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  • 7 - Fractional Brownian Motions in Financial Econometrics

  • from Part II - Continuous-Time Models and High-Frequency Financial Econometrics
  • Edited by Shuping Shi, Macquarie University, Sydney, Xiaohu Wang, Fudan University, Shanghai, Tao Zeng, Zhejiang University, China
  • Book:
    Financial Econometrics
    Published online:
    20 February 2025
    Print publication:
    27 February 2025, pp 198-234

  • Summary

    Fractional Brownian motion is a continuous-time zero mean Gaussian process with stationary increments. It has gained much attention in empirical finance and asset pricing. For example, it has been used to model the time series of volatility and interest rates. This chapter first introduces the basic properties of fractional Brownian motions and then reviews the statistical models driven by the fractional Brownian motions that have been used in financial econometrics such as the fractional Ornstein–Uhlenbeck model and the fractional stochastic volatility models. We also review the parameter estimation methods proposed in the literature. These methods are based on either continuous-time observations or discrete-time observations.