Estimating the Integrated Volatility with Tick Observations

We develop a volatility estimator that can be directly applied to tick-by-tick data. More specifically, we consider a model that allows for (i) irregular observation times that can be endogenous, (ii) dependent noise that can have diurnal features and be dependent on the latent price process, and (iii) jumps in the latent price process. We show that our estimator yields consistent estimates and enjoys the optimal rate of convergence. Simulation as well as empirical studies demonstrate favorable properties of our proposed estimator