TY - JOUR
T1 - A Second Order Numerical Scheme for Fractional Option Pricing Models
AU - Zhang , Ling-Xi
AU - Peng , Ren-Feng
AU - Yin , Jun-Feng
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 326
EP - 348
PY - 2021
DA - 2021/02
SN - 11
DO - http://doi.org/10.4208/eajam.020820.121120
UR - https://global-sci.org/intro/article_detail/eajam/18637.html
KW - Lévy process, fractional partial differential equation, option pricing, finite difference,
stock index option.
AB - <p style="text-align: justify;">A number of fractional option models (FMLS, CGMY, KoBol) are proposed
and studied under assumption that the motion of the underlying assets follows a Lévy
process. Numerical methods for these option pricing models are based on solution of
fractional partial differential equations. To discretise them, we employ a second order
numerical scheme and study its stability and convergence. Numerical experiments show
the efficiency of the method and its convergence. Simulations related to practical stock
markets, further confirm the robustness of the scheme and show that KoBol model has
advantage over the classical Black-Scholes model.</p>