CDO pricing with nested Archimedean copulas

Abstract

Companies in the same industry sector are usually stronger correlated than firms in different sectors, as they are similarly affected by macroeconomic effects, political decisions, and consumer trends. In spite of many stock return models taking account of this fact there are only a few credit default models taking it into consideration. In this paper we present a default model based on nested Archimedean copulas which 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; the sectors are then coupled via an outer copula. Consequently, our model implies a larger default correlation for companies in the same industry sector compared to companies in different sectors. A calibration to CDO tranche spreads of the European iTraxx portfolio is performed to demonstrate the fitting capability of our model. This portfolio consists of CDS on 125 companies from six different industry sectors. It is therefore an excellent portfolio to compare our generalized model to a traditional copula model of the same family, which does not account for different sectors.