Rounding Errors and Volatility Estimation

Financial prices are often discretized to the nearest cent, for example. Thus we can say that prices are observed with rounding error. Rounding errors affect the estimation of volatility. Understanding them becomes important especially when we use high frequency data. In this setting, we study the asymptotic behavior of the Realized Volatility (RV), which is commonly used as an estimator of the integrated volatility. We prove the convergence of the RV and scaled RV under different conditions on the rounding level and the number of observations. A bias-corrected volatility estimator is proposed and an associated central limit theorem is shown. Simulation and empirical results show that the improvement in statistical properties can be substantial.