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