The meshless local Petrov–Galerkin based on moving kriging interpolation for solving fractional Black–Scholes model

Abstract

In this paper, the fractional Black–Scholes equation in financial problem is solved by using the numerical techniques for the option price of a European call or European put under the Black–Scholes model. The MLPG and implicit finite difference method are used for discretizing the governing equation in option price and time variable, respectively. In MLPG method, the shape function is constructed by a moving kriging approximation. The Dirac delta function is chosen to be the test function. The numerical examples for varieties of variables are also included.

Keywords

• European option
• Fractional Black–Scholes equation
• MLPG
• Moving kriging interpolation