Innovative Option Pricing Using the Conformable Black Scholes Model

Abstract

Fractional calculus has become an important tool in financial modeling due to its ability to capture memory effects and anomalous diffusion observed in financial markets. In this paper, we develop a fractional extension of the classical Black–Scholes option pricing model using the conformable fractional derivative. Owing to its local nature and preservation of key properties of classical differentiation, the conformable derivative allows for an analytically tractable and arbitrage-free framework. We derive the conformable fractional Black–Scholes partial differential equation, obtain closed-form solutions for European options, and provide a financial interpretation of the fractional order parameter.