A2011
Title: Extremal vulnerability
Authors: Paolo Victor Redondo - King Abdullah University of Science and Technology (Saudi Arabia) [presenting]
Raphael Huser - King Abdullah University of Science and Technology (Saudi Arabia)
Hernando Ombao - King Abdullah University of Science and Technology (KAUST) (Saudi Arabia)
Miguel de Carvalho - University of Edinburgh and Universidade de Aveiro (Portugal)
Abstract: In many complex systems, identifying the most vulnerable components is essential for effective prevention, intervention, and risk management. Extreme events rarely occur in isolation but instead arise jointly across interconnected components. A method is developed to identify the nodes that are most vulnerable to such systemic shocks. These joint extreme occurrences provide insight into patterns of Tail Dependence and help identify the components that are systematically exposed to extreme shocks propagating through the network. The notion of Extremal Vulnerability is introduced, defined as the long-run tendency of a component to be affected by extreme events propagating from other components. A novel framework is developed that builds on the Tail Dependence Matrix (TDM), which captures directed Extremal Dependence, and leads to the Extremal Vulnerability Rank (XVRank)a PageRank-inspired algorithm for quantifying Extremal Vulnerability. Theoretical properties of the resulting estimators, including consistency and asymptotic normality, are established, and their performance is validated through Monte Carlo simulations. As an empirical application, the XVRank method is applied to the Magnificent Seven (MAG7) equities to identify assets most exposed to severe market downturns, and to 30 industry portfolios to characterize Extremal Vulnerability across sectors of the US economy.
