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Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized Facts

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

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Identification Number: 10.1093/jjfinec/nbac035

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: 04 Dec 2024 21:21
URI: http://eprints.lse.ac.uk/id/eprint/123972

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