Stochastic recovery rate: Impact of pricing measure's choice and financial consequences on single-name products

Gambetti, Paolo [UCL] Gauthier, Geneviève [HEC Montréal] Vrins, Frédéric [UCL]

The ISDA CDS pricer is the market-standard model to value credit default swaps (CDS). Since the Big Bang protocol moreover, it became a central quotation tool: just like options prices are quoted as implied vols with the help of the Black-Scholes formula, CDSs are quoted as running (conventional) spreads. The ISDA model sets the procedure to convert the latter to an upfront amount that compensates for the fact that the actual premia are now based on a standardized coupon rate. Finally, it naturally offers an easy way to extract a risk-neutral default probability measure from market quotes. However, this model relies on unrealistic assumptions, in particular about the deterministic nature of the recovery rate. In this paper, we compare the default probability curve implied by the ISDA model to that obtained from a simple variant accounting for stochastic recovery rate. We show that the former typically leads to underestimating the reference entity's credit risk compared to the latter. We illustrate our views by assessing the gap in terms of implied default probabilities as well as on credit value adjustments (CVA) figures and pricing mismatches of financial products like deep in-/out-of-the-money standard CDSs and digital CDSs (main building block of credit linked notes, CLNs).