Research on Fractional Option Pricing Model Under Real Brownian Motion Environment

Abstract

The self-similarity and long-range dependence properties make the fractional Brownian motion a suitable tool in mathematical finance. This paper uses the hypotheses that assert price follows geometric fractional Brownian motion to construct the ItA´ fractional Black-Scholes market. By the quasi-martingale method based on the fractional risk neutral measure, the fractional Black-Scholes model is given, which makes the original Black-Scholes equation being a special example. Then the fact that the long memory parameter is an important factor in option pricing is testified by a numerical case. Finally, two popular semiparametric methods are used to calculate the H value of Chinese stock markets.