Structuring and rating cash-flow CDOs with rating transition matrices

The objective of this article is to prepare a time-inhomogeneous intensity model for valuing cash-flow CDOs, which explicitly incorporates the credit rating of the firms in the collateral portfolio as the indicator of the likelihood of default. Our model can prove very useful for the pricing, structuring, rating and risk management of CDO notes, whenever the legal structure of the transaction, includes waterfall triggers linked to the credit ratings of the firms in the collateral portfolio. If the waterfall triggers are breached, they divert cash due to pay the interests of the junior notes to accelerate the amortisation of the more senior notes. For this reason, we believe that in order to measure the risk and value of the CDO notes, it is necessary to combine a credit risk model with the exact cash-flow waterfall model of the given structure. To reach our objective, we firstly need to model the rating transition process of each single obligor in the portfolio according to a set of time-inhomogeneous transition matrices, calibrated to historical default probabilities. Only then, to address the issue of modelling migration dependence, we rely on the concept of copula. The algorithms developed by Lando (1998a) and Israel, Rosenthal and Wei (2001) will be very useful for preparing the transition matrices to feed our cash-flow CDO model.