On the numerical solution of time fractional Black-Scholes equation

Abstract

In this study, we provide a numerical method to approximate the solution of the time fractional Black-Sholes equation by applying the multiquadric (MQ) quasi-interpolation scheme and the integrated radial basis function networks scheme. In the present approach, quadrature formula is used to discretize the temporal Caputo fractional derivative and the integrated form of the MQ quasi-interpolation scheme is used for approximation of the unknown function and its spatial derivatives. In order to show the accuracy and efficiency of the presented method, the $L_{\mathrm{\infty }}$, $L_2$ errors of several experiments are considered. Our numerical results are compared with the exact solutions as well as the results obtained from the other numerical schemes.

Keywords:

• Time fractional partial differential equation
• Multiquadric quasi-interpolation scheme
• Radial basis function
• Black-Scholes equation
• Meshless method

2020 Mathematics Subject Classifications:

• 34K37
• 97N50

Acknowledgements

The authors are grateful to the two anonymous referees and the editor-in-chief for their constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).