Modelling default correlation in bond portfolios

The performance of a CBO structure is critically dependent on the correlation of defaults in a medium-sized portfolio of bonds. We introduce two classes of purely probabilistic models to handle these interaction e ects. In the rst, we suppose that default of an issuer in a particular industry sector may trigger o defaults of other issuers in the same sector by an `infection' mechanism. As infection increases we nd that the default distribution has increased variance and heavier tails, quantifying the concentration risk. The second model is a continuous-time stochastic process called an enhanced-risk model, that exhibits very similar features. In this case the incremental default probability is increased for all other issuers for a certain random period following occurrence of a default. The paper concludes with some comments on parameter estimation and applications of these models in CBO analysis. Figure 1 shows the structure of a typical CBO (Collateralized Bond Obligation) transaction. The central box labelled SPV denotes a `special purpose vehicle', i.e. a company which is set up for this one transaction and dissolved when the transaction terminates. On the closing date of the transaction the SPV accepts principal payments from investors and purchases a portfolio of perhaps 60 high yield bonds. All subsequent payments made to investors are derived from income received from the bond portfolio. Figure 1: CBO Structure Bond Portfolio ! ! ! SPV ! Noteholders ! Equity Investors The investors are in two categories: Noteholders (contributing perhaps 85% of the total principal) and Equity Investors. The former receive a speci ed coupon (= m.h.a.davis@btinternet.com y violet.lo@t-mi.com