We analyze the properties of different estimators of multivariate volatilities in the presence of microstructure noise, with particular focus on the Fourier estimator. This estimator is consistent in the case of asynchronous data and robust to microstructure effects; further we prove the...

The finite sample properties of the Fourier estimator of integrated volatility under market microstructure noise are studied. Analytic expressions for the bias and the mean squared error (MSE) of the contaminated estimator are derived. These formulae can be practically used to design optimal...

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...