A New Version of Black Scholes Equation Presented by Time-Fractional Derivative

Abstract

In this article, a new time-fractional-order Black–Scholes equation has been derived. In this derivation, the asset price satisfies in a fractional-order stochastic differential equation. Here, the effect of trend memory in financial pricing is considered. Finally, a new approximate analytical method has been used to solve our new proposed time-fractional Black–Scholes equation