Option Pricing Model Under Fractional Brownian Motion And Its Numerical Analysis

This paper is devoted to numerical investigation of a new model used in financial mathematics,which is derived based on fractional Brownian motion.The contents of the paper are as follows:Firstly,we recall the classical Black-Scholes equation stemming from a description using Brownian motion,and derive the time Caputo fractional Black-Scholes equation based on fractional Brownian motion of white noise.For ease of numerical investigation,the Mittal-Leffer function is applied to transform the original problem into an easy-to-handle problem by introducing intermediate variables.Furthermore,suitable artificial boundary conditions are deduced to truncate the unbounded domain into a bounded domain.Then we construct an efficient numerical method for numerical solutions of the transformed problem.The proposed method combines a high order finite difference scheme in time and spectral method in space.Stability analysis in time and error estimates in space are provided.Finally,we give several numerical examples to verify the theoretical claims.