Journal of Applied Mathematics

Fractional Black-Scholes Model and Technical Analysis of Stock Price

Song Xu and Yujiao Yang

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 631795, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808291

Digital Object Identifier
doi:10.1155/2013/631795

Mathematical Reviews number (MathSciNet)
MR3142570

Zentralblatt MATH identifier
06950790

Citation

Xu, Song; Yang, Yujiao. Fractional Black-Scholes Model and Technical Analysis of Stock Price. J. Appl. Math. 2013 (2013), Article ID 631795, 7 pages. doi:10.1155/2013/631795. https://projecteuclid.org/euclid.jam/1394808291


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