Abstract
The speed of convergence of the truncated realized covariance to the integrated covariation between the Brownian parts of two semimartingales is heavily influenced by the presence of infinite activity jumps with infinite variation. Namely, the two small jumps processes play a crucial role through their degree of dependence, other than through their jump activity indices. This theoretical result is established when the marginal small jumps constitute alpha-stable processes and the semimartingales are observed discretely on a finite time horizon. The estimator in many (but not all) cases is less efficient than when the model only has finite variation jumps.The result of this paper is relevant in financial economics, since by the truncated realized covariance it is possible to separately estimate the common jumps among two assets, which has important implications in risk management and contagion modeling.
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