  We propose nonparametric estimators of the occupation measure and the
occupation density of the diffusion coefficient (stochastic volatility) of a
discretely observed It\^{o} semimartingale on a fixed interval when the mesh of
the observation grid shrinks to zero asymptotically. In a first step we
estimate the volatility locally over blocks of shrinking length, and then in a
second step we use these estimates to construct a sample analogue of the
volatility occupation time and a kernel-based estimator of its density. We
prove the consistency of our estimators and further derive bounds for their
rates of convergence. We use these results to estimate nonparametrically the
quantiles associated with the volatility occupation measure.
