Reduced‐Form versus Structural Models of Credit Risk: A Case Study of Three Models

Abstract

In this paper, we empirically compare two structural models (basic Merton and VasicekKealhofer (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 HW models exhibit comparable accuracy ratios on both the full sample and relevant sub-samples and 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 models 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. ∗The authors would like to thank Deepak Agrawal, Ittiphan Jearkjirm, Stephen Kealhofer, Hans Mikkelsen, Martha Sellers, Roger Stein, Shisheng Qu, Bin Zeng and seminar participants at MKMV and Prague Fixed Income Workshop (2004) for invaluable suggestions and advice. We are also grateful to Jong Park for providing the code involving the implementation of the Merton model. All remaining errors are ours. Address Correspondence to Dr. Jeffrey R. Bohn, Managing Director, Research Group, Moody’s KMV, 1620 Montgomery Street, San Francisco, CA 94111. E-mail: Jeff.Bohn@mkmv.com Reduced Form vs. Structural Models of Credit Risk: A Case Study of Three Models 1