ABSTRACT
In this chapter we study counterparty risk embedded within in a CDS contract. This topic, which corresponds to the emblematic case of AIG selling CDS protection on the distressed Lehman in the 2008 credit crisis, has received a lot of attention in the literature. The following is a partial list of works studying it:
• Huge and Lando (1999) propose a rating-based approach, • Hull and White (2001) use a static Gaussian copula model, • Jarrow and Yu (2001) use an intensity contagion model, further considered in Le-
ung and Kwok (2005),
• Brigo and Chourdakis (2008) work in a Gaussian copula model with CIR++ intensities, extended to bilateral counterparty credit risk in Brigo and Capponi (2008b),
• Blanchet-Scalliet and Patras (2011), Lipton and Sepp (2009b) and Lipton and Shelton (2012) develop
It can thus be considered as a benchmark topic in the area of counterparty risk. Some preliminary results regarding counterparty risk relative to CDS contracts have
already been discussed in Sect. 7.4.1. In this chapter we will, for the most part, work in the common-shock model of Chapter 8, in which the dependence between the counterparty in the contract and the reference name of the CDS is rendered by the possibility of their joint default. In the case of one CDS, the general computations of Chapter 8 can be pushed further and explicit formulas can be derived. We also provide comparative numerics regarding various specifications for the default intensities.
