Towards a Better Understanding of Fractional Brownian Motion and Its Application to Finance

The aim of this work is to first build the underlying theory behind fractional Brownian motion and applying fractional Brownian motion to financial market. By incorporating the Hurst parameter into geometric Brownian motion in order to characterize the long memory among disjoint increments, geometric fractional Brownian motion model is constructed to model S &P 500 stock price index. The empirical results show that the fitting effect of fractional Brownian motion model is better than ordinary Brownian motion.