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

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  • Carsten Chong
  • Thomas Delerue
  • Guoying Li

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 It\^o 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.

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  • Carsten Chong & Thomas Delerue & Guoying Li, 2021. "When Frictions are Fractional: Rough Noise in High-Frequency Data," Papers 2106.16149, arXiv.org, revised Apr 2022.
    • Handle: RePEc:arx:papers:2106.16149
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    Cited by:

    1. Carsten Chong & Marc Hoffmann & Yanghui Liu & Mathieu Rosenbaum & Gr'egoire Szymanski, 2022. "Statistical inference for rough volatility: Central limit theorems," Papers 2210.01216, arXiv.org, revised Jul 2023.
    2. Carsten Chong & Viktor Todorov, 2022. "Short-time expansion of characteristic functions in a rough volatility setting with applications," Papers 2208.00830, arXiv.org.

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