Toscano, Giacomo, Livieri, Giulia 
ORCID: 0000-0002-3777-7329, Mancino, Maria Elvira and Marmi, Stefano
(2022)
Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized Facts.
Journal of Financial Econometrics, 22 (1).
252 - 296.
ISSN 1479-8409
Abstract
We study the asymptotic normality of two feasible estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected estimator reaches the optimal rate n1=4, while the estimator without bias-correction has a slower convergence rate and a smaller asymptotic variance. Additionally, we provide simulation results that support the theoretical asymptotic distribution of the rate-efficient estimator and show the accuracy of the latter in comparison with a rate-optimal estimator based on the pre-estimation of the spot volatility. Finally, using the rate-optimal Fourier estimator, we reconstruct the series of the daily volatility of volatility of the S&P500 and EUROSTOXX50 indices over long samples and provide novel insight into the existence of stylized facts about the volatility of volatility dynamics.
| Item Type: | Article |
|---|---|
| Official URL: | https://academic.oup.com/jfec |
| Additional Information: | © The Author(s) 2022. Published by Oxford University Press. All rights reserved. |
| Divisions: | LSE |
| Subjects: | H Social Sciences > HB Economic Theory H Social Sciences > HG Finance |
| Date Deposited: | 25 Jun 2024 15:06 |
| Last Modified: | 15 Feb 2025 22:54 |
| URI: | http://eprints.lse.ac.uk/id/eprint/123972 |
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