Credit Default Swap Calibration and Counterparty Risk Valuation with a Scenario based First Passage Model ∗

In this work we develop a tractable structural model with analytical default probabilities depending on a random default barrier and possibly random volatility ideally associated with a scenario based underlying firm debt. We show how to calibrate this model using a chosen number of reference Credit Default Swap (CDS) market quotes. In general this model can be seen as a possible extension of the time-varying AT1P model in Brigo and Tarenghi (2004). The calibration capability of the Scenario Volatility/Barrier model (SVBAT1P), when keeping time-constant volatility, appears inferior to the one of AT1P with time-varying deterministic volatility. The SVBAT1P model, however, maintains the benefits of time-homogeneity and can lead to satisfactory calibration results, as we show in a case study where we compare different choices on scenarios and parameters. Similarly to AT1P, SVBAT1P is suited to pricing hybrid equity/credit derivatives and to evaluate counterparty risk in equity payoffs, and more generally to evaluate hybrid credit/equity payoffs. We consider the equity return swap in Brigo and Tarenghi (2004) and show its valuation under SVBAT1P with the same CDS and equity calibration input used earlier for AT1P, and further we hint at equity default swap valuation in the conclusions. ∗We are grateful towards Eymen Errais, for suggesting us to have a look at the random barrier approach, and to Kay Giesecke for helpful discussion and correspondence. D. Brigo, M. Tarenghi, CDS Calibration with a Scenario based 1st Passage Model 2 Duke of Alencon, this was your default, That, being captain of the watch to-night, Did look no better to that weighty charge. King Henry VI, Part 1, Act 2, Scene I.