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

A remark on the rates of convergence for integrated volatility estimation in the presence of jumps