NUMERICAL SOLUTION OF THE FRACTIONAL BLACK-SCHOLES MODEL

Abstract

Fractional-order models are widely used to describe phenomena exhibiting memory effects through fractional-order operators. In financial mathematics, the fractional Black-Scholes model extends the classical model by incorporating the influence of past values on the evolution of option prices. This model thus provides a better representation of the time dependence observed in financial markets. It is based on a fractional differential equation involving the risk-free interest rate, market volatility, the price of the underlying asset, and time. Several numerical methods exist for solving this model, and this Communicated by Youssri Hassan Youssri > paper proposes the use of the SBA method to obtain exact solutions for models with constant parameters and variable volatility. The analytical solutions obtained are expressed in terms of the Mittag-Leffler function \(E_{\alpha}\left(\beta \tau^{\alpha}\right), 0