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

22 Pages Posted: 6 Apr 2005

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Marco Tarenghi


Date Written: March 10, 2005


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.

Keywords: Credit Derivatives, Structural Models, Black Cox Model, Credit Default Swaps, Calibration, Analytical Tractability, Monte Carlo Simulation, Equity Return Swaps, Counterparty Risk, Barrier Options, Scenario Default Barrier, Scenario Volatility

JEL Classification: G13

Suggested Citation

Brigo, Damiano and Tarenghi, Marco, Credit Default Swap Calibration and Counterparty Risk Valuation with a Scenario Based First Passage Model (March 10, 2005). Available at SSRN: or

Damiano Brigo (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom


Marco Tarenghi

Mediobanca ( email )

Piazzetta Enrico Cuccia, 1
Milano, MI 20121

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