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,...

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 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...

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 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 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...

The estimation of the volatility with high-frequency data is plagued by the presence of microstructure noise, which leads to biased measures. Alternative estimators have been developed and tested either on specific structures of the noise or by the speed of convergence to their asymptotic...