An implied multi-factor model for bespoke collateralized debt obligation tranches and other portfolio credit derivatives

ABSTRACT This paper introduces a new semi-parametric approach to the pricing and risk management of bespoke collateralized debt obligation (CDO) tranches, giving particular attention to bespokes that need to be mapped onto more than one reference portfolio. The only user input in our framework is a multi-factor model (hereafter, a "prior" model) for index portfolios such as CDX.NA.IG or iTraxx Europe, which are chosen as benchmark securities for the pricing of a given bespoke CDO. Parameters of the prior model are fixed, and are not tuned to match prices of benchmark index tranches. Instead, our calibration procedure amounts to a proper reweighting of the prior measure using the minimum cross-entropy method. As the latter problem reduces to convex optimization in a low-dimensional space, our model is computationally efficient. Both the static (one-period) and dynamic versions of the model are presented. The latter can be used for pricing and risk management of more exotic instruments referencing bespoke portfolios, such as forward-starting tranches or tranche options, and for calculation of credit valuation adjustment for bespoke tranches.