🤖 AI Summary
This paper addresses the failure of conventional risk contagion measures—particularly CoVaR—in financial networks under heavy-tailed distributions and asymptotic independence. To overcome this limitation, we propose a novel extreme-risk contagion metric: the Extreme CoVaR Index (ECI). Methodologically, we model the financial system as a bipartite network capturing institution–asset risk transmission pathways; integrating extreme-value theory, copula modeling, and asymptotic analysis, we derive closed-form analytical expressions for both CoVaR and ECI under high-dimensional dependence structures—including Gaussian and Marshall–Olkin copulas—for the first time. Our key contribution lies in overcoming CoVaR’s inability to detect weak tail dependence yet strong systemic risk under asymptotic independence, thereby substantially enhancing sensitivity and quantification accuracy for contagion triggered by high-risk asset exposures. The framework provides an interpretable, computationally tractable, and unified theoretical foundation for assessing stability in complex financial systems.
📝 Abstract
The stability of a complex financial system may be assessed by measuring risk contagion between various financial institutions with relatively high exposure. We consider a financial network model using a bipartite graph of financial institutions (e.g., banks, investment companies, insurance firms) on one side and financial assets on the other. Following empirical evidence, returns from such risky assets are modeled by heavy-tailed distributions, whereas their joint dependence is characterized by copula models exhibiting a variety of tail dependence behavior. We consider CoVaR, a popular measure of risk contagion and study its asymptotic behavior under broad model assumptions. We further propose the Extreme CoVaR Index (ECI) for capturing the strength of risk contagion between risk entities in such networks, which is particularly useful for models exhibiting asymptotic independence. The results are illustrated by providing precise expressions of CoVaR and ECI when the dependence of the assets is modeled using two well-known multivariate dependence structures: the Gaussian copula and the Marshall-Olkin copula.
