Convergence rate of the Truncated Realized Covariance when prices have infinite variation jumps.

In this paper we consider two processes driven by Brownian motions plus drift and jumps with infinite activity. Given discrete observations on a finite time horizon, we study the truncated (threshold) realized covariance \hat{IC} to estimate the integrated covariation IC between the two Brownian parts and we establish how fast \hat{IC} converges when the small jumps of the processes are Lévy. We find that the speed is heavily influenced by the small jumps dependence structure other than by their jump activity indices. This work follows Mancini and Gobbi (2011) and Jacod (2008), where the asymptotic normality of \hat{IC} was obtained when the jump components have finite activity or finite variation. Separating the sources of covariation (IC and co-jumps) of two financial assets has important applications in portfolio risk management.