August 15, 2008
We derive a simple formula for calculating the CDS spread implied by the bond market price. Using no-arbitrage argument, the formula expresses the bond implied CDS spread as the sum of bond price, bond coupon and Libor zero curve weighted by risky annuities.
We show that the bond implied CDS spread is consistent with the standard CDS pricing model if the survival probabilities and recovery are consistent with the bond price.
A CDS contract is an OTC transaction between two parties in which the protection buyer pays a stream of coupon payment to the protection seller until the earlier of maturity or entity default in exchange for a default contingent payment. The common default settlement is the physical settlement where the protection buyer delivers a bond from a pool of eligible bonds to the protection seller in exchange for par. CDS contracts can also be cash settled where the protection buyer receives from the protection seller the cash amount of par less recovery.
With the physical settlement, the CDS protection buyer holds a delivery option where he can choose any bond from a pool of bonds to deliver into the CDS contract. Empirical evidence shows that bonds of the same entity do not necessarily have the same market value following default . As a result, the standard CDS pricing with a flat recovery rate cannot properly price in the value of the delivery option embedded in the CDS contracts.
Given the issuer default probability, the bond price is determined by the recovery and other fundamental and market technical factors such as supply and demand, and liquidity.
From modeling perspective, it is difficult to separate recovery, default probability, and other market fundamental and technical factors since they are intertwined. The recovery swap prices can be used as the expected recovery rate but the market has not yet fully
References:  R. Pullirsch, R. Jankowitsch, T. Veza, The Delivery Option in Credit Default Swaps, Working paper, October 25, 2007. Finance, V28, pp 2789-2811, 2004.  M. Davies, D. Pugachevsky, Bond spreads as a proxy for credit default swap spreads, Risk magazine, 2005.  D. Lando, On Cox processes and credit risky securities, working paper, 1998.  X. Guo, R. Jarrow, C. Menn, A Note on Lando’s Formula and Conditional Independence, working paper May, 2007.