Black–Scholes option pricing equations described by the Caputo generalized fractional derivative

Abstract

Abstract Fractional Black–Scholes equation is a constructive financial equation. The model is used to determine the value of the option without a transaction cost. The analytical solutions of the fractional Black–Scholes equations have been addressed. The Caputo generalized fractional derivative has been used. The homotopy perturbation method has been developed for obtaining the analytical solutions of the fractional Black–Scholes equation (BSE) and the generalized fractionalBSE. The analytical solutions of the fractionalBSE and the generalized fractionalBSE have been represented graphically. The effect of the order ρ of the generalized fractional derivative in the diffusion processes has been analyzed.