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
2024
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.File | Dimensione | Formato | |
---|---|---|---|
2112.14529.pdf
Open Access dal 03/11/2024
Descrizione: Published source: https://academic.oup.com/jfec/advance-article/doi/10.1093/jjfinec/nbac035/6794250
Tipologia:
Accepted version (post-print)
Licenza:
Solo Lettura
Dimensione
773.05 kB
Formato
Adobe PDF
|
773.05 kB | Adobe PDF | |
nbac035.pdf
Accesso chiuso
Tipologia:
Published version
Licenza:
Non pubblico
Dimensione
1.1 MB
Formato
Adobe PDF
|
1.1 MB | Adobe PDF | Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.