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

Journal of Investment Management, Vol. 3, No. 4, Fourth Quarter 2005

Posted: 27 Jul 2005

See all articles by Navneet Arora

Navneet Arora

American Century Investments

Jeffrey Bohn

University of California, Berkeley - Center for Risk Management Research; State Street Corporate

Fanlin Zhu

affiliation not provided to SSRN

Abstract

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.

Keywords: Credit risk, default risk, default probability, structural model, reduced-form model, Merton model, equity, corporate bonds, credit default swaps (CDS), power curves, credit spreads

JEL Classification: G00

Suggested Citation

Arora, Navneet and Bohn, Jeffrey and Zhu, Fanlin, Reduced Form vs. Structural Models of Credit Risk: A Case Study of Three Models. Journal of Investment Management, Vol. 3, No. 4, Fourth Quarter 2005. Available at SSRN: https://ssrn.com/abstract=723041

Navneet Arora (Contact Author)

American Century Investments ( email )

1665 Charleston Road
Mountain View, CA 94043
United States

Jeffrey Bohn

University of California, Berkeley - Center for Risk Management Research ( email )

581 Evans Hall
Berkely, CA
United States

State Street Corporate ( email )

1 Lincoln Street
Boston, MA 02111
United States

Fanlin Zhu

affiliation not provided to SSRN

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