  The optimal rate of convergence of estimators of the integrated volatility,
for a discontinuous It\^{o} semimartingale sampled at regularly spaced times
and over a fixed time interval, has been a long-standing problem, at least when
the jumps are not summable. In this paper, we study this optimal rate, in the
minimax sense and for appropriate "bounded" nonparametric classes of
semimartingales. We show that, if the $r$th powers of the jumps are summable
for some $r\in[0,2)$, the minimax rate is equal to $\min(\sqrt{n},(n\log
n)^{(2-r)/2})$, where $n$ is the number of observations.
