A quantitative approach to fractional option pricing problems with decomposition series

Abstract

In this study, we get a novel identification of Adomian Decomposition Method (ADM) to have an accurate and quick solution for the European option pricing problem by using Black-Scholes equation of time-fractional order (FBSE) with the initial condition and generalized Black-Scholes equation of fractional order (GFBSE). The fractional operator is understood in the Caputo sense. First of all, we redefine the Black-Scholes equation as fractional mean which computes the option price for fractional values. Then we have applied the ADM to the FBSE and GFBSE, so we have obtained accurate and quick approximate analytical solutions for these equations. The results related to the solutions have been presented in figures.