Computational modeling of the time-fractional Black–Scholes equations and its numerical solution using a fourth-order improvised cubic B-spline collocation method

In this paper, an improvised cubic B-spline method (ICSCM) for the time-fractional Black–Scholes model (TFBSM) governing European option pricing is presented. The numerical method utilizes the ICSCM for spatial discretization and employs a finite difference method for temporal discretization. Stability analysis of the scheme is performed using the von Neumann scheme. Also, the method is proved to be convergent of order [Formula: see text] in temporal directions, where [Formula: see text] is order of the fractional derivative. Three test examples verify the effectiveness and accuracy of the proposed method. Numerical and graphical results show that the results obtained by this method to solve the equation are in good agreement with the analytical solution, and achieve smaller error norms and perform better in numerical accuracy.