An efficient numerical method based on cubic B--splines for the time--fractional Black--Scholes European option pricing model

In this study, we develop a precise and effective numerical approach to solve the time--fractional Black--Scholes equation, which is used to calculate European options. The method employs cubic B-spline collocation for spatial discretization and a finite difference method for time discretization. An  analysis of the method's stability is conducted. Finally, two numerical examples are included to show the effectiveness and applicability of the suggested method.

Keywords:

Cubic B-spline , time-fractional , Black-Scholes , European option pricing model