The speed of convergence of the Threshold estimator of integrated variance

In this paper we consider a semimartingale model for the evolution of the price of a financial asset, driven by a Brownian motion (plus drift) and possibly infinite activity jumps. Given discrete observations, the Threshold estimator is able to separate the integrated variance IV from the sum of the squared jumps. This has importance in measuring and forecasting the asset risks. In this paper we provide the exact speed of convergence of I V ˆ h , a result which was known in the literature only in the case of jumps with finite variation. This has practical relevance since many models used have jumps of infinite variation (see e.g. Carr et al. (2002) [4]).