The one-factor Gaussian model is well-known not to fit simultaneously the prices of the different tranches of a collateralized debt obligation (CDO), leading
to the implied correlation smile. Recently, other one-factor models based on different distributions have been proposed. Moosbrucker  used a one-factor Variance
Gamma model, Kalemanova et al.  and Guégan and Houdain  worked with a NIG factor model and Baxter  introduced the BVG model. These models bring
more flexibility into the dependence structure and allow tail dependence. We unify these approaches, describe a generic one-factor Levy model and work out the large
homogeneous portfolio (LHP) approximation. Then, we discuss several examples and calibrate a battery of models to market data.