Based on the Merton model numerous so called structural credit risk models were developed. Their main property is that the default time is modelled as the first passage time of a stochastic process. As an example we survey a model introduced by Albanese and co-authors in 2003. The utilized process results from a stochastic transformation applied to a Squared Bessel process.
In order to be able to consider dependencies between different obligors, in the main chapter of this thesis we introduce a model where the ability to pay process is described as the sum of two independent Squared Bessel processes. One process represents the individual risk and the second process represents the common risk. The default barrier is considered to be zero. The first passage time of the ability to pay process and thus the default time is composed as the sum of the first passage time T of the common process and the first hitting of zero of the individual process after time T.
In the next chapter two further approaches are presented shortly. The last chapter depicts the major part of an already published article about the role of copulas in the CreditRisk+ model.
