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7 - Fractional Brownian Motions in Financial Econometrics

from Part II - Continuous-Time Models and High-Frequency Financial Econometrics

Published online by Cambridge University Press:  20 February 2025

Edited by
Shuping Shi ,
Xiaohu Wang  and
Tao Zeng
Shuping Shi
Affiliation:
Macquarie University, Sydney
Xiaohu Wang
Affiliation:
Fudan University, Shanghai
Tao Zeng
Affiliation:
Zhejiang University, China
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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.

Keywords

fractional Brownian motionlong-range dependencearbitrage opportunitiesfractional Vasicek modelrough volatility model
Type
Chapter
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Financial Econometrics
Theory and Applications
 , pp. 198 - 234
Publisher: Cambridge University Press
Print publication year: 2025

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