Model Risk and the Design of CDO Tranches

Abstract

The goal of this paper is to explore the model risk inherent in the rating and design of structured finance products. We seek to illustrate the consequences of neglecting state-dependent correlations on the methodologies and criteria employed by the major ratings agencies. In contrast to related studies, we focus exclusively on asymptotic analysis. A variety of tractable asymptotics are derived for “first-generation” securitizations, such as asset-backed securities (ABS), as well as “second-generation” securitizations, such as collateralized debt obligations (CDO) backed by tranches of ABS. Consistent with the recent work of Hull and White [2009], who explore alternative sources of model risk, we find that in the case of first-generation securitizations, the implications are substantial but not catastrophic; in the case of second-generation securitizations, however, the implications are dire. This is due to the fact that our analysis provides a parsimonious description of thin mezzanine tranches as “nearly binary” assets which tend to “go bad” at the same time; a phenomenon which is notably absent in the notorious (and industry standard) Gaussian factor models.