Truncated Realized Covariance when prices have infinite variation jumps

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