Candidate Market Models and the Calibrated CIR++ Stochastic Intensity Model for Credit Default Swap Options and Callable Floaters

Abstract

We consider the standard Credit Default Swap (CDS) payoff and some alternative approximated versions, stemming from different conventions on the premium and protection legs. We consider standard running CDS (RCDS), upfront CDS and postponed-payments running CDS (PRCDS). Each different definition implies a different definition of forward CDS rate, which we consider with some detail. We introduce defaultable floating rate notes (FRN)'s. We point out which kind of CDS payoff produces a forward CDS rate that is equal to the fair spread in the considered defaultable FRN. An approximated equivalence between CDS's and defaultable FRN's is established, which allows to view CDS options as structurally similar to the optional component in defaultable callable notes. We briefly investigate the possibility to express forward CDS rates in terms of some basic rates and discuss a possible analogy with the LIBOR and swap default free models. Finally, we discuss the change of numeraire approach for deriving a Black-like formula for CDS options or, equivalently, defaultable callable FRN's. We also introduce an analytical formula for CDS option prices under the CDS-calibrated SSRD stochastic-intensity model, and discuss the impact of the different CIR++ dynamics parameters on the related CDS options implied volatilities. Hints on possible methods for smile modeling of CDS options are given for possible future developments of the CDS option market.