Tail risk measures with application for mixtures of elliptical distributions

Abstract

In this paper we derive explicit formulas of tail conditional expectation (TCE) and tail variance (TV) for the class of location-scale mixtures of elliptical distributions, which includes the generalized hyper-elliptical (GHE) distribution. We also develop portfolio risk decomposition with TCE for multivariate location-scale mixtures of elliptical distributions. To illustrate our findings, we focus on the generalized hyperbolic (GH) family which is a popular subclass of the GHE for stocks modelling.

Keywords

• tail conditional expectations
• tail variance
• portfolio risk decomposition with tce
• location-scale mixtures
• elliptical distributions