Fractional Black-Scholes Model and Technical Analysis of Stock Price

Abstract

In the stock market, some popular technical analysis indicators (e.g., Bollinger bands, RSI, ROC, etc.) are widely used to forecast the direction of prices. The validity is shown by observed relative frequency of certain statistics, using the daily (hourly, weekly, etc.) stock prices as samples. However, those samples are not independent. In earlier research, the stationary property and the law of large numbers related to those observations under Black-Scholes stock price model and stochastic volatility model have been discussed. Since the fitness of both Black-Scholes model and short-range dependent process has been questioned, we extend the above results to fractional Black-Scholes model with Hurst parameter $H>1/2$, under which the stock returns follow a kind of long-range dependent process. We also obtain the rate of convergence.