Financial prices are often discretized�with smallest tick size of one
cent, for example. Thus prices involve rounding errors. Rounding
errors affect the estimation of volatility, and understanding them is
critical, particularly when using high frequency data. We study the
asymptotic behavior of realized volatility (RV), which is commonly used
as an estimator of integrated volatility. We prove the convergence
of the RV and scaled RV under varous 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. The simulation and empirical results demonstrate that
the proposed method can yield substantial statistical improvement.