Credit Default Swaps: A Cash Flow Analysis

Abstract

Credit default swap (CDS) contracts are often considered synthetic versions of obligors’ bonds funded at LIBOR.Accordingly, in the absence of financial frictions and market segmentation, an obligor’s bond yield spread to LIBOR and its CDS premium at the same maturity should be zero.That analogy also underlies the consistent application of riskneutral pricing theory to both bonds and CDS.The authors describe difficulties in replicating a bond synthetically in the CDS, interest-rate swap, and repo markets and demonstrate that risk-neutral pricing theory implies different premiums for default protection on two bonds of the same maturity from the same obligor but having different coupons. They introduce a method for calculating CDS premiums and contingent payments under physical (i.e., actuarial) measure. The model derives physical probabilities from a combination of model-based estimates and historical values, and these are used to specify expected cash flows on CDS premium and default-contingent legs.The expected cash flows are then discounted at risk-free rates. The authors use this method to derive CDS premiums necessary to compensate for default and designate resulting excess market spreads as CDS risk premiums. They observe that, for certain historical periods, market CDS spreads were insufficient to compensate sellers of protection for expected payouts from default.