5 - Valuation of default baskets

Summary

Introduction

In this chapter we introduce and analyse default baskets. As we will see in subsequent chapters there are many similarities between the modelling of default baskets and synthetic CDOs, and a lot of the technology applied to default baskets carries over to CDOs. It is these modelling similarities that motivate starting with default baskets; much of what we learn about them will prove to be useful when looking at synthetic CDOs.

The chapter begins in Section 5.2 with a brief description of what default baskets are, their economic rationale (for both buyers and sellers of protection) and the mechanics of default basket trades. Section 5.3 describes the general approach to valuing default baskets. We have already met in Chapter 2 the concepts of modelling individual obligor default as a Poisson process and saw how default correlation could be captured by the use of copula functions. In the limits of no correlation between default events or perfect correlation between default events, a default basket can be valued analytically within the standard hazard rate model. Section 5.4 describes the details of these calculations. Although these analytic limits correspond to unrealistic limiting cases, they can provide useful insight into the overall behaviour of default baskets and are therefore worthy of study.