Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

  • Ahmad GolbabaiEmail author
  • Omid Nikan
  • Touraj Nikazad


The price variation of the correlated fractal transmission system is used to deduce the fractional Black–Scholes model that has an \(\alpha \)-order time fractional derivative. The fractional Black–Scholes model is employed to price American or European call and put options on a stock paying on a non-dividend basis. Upon encountering fractional differential equations, the efficient and relatively reliable numerical schemes must be obtained for their solution due to fractional derivatives being non-local. The present paper is aimed at determining the numerical solution of the time fractional Black–Scholes model (TFBSM) with boundary conditions for a problem of European option pricing involved with the method of radial basis functions (RBFs), which is a truly meshfree scheme. The TFBSM is discretized in the temporal sense based on finite difference scheme of order \({\mathcal {O}}(\delta t^{2-\alpha })\) for \( 0< \alpha <1\) and approximated with the help of the RBF in the spatial derivative terms. In addition, the stability and convergence of the proposed method are theoretically proven. Numerical results illustrate the accuracy and efficiency of the presented technique which is examined in the present study.


Time fractional Black–Scholes model European option Radial basis functions Collocation methods Stability Convergence 

Mathematics Subject Classification

34K37 97N50 91G80 



The authors would like to express their sincere gratitude to the anonymous referees for their detailed comments and efforts to improve the original manuscript. The authors are also very much grateful to Editor-in-Chief (Prof. José E. Souza de Cursi), Associate Editor (Prof. José A. Tenreiro Machado) for their pursuances.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of MathematicsIran University of Science and TechnologyTehranIran

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