Properties of range-based volatility estimators

Volatility is not directly observable and must be estimated. Estimator based on daily close data is imprecise. Range-based volatility estimators provide significantly more precision, but still remain noisy volatility estimates, something that is sometimes forgotten when these estimators are used in further calculations.First, we analyze properties of these estimators and find that the best estimator is the Garman-Klass (1980) estimator. Second, we correct some mistakes in existing literature. Third, the use of the Garman-Klass estimator allows us to obtain an interesting result: returns normalized by their standard deviations are approximately normally distributed. This result, which is in line with results obtained from high frequency data, but has never previously been recognized in low frequency (daily) data, is important for building simpler and more precise volatility models.