Reduced Form vs. Structural Models of Credit Risk : A Case Study of Three Models

In this paper, we empirically compare two structural models (basic Merton and Vasicek-Kealhofer (VK)) and one reduced-form model (Hull-White (HW)) of credit risk. We propose here that two useful purposes for credit models are default discrimination and relative value analysis. We test the ability of the Merton and VK models to discriminate defaulters from non-defaulters based on default probabilities generated from information in the equity market. We test the ability of the HW model to discriminate defaulters from non-defaulters based on default probabilities generated from information in the bond market. We find the VK and the HW models exhibit comparable accuracy ratios as well as substantially outperform the simple Merton model. We also test the ability of each model to predict spreads in the credit default swap (CDS) market as an indication of each model's strength as a relative value analysis tool. We find the VK model tends to do the best across the full sample and relative sub-samples except for cases where an issuer has many bonds in the market. In this case, the HW model tends to do the best. The empirical evidence will assist market participants in determining which model is most useful based on their purpose in hand. On the structural side, a basic Merton model is not good enough; appropriate modifications to the framework make a difference. On the reduced-form side, the quality and quantity of data make a difference; many traded issuers will not be well modeled in this way unless they issue more traded debt. In addition, bond spreads at shorter tenors (less than two years) tend to be less correlated with CDS spreads. This makes accurate calibration of the term-structure of credit risk difficult from bond data