*Tid:***19 september 2005 kl 1615-1700 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Magnus Kullberg
**

**Titel:** **
Valuing Credit Default Swaps
**

* Sammanfattning: *
This thesis looks at different ways of valuing a credit default
swap, CDS, on one or several underlying credit risks. A CDS pays
the holder a certain compensation if a particular underlying credit
risk is triggered. In this thesis the credit risk is modelled using
the intensity rate of default. We will go through the theoretical
foundation for valuation methods based on the intensity rate
approach, and then the specific valuation approaches are described.

Three methods of valuing a CDS on a single underlying risk are evaluated. It is concluded that a method that draws specific stopping times is less efficient than a method that calculates probable payouts without drawing a specific stopping time. However, the method that does draw specific stopping times is more flexible. The fastest method is derived straight from a simple Vasicek process and has analytic steps, but it is of course also the least flexible method.

Also, three approaches to valuing a CDS on several underlying credit risks are evaluated. A first approach is to use a Gaussian copula to mix the risks together. The lack of computational tractability and mathematical simplicity makes this approach less appealing than the second approach of a Gaussian factor copula which uses industry factors to link the risks together. If, as a third approach, an Archimedean Gumbel copula can be calibrated, it allows for a direct specification of the intensity rate for a first to default, FtD, CDS.

Even though the model for CDS valuation on one underlying risk that calculates probable payments seems to mix exactness with flexibility, the method that draws stopping times is very easy to use even for valuing a CDS on several underlying risks. Moreover, when valuing a CDS on a number of underlying risks, the Gaussian factor copula method seems to provide the best overall mix between tractability and accuracy.