TY - JOUR
ID - 10335
TI - A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Rezaei Mirarkolaei, Maryam
AU - Yazdanian, Ahmadreza
AU - Mahmoudi, Seyed Mahdi
AU - Ashrafi, Ali
AD - Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.
AD - Faculty of Finance Sciences
Kharazmi University, Tehran, Iran.
AD - Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Y1 - 2021
PY - 2021
VL - 9
IS - 2
SP - 523
EP - 552
KW - CEV model
KW - Time-dependent parameters
KW - Option pricing
KW - American option
KW - Fractional BlackScholes equation
KW - Compact difference scheme
DO - 10.22034/cmde.2020.36000.1623
N2 - The Black-Scholes equation is one of the most important mathematical models in option pricing theory, but this model is far from market realities and cannot show memory effect in the financial market. This paper investigates an American option based on a time-fractional Black-Scholes equation under the constant elasticity of variance (CEV) model, which parameters of interest rate and dividend yield supposed as deterministic functions of time, and the price change of the underlying asset follows a fractal transmission system. This model does not have a closed-form solution; hence, we numerically price the American option by using a compact difference scheme. Also, we compare the time-fractional Black-Scholes equation under the CEV model with its generalized Black-Scholes model as α = 1 and β = 0. Moreover, we demonstrate that the introduced difference scheme is unconditionally stable and convergent using Fourier analysis. The numerical examples illustrate the efficiency and accuracy of the introduced difference scheme.
UR - https://cmde.tabrizu.ac.ir/article_10335.html
L1 - https://cmde.tabrizu.ac.ir/article_10335_264b729cd71d9f412f817b6d5634349e.pdf
ER -