Realized Covariance Tick-by-Tick in Presence of Rounded Time Stamps and General Microstructure Effects

This paper presents two classes of tick-by-tick covariance estimators adapted to the case of rounding in the price time stamps to a frequency lower than the typical arrival rate of tick prices. We investigate, through Monte Carlo simulations, the behavior of such estimators under realistic market microstructure conditions analogous to that of the financial data studied in the empirical section; that is, non-synchronous trading, general ARMA structure for microstructure noise, and true lead-lag cross-covariance. Simulation results show the robustness of the proposed tick-by-tick covariance estimators to time stamps rounding, and their overall performance superior to competing covariance estimators under empirically realistic microstructure conditions