Credit portfolio modelling with elliptically contoured distributions - approximation, pricing, dynamisation

Abstract

The aim of this thesis is to introduce a new set of factor models for the pricing of portfolio credit derivatives, which match the observations on the derivatives markets better than the standard Gaussian model. These new models will be based on elliptical distributions, and will extend the Gaussian model in a consistent way. We will identify that mixtures of Normal distributions must be used within the class of elliptical distributions, and will classify which of these distributions can be used to produce more adequate probabilities for joint defaults in the underlying portfolio. On the basis of this elliptical factor setup, we will derive a very general large homogeneous portfolio approximation result, which helps us to deal with multi-name credit derivatives written on a large portfolio. We will provide a diligent study on the impact of our modelling framework to the pricing of Collateralized Debt Obligations and apply this to the valuation of iTraxx tranches. Finally, sundry possibilities to generate stochastic processes with Gaussian mixture marginals are analysed with regard to their applications within the previously discussed elliptical factor model.