Measuring persistence in volatility spillovers

This paper analyzes volatility spillovers in multivariate GARCH-type models. We show that the cross-effects between the conditional variances determine the persistence of the transmitted volatility innovations. In particular, the effect of a foreign volatility innovation on a conditional variance is even more persistent than the effect of an own innovation unless it is offset by an accompanying negative variance spillover of sufficient size. Moreover, ignoring a negative variance spillover causes a downward bias in the estimate of the initial impact of the foreign volatility innovation. Applying the concept to portfolios of small and large firms, we find that shocks to small firm returns affect the large firm conditional variance once we allow for (negative) spillovers between the conditional variances themselves.