A model for the pricing of CDO tranches is discussed in which the dependence between the default times of the portfolio constituents is induced by a latent market factor with heavy-tailed stable distribution. Being primarily intended for a quick access to CDO pricing and the daily tracking of market prices in front office systems, the model relies on the simplifying large homogeneous portfolio. It is parameterized conveniently by only a single correlation parameter so that it can be compared directly to the well-known Gaussian one-factor copula model that is widely applied in the industry. In fact, it is our purpose to propose the presented model as a decent alternative to the one-factor Gaussian copula model, and to highlight that fat-tailed distributions, such as the stable law, are nothing to dismay. We review the numerical techniques that render the implementation of the stable model as straightforward and efficient as for the Gaussian model, although the fitting capacity to observed CDO data is a lot better. In particular, for the presented stable model we develop a concept which is equivalent to the concept of base correlations in the Gaussian model – and therefore allows for a quick access by traders.
CDO tranche pricing - volume 1