We provide a set of probabilistic laws for range-based estimation of integrated variance
of a continuous semi-martingale. To accomplish this, we exploit the properties of the price
range as a volatility proxy and suggest a new method for non-parametric measurement
of return variation. Assuming the entire sample path realization of the log-price process
is available - and given weak technical conditions - we prove that the high-low statistic
converges in probability to the integrated variance. Moreover, with slightly stronger condi-
tions, in particular a zero drift-term, we ¯nd an asymptotic distribution theory. To relax
the mean-zero constraint, we modify the estimator using an adjusted range. A weak law
of large numbers and central limit theorem is then derived under more general assump-
tions about drift. In practice, inference about integrated variance is drawn from discretely
sampled data. Here, we split the sampling period into sub-intervals containing the same
number of price recordings and estimate the true range. In this setting, we also prove
consistency and asymptotic normality. Finally, we analyze our framework in the presence
of microstructure noise.
JEL Classification: C10; C22; C80
