Forecasting the behaviour of fractional Black-Scholes option pricing equation by laplace perturbation iteration algorithm

Abstract

Financial derivatives plays a major role in all financial deals these days. Black–Scholes option pricing model gives a risk free analysis for investing in options. In the current work, a method called the Laplace Perturbation Iteration Algorithm is being applied on Fractional Black–Scholes Equation to obtain its fractional analytical solutions in series form to analyze its results for the European and American option pricing problem, quickly and accurately. Laplace Perturbation Iteration Algorithm incorporates Laplace transform and Perturbation Iteration Algorithm and forms an iterative scheme that derives the analytical solutions without any inconvenience. The Fractional Black–Scholes Equation analytical solution is obtained as a convergent power series of conveniently computed components. Four examples have been solved and their results have been discussed in this paper, in order to check the efficacy of Laplace Perturbation Iteration Algorithm.