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

Payandehdoost Masouleh, Hamed; Esmailzadeh, Mojgan

doi:10.22124/jmm.2024.26551.2341

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

10.22124/jmm.2024.26551.2341

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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