Analysing time-fractional exotic options via efficient local meshless method

Abstract

In this article, we analyse the numerical simulation of the time-fractional Black-Scholes model governing butterfly spread option, digital option and double barrier option. For this purpose, a local meshless collocation method based on multiquadric radial basis function is used. The model equation is discretized in the temporal sense by Liouville-Caputo fractional derivative scheme for 0 < beta < 1, whereas the space derivatives are discretized by the suggested meshless method. Numerical experiments are performed for butterfly spread option, digital option and double barrier option. Efficiency and accuracy of the proposed meshless method are assessed in terms of double mesh procedure since the exact solution of these options are not available. Furthermore, the greeks (delta and gamma) of the options are also computed.