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 amodification of the famous Black (1976) futures pricing formula which appliesto options on CDS, and show how other pricing formulae can be easily derivedif the dynamics of the forward CDS rates are specified differently. The maintool in the derivation of the pricing formulae is to express prices and payoffs interms of a defaultable numeraire asset, the fee stream of the underlying forward-starting CDS. As this numeraire becomes worthless in default, certain technicaldiffculties 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 pricingmeasures are a second focus of this note.