CDO pricing with nested Archimedean copulas

Abstract

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.Nested Archimedean copula, Hierarchial dependence structure, CDO, Monte-Carlo pricing,

Hierarchical Copulae in Credit Risk Modeling

“…This type of copulae is called hierarchical dependency. Such dependency is reviewed in proceedings referred in the references 5 [9][10][11].…”

The Realized Hierarchical Archimedean Copula in Risk Modelling

“…The current paper builds on two actively developing areas of financial econometrics: copulae and high-frequency data. On the one hand, copulae appear to be a helpful tool to analyse complex dependence structures, evaluate the risk, and are therefore widely used to price financial derivatives, see Embrechts et al (2003), Rodriguez (2007), Hofert and Scherer (2011), Krämer et al (2013). On the other hand, models based on high-frequency data yield superior predictions in comparison to approaches based on daily data.…”

Dependent defaults and losses with factor copula models

“…For a given joint distribution, such a construction is not unique, but all possible decompositions can be organized as graphical structures, the so-called vines. Assuming the copula linking default times as in [35,36], an interesting aspect of our approach is that it nests the standard models described for instance in [13,28,38,51] as special cases.…”