The main contribution of the paper is proving that the Fourier spot volatility estimator introduced in [Malliavin and Mancino, 2002] is consistent and asymptotically efficient if the price process is contaminated by microstructure noise. Specifically, in the presence of additive microstructure...

We empirically investigate the functional link between the variance swap rate and the spot variance. Using S&P500 data over the period 2006-2018, we find overwhelming empirical evidence supporting the affine link analytically found by Kallsen et al. (2011) in the context of exponentially affine...

We derive a feasible criterion for the bias-optimal selection of the tuning parameters involved in estimating the integrated volatility of the spot volatility via the simple realized estimator by Barndorff-Nielsen and Veraart (2009). Our analytic results are obtained assuming that the spot...

We prove a Central Limit Theorem for two estimators of the leverage process based on the Fourier method of [Malliavin and Mancino, 2009], showing that they reach the optimal rate 1/4 and a smaller variance with respect to different estimators based on a pre-estimation of the instantaneous...

We study the sensitivity of the leverage effect to changes in the volatilityand the price, showing the existence of an analytical link between the latterand the price-leverage covariation in settings with, respectively, stochasticand level-dependent volatility. From the financial standpoint, the...

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 1/4, while the estimator without...

We propose a novel stochastic volatility model with price and volatility co-jumps driven by Hawkes processes and develop a feasible maximum-likelihood based procedure to estimate the parameters driving the jump intensity. Using S&P500 high-frequency prices over the period May 2007 - August 2021,...