  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.
