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CDS Calibration with Tractable Structural Models Under Uncertain Credit Quality

by Damiano Brigo of Banca IMI, and
Massimo Morini of the UniversitÓ di Milano - Bicocca

November 2005

Abstract: In this paper we develop structural first passage models (AT1P and SBTV) with time-varying volatility and characterized by high tractability. The models can be calibrated exactly to credit spreads using efficient closed-form formulas for default probabilities. In these models default events are caused by the value of the firm assets hitting a safety threshold, which depends on the financial situation of the company and on market conditions. In AT1P this default barrier is deterministic. Instead SBTV assumes two possible scenarios for the initial level of the default barrier, for taking into account uncertainty on balance sheet information and in particular risk of fraud. We apply the models to exact calibration of Parmalat Credit Default Swap (CDS) data during the months preceding default. In some cases these models show more calibration capability than a reduced-form model. The results we obtain with AT1P and SBTV have reasonable economic interpretation, and are particularly realistic when SBTV is considered. These results are analyzed in relation with the progressive unfolding of news on Parmalat crisis, and compared to the results we obtain for a company with higher credit quality.

JEL Classification: G13.

Keywords: Structural Models, Black Cox Model, CDS, Parmalat, Calibration, Risk of Fraud.

Published in: RISK, Vol. 19, No. 4, (April 2006).

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