Companies in the same industry sector are usually more correlated than firms in different sectors, as they are similarly affected by macroeconomic effects, political decisions, and consumer trends. Despite the many stock return models taking this fact into account, there are only a
few credit default models that take it into consideration. In this paper we present a default model based on nested Archimedean copulas that is able to capture hierarchical dependence structures among the obligors in a credit portfolio. Nested Archimedean copulas have a surprisingly simple
and intuitive interpretation. The dependence among all companies in the same sector is described by an inner copula and the sectors are then coupled via an outer copula. Consequently, our model implies a larger default correlation for companies in the same industry sector than for companies
in different sectors. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of the model. This portfolio consists of CDS on 125 companies from six different industry sectors and is therefore an excellent portfolio for a comparison
of our generalized model with a traditional copula model of the same family that does not take different sectors into account.
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Hierarchial dependence structure;
Nested Archimedean copula
Document Type: Research Article
Institute of Number Theory and Probability Theory, Ulm University, Helmholtzstraße 18 89081 Ulm, Germany
HVB Stiftungsinstitut für Finanzmathematik, Technische Universität München, Boltzmannstraße 3 85748 Garching, Germany
Publication date: May 1, 2011