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Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps

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  • Li, Yingying
  • Liu, Guangying
  • Zhang, Zhiyuan

Abstract

We establish a feasible central limit theorem with convergence rate n1/8 for the estimation of the integrated volatility of volatility (VoV) based on noisy high-frequency data with jumps. This is the first inference theory ever built for VoV estimation under such a general setup. The central limit theorem is applied to provide interval estimates of the VoV and conduct hypothesis tests. Furthermore, when one is interested in the null hypothesis that the VoV is zero, we show that a more powerful test can be established based on a VoV estimator with a convergence rate n1/5 under the null. Empirical results on the S&P 500 and individual stocks show strong evidence of non-zero VoV.

Suggested Citation

  • Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.
    • Handle: RePEc:eee:econom:v:229:y:2022:i:2:p:422-451
    DOI: 10.1016/j.jeconom.2021.02.007
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    Citations

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    Cited by:

    1. Carsten H. Chong & Viktor Todorov, 2023. "Asymptotic Expansions for High-Frequency Option Data," Papers 2304.12450, arXiv.org.
    2. Alessio Brini & Giacomo Toscano, 2024. "SpotV2Net: Multivariate Intraday Spot Volatility Forecasting via Vol-of-Vol-Informed Graph Attention Networks," Papers 2401.06249, arXiv.org, revised Jan 2025.
    3. Carsten H. Chong & Viktor Todorov, 2023. "Volatility of Volatility and Leverage Effect from Options," Papers 2305.04137, arXiv.org, revised Jan 2024.
    4. Wu, Xinyu & Zhao, An & Cheng, Tengfei, 2023. "A Real-Time GARCH-MIDAS model," Finance Research Letters, Elsevier, vol. 56(C).
    5. Claudiu Vințe & Marcel Ausloos, 2023. "Portfolio Volatility Estimation Relative to Stock Market Cross-Sectional Intrinsic Entropy," JRFM, MDPI, vol. 16(2), pages 1-24, February.
    6. 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 Jun 2024.
    7. Chong, Carsten H. & Todorov, Viktor, 2024. "Volatility of volatility and leverage effect from options," Journal of Econometrics, Elsevier, vol. 240(1).

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    More about this item

    Keywords

    Volatility of volatility; Central limit theorem; High frequency data; Microstructure noise; Semimartingale;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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