Measuring spot variance spillovers when (co)variances are time-varying - the case of multivariate GARCH models

In highly integrated markets, news spreads at a fast pace and bedevils risk
monitoring and optimal asset allocation. We therefore propose global and dis-
aggregated measures of variance transmission that allow one to assess spillovers
locally in time. Key to our approach is the vector ARMA representation of the
second-order dynamics of the popular BEKK model. In an empirical applica-
tion to a four-dimensional system of US asset classes - equity, fixed income,
foreign exchange and commodities - we illustrate the second-order transmis-
sions at various levels of (dis)aggregation. Moreover, we demonstrate that the
proposed spillover indices are informative on the value-at-risk violations of port-
folios composed of the considered asset classes.