A Note on Survival Measures and the Pricing of Options on Credit Default Swaps

In this note the pricing of options on credit default swaps using the survival-measure-pricing technique is discussed. In particular, we derive a modification of the famous Black (1976) futures pricing formula which applies to options on CDS, and show how other pricing formulae can be easily derived if the dynamics of the forward CDS rates are specified differently. The main tool in the derivation of the pricing formulae is to express prices and payoffs in terms of a defaultable numeraire asset, the fee stream of the underlying forwardstarting CDS. As this numeraire becomes worthless in default, certain technical difficulties arise which can be solved using the mathematical tool of the T forward survival measure (first introduced in Schönbucher (1999)), a pricing measure which is conditioned on survival until T . The properties of such pricing measures are a second focus of this note. With increasing liquidity of the plain-vanilla CDS markets, the first derivatives on these basic credit derivatives have been introduced. In particular the market options on credit default swaps, or credit default swaptions is growing, be it as embedded options to extend or cancel an existing CDS, or as explicit options on the CDS. In the cover article of the May 2003 issue of Risk magazine, Patel (2003) discussed the growing market for options on credit default swaps, or credit default swaptions, and their practical applications. In this note we explain in more detail some of the methods which were first used in Schönbucher (1999) to price such options. In particular, we derive a modification of the famous Black (1976) futures pricing formula which applies to options on CDS and show how the methods can be extended to other models if you do not like the lognormality assumption. The main tool in the derivation of this formula