-sci.org/intro/article_detail/eajam/10747.html
KW - Finite volume method, option pricing, jump-diffusion models, linear complementarity
problems, GMRES method, modulus-based successive overrelaxation method.
AB - <p style="text-align: justify;">A class of finite volume methods is developed for pricing either European or
American options under jump-diffusion models based on a linear finite element space.
An easy to implement linear interpolation technique is derived to evaluate the integral
term involved, and numerical analyses show that the full discrete system matrices are
M-matrices. For European option pricing, the resulting dense linear systems are solved
by the generalised minimal residual (GMRES) method; while for American options the
resulting linear complementarity problems (LCP) are solved using the modulus-based
successive overrelaxation (MSOR) method, where the $H_+$-matrix property of the system
matrix guarantees convergence. Numerical results are presented to demonstrate the
accuracy, efficiency and robustness of these methods.</p>