CDOs in the Light of the Current Crisis
FINANCIAL RISKS: NEW DEVELOPMENTS IN STRUCTURED PORDUCT & CREDIT DERIVATIVES, C. Gourieroux and M. Jeanblanc, EDS., Chapter 4, pp.33-48, Economica
12 Pages Posted: 3 Jul 2008 Last revised: 15 Dec 2010
Date Written: 2009
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 Filipovic, Overbeck, and Schmidt (2008), but generalize their affine specification byincluding 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 possibility 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.
Keywords: CDOs, credit risk, Affine, Shot-noise, Top-down
JEL Classification: G12
Suggested Citation: Suggested Citation