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Jumarie, G. (2010) Derivation and Solutions of Some Fractional Black-Scholes Equations in Coarse-Grained Space and Time. Application to Merton’s Optimal Portfolio. Computers & Mathematics with Applications, 59, 1142-1164.
https://doi.org/10.1016/j.camwa.2009.05.015

has been cited by the following article:

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

  AUTHORS: Xuebin Yang, Lifei Wu, Yu Zhang

  KEYWORDS: Time Fractional B-S Model, MASC-N Scheme, Stability, Convergence, Numerical Experiments

  JOURNAL NAME: Journal of Mathematical Finance, Vol.12 No.4, November 3, 2022

  ABSTRACT: 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.