A unified approach to volatility estimation in the presence of both rounding and random market microstructure noise

Widely used volatility estimation methods mainly consider one of the following two simple microstructure noise models: random additive noise on log prices, or pure rounding errors. Apparently in real data these two types of noise co-exist. In this paper, we discover a common feature of these two types of noise and propose a unified volatility estimation approach in the presence of both rounding and random noise. Our data-driven method enjoys superior properties in terms of bias and convergence rate. We establish feasible central limit theorems and show their superior performance via simulations. Empirical studies show clear advantages of our method when applied to both stocks data and currency exchange data.