A new iterative method based solution for fractional Black–Scholes option pricing equations (BSOPE)

Abstract

In this manuscript, a new expansion technique namely residual power series method is used for finding the analytical solution of the Fractional Black–Scholes equation with an initial condition for European option pricing problem. The Black–Scholes formula is important for estimating European call and put option on a non-dividend paying stock in particular when it contains time-fractional derivatives. The fractional derivative is defined in Caputo sense. This technique is based on fractional power series expansion. The convergence analysis of the present method is also deliberated. Example problems are given to examine the efficacy of the proposed method. Obtained solutions are compared with exact solutions solved by other techniques which demonstrate that the present method is robust and easy to implement for other fractional problems arising in science and engineering.