New nonparametric measures for instantaneous and granger-causality tail co-dependence

We propose a new methodology to asses risk spillovers in a time-series framework. Firstly, we introduce an explicit nonparametric measure of cross-sectional conditional tail co-movement, which is intuitively comparable to the Conditional Value-at-Risk (CoVaR). We show that nonlinear CoVaR (NCoVaR) is able to capture even highly nonlinear dependence structures. Secondly, for the purpose of potential contagion analysis, we adapt the measure to be informative about the causality direction between the variables in the Granger causality sense. By showing that the natural estimators of the two metrics are U-statistics, we construct formal nonparametric tests for independence and Granger non-causality. Numerical simulations confirm that in common situations the nonparametric tests have better size and power properties than their parametric counterparts. The methodology is illustrated empirically by assessing risk transmissions between sovereigns and banking sectors in the euro area, which observed highly irregular co-movements between asset prices after the global financial crisis. The new measures seem to be less susceptible to these irregularities than their parametric analogues, providing a clearer overview of the underlying sovereign-bank risk feedback loops.