When Frictions are Fractional: Rough Noise in High-Frequency Data

59 Pages Posted: 8 Jul 2021 Last revised: 11 Apr 2022

See all articles by Carsten Chong

Carsten Chong

Columbia University - Department of Statistics

Thomas Delerue

Technische Universität München (TUM) - Department of Mathematics

Guoying Li

affiliation not provided to SSRN

Date Written: April 10, 2022

Abstract

The analysis of high-frequency financial data is often impeded by the presence of noise. This article is motivated by intraday transactions data in which market microstructure noise appears to be rough, that is, best captured by a continuous-time stochastic process that locally behaves as fractional Brownian motion. Assuming that the underlying efficient price process follows a continuous Itô semimartingale, we derive consistent estimators and asymptotic confidence intervals for the roughness parameter of the noise and the integrated price and noise volatilities, in all cases where these quantities are identifiable. In addition to desirable features such as serial dependence of increments, compatibility between different sampling frequencies and diurnal effects, the rough noise model can further explain divergence rates in volatility signature plots that vary considerably over time and between assets.

Keywords: Hurst parameter, market microstructure noise, mixed fractional Brownian motion, mixed semimartingales, volatility estimation, volatility signature plot.

JEL Classification: C13, C14, C51, C55, C58

Suggested Citation

Chong, Carsten and Delerue, Thomas and Li, Guoying, When Frictions are Fractional: Rough Noise in High-Frequency Data (April 10, 2022). Available at SSRN: https://ssrn.com/abstract=3878809 or http://dx.doi.org/10.2139/ssrn.3878809

Carsten Chong (Contact Author)

Columbia University - Department of Statistics ( email )

3022 Broadway
New York, NY 10027
United States

Thomas Delerue

Technische Universität München (TUM) - Department of Mathematics ( email )

Boltzmannstr. 3
Garching bei München, Bavaria 85748
Germany

Guoying Li

affiliation not provided to SSRN

No Address Available

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