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Black-Scholes Models with Inherited Time and Price Memory

In this study, we examine three Black-Scholes option pricing models with inherited time and assess price memories. In other words, we take into consideration the reliance of these models on both the current state and the history of changes. A solution in the form of a bivariate time-price fractional power series is proposed for these models to study the shared influence of the memory index in both the time and price values. The findings of this study agree with the existing solutions in the literature for the classical option pricing integerorder cases. Therefore, the suggested scheme is strongly recommended to study further memory indexed financial models.