A Hierarchical Model of Tail Dependent Asset Returns for Assessing Portfolio Credit Risk

by Natalia Puzanova of Deutsche Bundesbank

December 2011

Abstract: This paper introduces a multivariate pure-jump Lévy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a two-stage stochastic time change to Brownian motions, I derive a hierarchical structure with different properties of inter- and intra-sector dependence. I investigate the properties of the implied static copula families and come to the conclusion that they are ordered with respect to their parameters and that the lower-tail dependence of the intra-sector copula is increasing in the absolute values of skewness parameters. Furthermore, I show that the joint characteristic function of the VCG asset returns can be explicitly given as a nested Archimedean copula of their marginal characteristic functions. Applied to credit portfolio modelling, the framework introduced results in a more conservative tail risk assessment than a Gaussian framework with the same linear correlation structure, as I show in a simulation study. To foster the simulation efficiency, I provide an Importance Sampling algorithm for the VCG portfolio setting.

JEL Classification: C46, C63, G12, G21.

AMS Classification: 60G51, 62H20.

Keywords: Portfolio Credit Risk, Stochastic Time Change, Brownian Subordination, Jumps, Tail Dependence, Hierarchical Dependence Structure.

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