A Note on Survival Measures and the Pricing of Options on Credit Default Swaps
by Philipp J. Schönbucher of ETH Zürich
Abstract: 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)[REF] 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 forward starting CDS. As this numeraire becomes worthless in default, certain technical difficulties arise which can be solved using the mathematical tool of the 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.