Multiple risk measures for multivariate dynamic heavy-tailed models

The dynamic evolution of tail-risk interdependence among institutions is of primary importance when extreme events such as financial crisis occur. In this paper we introduce two new risk measures that generalise the Conditional Value-at-Risk and the Conditional Expected Shortfall in a multiple setting. The proposed risk measures aim to capture extreme tail co-movements among several multivariate connected market participants experiencing contemporaneous distress instances. Analytical expressions for the risk measures are obtained under a parametric model that postulates a joint dynamic evolution of the underlying institutions' losses and gains. We consider a multivariate Student-t version of Markov Switching models as a robust alternative to the usual multivariate Gaussian specification, accounting for heavy-tails and time varying non-linear correlations. An empirical application to US banks is considered to show that our model-based risk measurement framework provides a better characterisation of the dynamic evolution of the overall risk of a financial system and a more complete picture of how the risk spreads among institutions.