Valuation of Credit Default Swaps and Swaptions
by Farshid Jamshidian of NIB Capital Bank
October 12, 2002
Abstract: This paper presents a conceptual framework for valuation of single-name credit derivatives, and recuperates, in some cases generalizing, a few of known results in credit risk theory. Valuation is viewed with respect to a given state price density and relative to a general numeraire. Default probabilities and recoveries are considered as processes adapted to a subfiltration, following Jeanblanc and Rutosksy [JR], or, in the special case of Cox processes, Lando [L]. A result of Duffie and Singleton [DS] on pricing bonds with recovery in terms of loss ratio is reproduced. The notion of coadapted change of numeraire is introduced, and its invariants identified and studied. The concept of a credit claim is formalized by introducing notions of T-claims, τ -claims, and Τ eams. Application is made to credit default swaps and swaption, and a known Black-Scholes approximation for the latter is derived.
Keywords: Credit default swap, swaption, swap rate, subfiltration, conditional survival probability, preprice, prenumeraire, recovery, coadapted numeraires.
Published in: Finance and Stochastics, Vol. 8, No. 3, (August 2004), pp. 343-371.
Previously titled: "Valuation of Credit Default Swap and Swaptions"