Identifying the Brownian Covariation From the Co-Jumps Given Discrete Observations

Abstract

When the covariance between the risk factors of asset prices is due to both Brownian and jump components, the realized covariation (RC) approaches the sum of the integrated covariation (IC) with the sum of the co-jumps, as the observation frequency increases to infinity, in a finite and fixed time horizon. In this paper the two components are consistently separately estimated within a semimartingale framework with possibly infinite activity jumps. The threshold (or truncated) estimator $I\hat C_n $ is used, which substantially excludes from RC all terms containing jumps. Unlike in Jacod (2007, Universite de Paris-6) and Jacod (2008, Stochastic Processes and Their Applications 118, 517–559), no assumptions on the volatilities’ dynamics are required. In the presence of only finite activity jumps: 1) central limit theorems (CLTs) for $I\hat C_n $ and for further measures of dependence between the two Brownian parts are obtained; the estimation error asymptotic variance is shown to be smaller than for the alternative estimators of IC in the literature; 2) by also selecting the observations as in Hayashi and Yoshida (2005, Bernoulli 11, 359–379), robustness to nonsynchronous data is obtained. The proposed estimators are shown to have good finite sample performances in Monte Carlo simulations even with an observation frequency low enough to make microstructure noises’ impact on data negligible.

Large and moderate deviations of realized covolatility

“…Here we do not consider the asynchronous case. In the bivariate case we also mention the work of Mancini and Gobbi [9] which deal with the problem of distinguishing the Brownian covariation from the co-jumps using a discrete set of observations.…”

Disentangled Jump-Robust Realized Covariances and Correlations with Non-Synchronous Prices

“…The aggregation scheme can be used with different versions of the cumulative covariance estimator as, for example, the thresholds realized covariances of Mancini and Gobbi (2012). However, the class of DRC does not map naturally into the construction of aggregated returns and hence we only apply it to the realized covariances of Andersen et al (2003) and the thresholds realized covariances of Mancini and Gobbi (2012).…”

“…Following Mancini and Gobbi (2012), RC and TC are implemented with the pseudo-aggregation scheme proposed by Hayashi and Yoshida (2005);…”

“…bipower variation (Barndorff-Nielsen and Shephard (2004b)), quantile-based realized variances (Christensen et al (2010b)), and MinRV and MedRV (Andersen et al (2012)). In the multivariate case, bipower covariations are proposed in Barndorff-Nielsen and Shephard (2004a), thresholds covariances in Mancini and Gobbi (2012), outlyingness weighted covariances in Boudt et al (2011b), and disentangled covariances in Boudt et al (2012).…”

Do Co-Jumps Impact Correlations in Currency Markets?

“…While the continuous covariation part of asset components can be well diversified in the portfolio, the presence of co-jumps implies that the construction of a hedging portfolio has to consider new constraints (Mancini and Gobbi, 2012). Moreover, separating the contribution of continuous and (co-)jump covariation in asset prices is crucial for investors.…”