Consistent Calibration of CDO Tranches with the Generalized-Poisson Loss dynamical model

We consider a dynamical model for the loss distribution of a pool of names. The model is based on the notion of generalized Poisson process, allowing for the possibility of more than one jump in small time intervals. We introduce extensions of the basic model based on piecewise-gamma or scenario-based random intensity in the constituent Poisson processes. The models are tractable, pricing and in particular simulation is easy, and consistent calibration to quoted index CDO tranches and tranchelets for several maturities is feasible, as we illustrate with detailed numerical examples.