Closed-form Solutions of the Time-fractional Standard Black-Scholes Model for Option Pricing using He-separation of Variable Approach

Abstract

The Black-Scholes option pricing model in classical form remains a benchmark model in Financial Engineering and Mathematics concerning option valuation. Though, it has received a series of modifications as regards its initial constancy assumptions. Most of the resulting modifications are nonlinear or time-fractional, whose exact or analytical solutions are difficult to obtain. This paper, therefore, presents exact (closed-form) solutions to the time-fractional classical Black-Scholes option pricing model by means of the He-Separation of Variable Transformation Method (HSVTM). The HSVTM combines the features of the He’s polynomials, the Homo-separation variable, the modified DTM, which increases the efficiency and effectiveness of the proposed method. The proposed method is direct and straight forward. Hence, it is recommended for obtaining solutions to financial models resulting from either Ito or Stratonovich Stochastic Differential Equations (SDEs).