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

Guangyu Fan () and Beibei Wu
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Guangyu Fan: School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, P. R. China
Beibei Wu: School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, P. R. China

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 11, 1-28

Abstract: 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 2−β in temporal directions, where β 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.

Keywords: Time-fractional Black–Scholes equation; cubic B-splines; improvised collocation method; von-Neumann; L2 and L∞ error norms (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183125500263

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