Implicit cubic B-spline scheme for the fractional Black-Scholes model with Caputo-Hadamard derivative

In this study, we introduce a novel numerical scheme for solving the Black–Scholes equation endowed with a Caputo-Hadamard fractional time derivative. The temporal derivative is discretized via a finite-difference approach, ensuring both stability and high accuracy in capturing the model’s dynamics. For spatial discretization, we employ a cubic B-spline quasi-interpolation technique, which delivers a robust and efficient framework. A rigorous error analysis is carried out, establishing theoretical bounds that confirm the method’s reliability. Finally, we validate the proposed scheme through a series of numerical experiments, demonstrating its effectiveness in practical financial modeling and its ability to address the challenges posed by fractional differential equations.

کلیدواژه ها:

Caputo-Hadamard ، Black-Scholes ، Quasi-interpolation ، Spline