A Closed-Formula Characterization of the Epps Effect

In this study we provide an analytical characterization of the impact of zero returns on the popular realized covariance estimator of Barndorff-Nielsen and Shephard (2004). In our framework, efficient price processes evolve as a semimartingale with some likelihood of repeated prices. We show that the standard realized covariance estimator is asymptotically affected by a downward bias, and the size of the bias depends on these likelihoods. We demonstrate that this result can be used to construct a consistent estimator of the integrated covariance of a vector semimartingale. The advantages with respect to other estimators are discussed in data.