CDOs in the light of the Current Crisis

This paper proposes a top-down model for pricing Collateralized Debt Obligation (CDOs). Our proposal is both treatable and realistic, in the sense we are able to obtain closed-form solutions to single tranche CDOs and capturing extreme credit events. We use as key ingredients the so-called (T, x)-bonds, as proposed in Fil-ipović, Overbeck, and Schmidt (2008), but generalize their affine specification by including shot-noise processes. Our claim is that affine diffusions combined with shot-noise processes lead to an improved modeling of CDO spreads in comparison to existing affine jump-diffusion models. The proposed approach allows in particular for better capturing the pos-sibility of extreme events, like the ones underlying the current crisis. We illustrate our results with a very concrete (simple) instance of our class of models. Finally, we identify the connections between the top-down and bottom-up approaches for modeling credit risk, within our class of models. In particular, we show that even when taking a bottom-up approach the aggregate loss process would be a process of affine shot-noise type. 1