A New Parallel Difference Method for Solving Time Fractional Black-Scholes Model

A modified Black-Scholes (B-S) model with time fractional derivative is studied when the price change of the underlying is considered as a fractal transmission system.It is very practical in application to study the numerical computation of this time fractional B-S model (TFBSM) governing European options.This paper constructs mixed alternative segment Crank-Nicolson (MASC-N) parallel difference scheme, which accuracy is spatially 2 order and temporally 2-α order.In addition, we have provided a theoretical proof for the stability and convergence of the MASC-N scheme, and demonstrated the accuracy and effectiveness of the proposed method through numerical experiments.The numerical results show that the MASC-N scheme is easy to implement when applied to time fractional B-S model.