Measuring risk contagion in financial networks with CoVaR

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 modelled by heavy-tailed distributions, whereas their joint dependence is characterised by copula models exhibiting a variety of tail-dependence behaviour. We consider CoVaR, a popular measure of risk contagion, and study its asymptotic behaviour 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 modelled using two well-known multivariate dependence structures: the Gaussian copula and the Marshall–Olkin copula.