Truncated Realized Covariance when prices have infinite variation jumps

The speed of convergence of the Truncated Realized Covariance (TRC) to the Integrated Covariationbetween the Brownian parts of two semimartingales is heavily influenced by the presence of infiniteactivity jumps with infinite variation (iV), through both the degree of dependence and the jump activityindices of the two small jumps processes. To show this, marginal stable small jumps with a parametricdependence structure are considered. The estimator is efficient only when the iV jumps have moderateactivity.The results presented in this paper are relevant to financial economics, since through the TRC it ispossible to separately estimate the common jumps between two assets, which has important implications inrisk management and contagion modeling.