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 $n^1/4$, 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 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 time 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.

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

Livieri, Giulia;Marmi, Stefano
2022-01-01

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 $n^1/4$, 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 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 time 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.
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore SECS-P/01 - Economia Politica
Settore SECS-P/02 - Politica Economica
Settore SECS-P/06 - Economia Applicata
Settore SECS-P/05 - Econometria
Settore SECS-P/07 - Economia Aziendale
Settore SECS-P/08 - Economia e Gestione delle Imprese
Settore SECS-P/10 - Organizzazione Aziendale
Settore SECS-P/11 - Economia degli Intermediari Finanziari
Settore SECS-P/13 - Scienze Merceologiche
Settore SECS-P/12 - Storia Economica
Settore SECS-P/04 - Storia del Pensiero Economico
Settore SECS-S/01 - Statistica
Settore SECS-S/02 - Statistica per La Ricerca Sperimentale e Tecnologica
Settore SECS-S/03 - Statistica Economica
Settore SECS-S/04 - Demografia
Settore SECS-S/05 - Statistica Sociale
volatility of volatility; non-parametric estimation; central limit theorem; stochastic volatility; Fourier analysis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/125422
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