Risk Contagion under Extremes: Interplay of Tail Heaviness and Dependence

The inference and estimation of extreme risk contagion (ERC) at significance levels below 1% are challenging due to the scarcity of extreme observations. Based on extreme value theory, we introduce a novel ERC measure and ERC index (ERCI) to capture the heaviness and dependence of tails for multivariate risk sources. It refines the marginal expected shortfall with flexible and extensive dependence structures. We provide the limiting properties of the ERC and nonparametric estimator, along with its consistency, under fairly general assumptions. This enables reliable extrapolation at extreme risk levels beyond the range of available observations. We demonstrate the strong performance of the extrapolated estimator numerically in finite-samples. The empirical applications to market-to-market contagion, network analysis, and systemic risk allocation among globally systemically important financial institutions (G-SIFIs) reveal novel contagion patterns, providing practical tools for regulators to assess and monitor global systemic risk.