Before revision:  Our estimate obtains minimax convergence rates, and is unaffected by arbitrary jump activity. Furthermore, it remains valid for the volatility in the general semimartingale model , obtaining convergence rates as good as any previously implied in the literature.
After revision:  Our estimate obtains minimax convergence rates, and is unaffected by infinite-variation jumps. In the semimartingale model, our estimate remains accurate for the normalised volatility , obtaining convergence rates as good as any previously implied in the literature.