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

Document Type : Research Article

Authors

1 Department of Accounting, Bandaranzali Branch, Islamic Azad University, Bandaranzali, Iran

2 Department of Applied Mathematics, Bandaranzali Branch, Islamic Azad University, Bandaranzali, Iran

Abstract

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.

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References

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Journal of Mathematical Modeling
Volume 12, Issue 3
September 2024
Pages 405-417

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