Calibration of CDO Tranches with the Dynamical Generalized-Poisson Loss Model

In the first part we consider a dynamical model for the number of defaults of a pool of names. The model is based on the notion of generalized Poisson process, allowing for more than one default in small time intervals, contrary to many alternative approaches to loss modeling. We illustrate how to define the pool default intensity and discuss recovery assumptions. The models are tractable, pricing and simulation are straightforward, and consistent calibration to quoted index CDO tranches and tranchelets for several maturities is feasible, as we illustrate with numerical examples. In the second part we model directly the pool loss and we introduce extensions based on piecewise-gamma, scenario-based or CIR random intensities, leading to richer spread dynamics, investigating calibration improvements and stability