A Multi-Portfolio Model for Bespoke CDO Pricing Part I: Methodology

Abstract

This paper presents a dynamic multi-portfolio default model for consistent and arbitrage-free pricing synthetic CDO tranches that reference a bespoke portfolio. In order to incorporate standard tranche price information, we assume that the bespoke portfolio has name overlapping with some index portfolios.Dividing the total portfolio (parent) into non-overlapping sub-portfolios (children), and assuming homogeneity for both the parent and the children, we use a top-down dynamic default intensity model for the parent, and specify the conditional probability of default in the children given imminent default in the parent. We consider two fundamental cases which are building blocks of more complex applications: (a) the parent is an index and the bespoke is a child; and (b) the bespoke is the parent that contains one or more indices as children.When the parent is the index, the parent default process is uniquely determined independent of the children, and the child conditional default probability distribution is calibrated to the spreads of the children. When the bespoke is the parent and one or more children are indexes, we simultaneously calibrate the parent default intensity model and the child default probability to the standard tranches and child portfolio spreads. The model is designed to establish consistency between the pricing of standard tranches and the pricing of bespoke tranches. Application may include:• Portfolio enlargement where the bespoke tranche references a “global” portfolio that contains “regional” indexes as sub-portfolio. For example, tranches referencing CDX.NA.IG and iTraxx Europe.• Portfolio thinning where the bespoke tranche references a sub-portfolio of an index.• Combination of portfolio enlargement and thinning. For example, tranche referencing a subset of CDX and a subset of iTraxx.