Risk Neutral Versus Objective Loss Distribution and CDO Tranches Valuation

Abstract:     
We consider the risk neutral loss distribution as implied by index CDO tranche quotes through a "scenario default rate" model as opposed to the objective measure loss distribution based on historical analysis. The risk neutral loss distribution turns out to privilege large realizations of the loss with respect to the objective distribution, thus implying the well known presence of a risk premium. We quantify this difference numerically by pricing CDO tranches and indices under the two distributions. En passant we analyze the implied risk neutral default rate distributions calibrated from April-2004 throughout April-2006, pointing out its distinctive "bump feature" in the tail.

Keywords: Default Rate distribution, CDO, CDO tranches, Perfect Copula, Transition Matrices, Rating Classes, Risk Premium, Recovery Rate

JEL Classifications: G13

Working Paper Series