We study the asymptotic normality of two 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 $n^{1/4}$, 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 Fourier estimator in comparison with a rate-optimal estimator based on the pre-estimation of the spot volatility. Finally, we reconstruct the daily volatility of volatility of the S&P500 and EUROSTOXX50 indices over long samples via the rate-optimal Fourier estimator and provide novel insight into the existence of stylized facts about its dynamics.

Volatility of volatility estimation: central limit theorems for the Fourier transform estimator and empirical study of the daily time series stylized facts / Giacomo Toscano; Giulia Livieri; Maria Elvira Mancino; Stefano Marmi. - In: JOURNAL OF FINANCIAL ECONOMETRICS. - ISSN 1479-8409. - ELETTRONICO. - (2022), pp. 0-0. [10.1093/jjfinec/nbac035]

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

Giacomo Toscano
;
Giulia Livieri;Maria Elvira Mancino;Stefano Marmi
2022

Abstract

We study the asymptotic normality of two 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 $n^{1/4}$, 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 Fourier estimator in comparison with a rate-optimal estimator based on the pre-estimation of the spot volatility. Finally, we reconstruct the daily volatility of volatility of the S&P500 and EUROSTOXX50 indices over long samples via the rate-optimal Fourier estimator and provide novel insight into the existence of stylized facts about its dynamics.
2022
0
0
Giacomo Toscano; Giulia Livieri; Maria Elvira Mancino; Stefano Marmi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1280939
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