TITLE:
Exact Solution of Fractional Black-Scholes European Option Pricing Equations
AUTHORS:
Maryeme Ouafoudi, Fei Gao
KEYWORDS:
Homotopy Perturbation Method, Modified Homotopy Perturbation Method, Sumudu Transform, Black-Scholes Equations
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.1,
January
30,
2018
ABSTRACT: We introduce two algorithms in order to find the exact solution of the nonlinear
Time-fractional Partial differential equation, in this research work. Those
algorithms are proposed in the following structure: The Modified Homotopy
Perturbation Method (MHPM), The Homotopy Perturbation and Sumudu
Transform Method. The results achieved using the both methods are the
same. However, we calculate the approached theoretical solution of the
Black-Scholes model in the form of a convergent power series with a regularly
calculated element. Finally, we propose a descriptive example to demonstrate
the efficiency and the simplicity of the methods.