Pricing options in new generalized fractional Black-Scholes model

Abstract

The recent introduction of significant features in conformable integrals and derivatives has paved the way for advancements in the field of fractional calculus [1-4]. This study provides a comprehensive exploration of this emerging area, with a particular focus on the various definitions and distinct fractional derivatives that have been proposed. Of particular interest is the concept of ?new conformable derivatives,? as introduced in [1], which we thoroughly investigate. (D?F)(t)=lim l?0 F(t+le(?-1)t-F(t)/l, where ? ? (0, 1], this derivative is explored in terms of its origin, unique characteristics, and how it com-pares to other conformable fractional derivatives. Furthermore, the study extends its analysis to the practical applications of these derivatives in financial mathematics. Specifically, we examine the construction of a new fractional Black-Scholes option pricing model, highlighting the potential of these mathematical tools in addressing complex problems in finance. This investigation not only enriches the theoretical framework of fractional calculus but also opens up new avenues for applying these concepts in real-world scenarios.