Abstract: This paper aims at the empirical statistical test of the long range dependence of Shanghai Composite Index and finishes statistical modeling for corresponding financial data and derives the valuation formula for European call option under the model we proposed. Theoretical analysis and numerical examples are given to illustrate the impact of the long range dependence on the option pricing by comparing the option valuation formula under fractional Brownian motion (fBm for short) model and the one under Black-Scholes model. The main statistics we adopted are R/S and modified R/S statistics. Numerical results show that the valuation formula under fBm are much more stable than the one under Black-Scholes model due to the former one has the long range dependence property.

Key words: Log-return rate, Long-range dependence, Classical Rescaled Range Analysis, Hurst Exponent, Fractional Brownian Motion