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A Hierarchical Archimedean Copula for Portfolio Credit Risk Modelling

by Natalia Puzanova of Deutsche Bundesbank

November 2011

Abstract: I introduce a novel, hierarchical model of tail dependent asset returns which can be particularly useful for measuring portfolio credit risk within the structural framework. To allow for a stronger dependence within sub-portfolios than between them, I utilise the concept of nested Archimedean copulas, but modify the nesting procedure to ensure the compatibility of copula generators by construction. This makes sampling straightforward. Moreover, I provide details on a particular specification based on a gamma mixture of powers. This model allows for lower tail dependence, resulting in a more conservative credit risk assessment than a comparable Gaussian model. I illustrate the extent of model risk when calculating VaR or Expected Shortfall for a credit portfolio.

JEL Classification: C46,C63,G21.

Keywords: Portfolio Credit Risk, Nested Archimedean Copula, Tail Dependence, Hierarchical Dependence Structure.

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