Advanced ccredit portfolio modelling and CDO pricing

Credit risk represents by far the biggest risk in the activities of a traditional bank. In particular, during recession periods financial institutions loose enormous amounts as a consequence of bad loans and default events. Traditionally the risk arising from a loan contract could not be transferred and remained in the books of the lending institution until maturity. This has changed completely since the introduction of credit derivatives such as credit default swaps (CDSs) and collaterized debt obligations (CDOs) roughly fifteen years ago. The volume in trading these products at the exchanges and directly between individual parties (OTC) has increased enormously. This success is due to the fact that credit derivatives allow the transfer of credit risk to a larger community of investors. The risk profile of a bank can now be shaped according to specified limits, and concentrations of risk caused by geographic and industry sector factors can be reduced. However, credit derivatives are complex products, and a sound risk-management methodology based on appropriate quantitative models is needed to judge and control the risks involved in a portfolio of such instruments. Quantitative approaches are particularly important in order to understand the risks involved in portfolio products such as CDOs. Here we need mathematical models which allow to derive the statistical distribution of portfolio losses. This distribution is influenced by the default probabilities of the individual instruments in the portfolio, and, more importantly, by the joint behaviour of the components of the portfolio. Therefore the probabilistic dependence structure of default events has to be modeled appropriately. In this paper we use two different approaches for modeling dependence. To begin with, we extend the factor model approach of Vasiˇcek [32, 33] by using more sophisticated distributions for the factors. Due to their greater