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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.

JEL Classification: E43, G13.

AMS Classification: 91B28, 60G44, 60G40.

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"

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