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This chapter starts the credit part of the book. In this first chapter we are going to introduce the financial payoffs and the families of rates we are dealing with in the following. But before doing so, we present a guided tour to give some orientation and general feeling for this credit part of the book. The guided tour is given in Section 21.1. Then we introduce as first credit payoffs the prototypical defaultable bonds in Section 21.2. Credit Default Swaps (CDS) payoffs and defaultable floaters, including a relationship between the two, are presented in Section 21.3. In particular, in Section 21.3.5 we explain that CDS’ allow in principle to strip default or survival probabilities in a model independent way, and in Section 21.3.7 we consider some different definitions of CDS forward rates, with analogies with earlier parts of the book, and with LIBOR vs swap rates in particular. In Section 21.3.8 instead we explore in detail possible equivalence between CDS payoffs and rates and defaultable floaters payoffs and rates. We anticipate some facts on intensity models that will be clarified completely later on in Chapter 22, where we also present more detailed results on CDS calibration.

In this chapter we focus completely on intensity models, exploring in details also the issues we have anticipated in the earlier chapter in order to be able to deal with Credit Default Swap (CDS) and notions of implied hazard rates and functions. Before proceeding further with the chapter we advise the reader that has not done so yet to have a look at the guided tour in Section 21.1, especially at the subsection on intensity models, just to put the intensity models we are going to examine here into perspective. In the introductory section we recall some of the aspects seen earlier on intensity models in general and also present the detailed structure of the chapter.

In this final chapter devoted to credit we close an ideal path going through the following steps: