  In quantitative finance, we often model asset prices as semimartingales, with
drift, diffusion and jump components. The jump activity index measures the
strength of the jumps at high frequencies, and is of interest both in model
selection and fitting, and in volatility estimation. In this paper, we give a
novel estimate of the jump activity, together with corresponding confidence
intervals. Our estimate improves upon previous work, achieving near-optimal
rates of convergence, and good finite-sample performance in Monte-Carlo
experiments.
