Volatility of Volatility Estimation: Central Limit Theorems for the Fourier Transform Estimator and Empirical Study of the Daily Time Series Stylized Facts
研究了基于傅里叶方法的两种可行波动率波动率估计量的渐近正态性，证明了偏差校正估计量达到最优收敛速度，并用该估计量重构了S&P500和EUROSTOXX50指数的日波动率波动率序列，揭示了其动态的典型事实。
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.