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Bias optimal vol-of-vol estimation: the role of window overlapping

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  • Giacomo Toscano
  • Maria Cristina Recchioni

Abstract

We derive a feasible criterion for the bias-optimal selection of the tuning parameters involved in estimating the integrated volatility of the spot volatility via the simple realized estimator by Barndorff-Nielsen and Veraart (2009). Our analytic results are obtained assuming that the spot volatility is a continuous mean-reverting process and that consecutive local windows for estimating the spot volatility are allowed to overlap in a finite sample setting. Moreover, our analytic results support some optimal selections of tuning parameters prescribed in the literature, based on numerical evidence. Interestingly, it emerges that window-overlapping is crucial for optimizing the finite-sample bias of volatility-of-volatility estimates.

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  • Giacomo Toscano & Maria Cristina Recchioni, 2020. "Bias optimal vol-of-vol estimation: the role of window overlapping," Papers 2004.04013, arXiv.org, revised Jul 2021.
    • Handle: RePEc:arx:papers:2004.04013
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    1. Sanfelici, Simona & Toscano, Giacomo, 2024. "The Fourier–Malliavin Volatility (FMVol) MATLAB® library," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 338-353.
    2. Giacomo Toscano & Giulia Livieri & Maria Elvira Mancino & Stefano Marmi, 2021. "Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized facts," Papers 2112.14529, arXiv.org, revised Sep 2022.

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