  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.
