Can the Performance of Structural Corporate Bond Models Be Improved?

51 Pages Posted: 21 Sep 2008 Last revised: 11 Sep 2015

Date Written: November 18, 2008


I develop variations of three default-risk determinants of structural corporate bond models. The three determinants are the asset return distribution law, recovery rule, and default time. First, I replace the Gaussian distribution of an asset return with three alternative non-Gaussian distributions. The firm asset follows a jump-diffusion process, or the volatility of the asset return is stochastic, or both. Second, I replace the single recovery rate with two different recovery rules for a mild default and a possible severe default. Third, I consider both non-early default and early default. I have tested a sample of 79 corporate bonds from 1987 to 1998. This paper has three main empirical findings. First, the best model is able to reduce the out-of-sample pricing error to 40 bps, or 40% of the observed spreads. By contrast, the pricing error of previous structural models is 94 bps in one study, or 66% of the observed spreads in a different study. This is the first empirical evidence that a structural model is able to capture a large percentage of credit spreads in corporate bond markets. Second, I show that credit spreads and default risk are heterogeneous. The heterogeneity exists both across credit ratings and within the same credit rating. The term structure of credit spreads could be explained by default risk at different levels, which is captured by different combinations of the three default-risk determinants. Non-Gaussian distribution is necessary but not sufficient to capture a wide spectrum of corporate default risk. For bonds with low credit ratings and long maturities, early default and the two-component recovery rule are necessary. For bonds with high ratings and short maturities, non-early default and the market median recovery rate are appropriate. This paper could explain why a triple B bond with a short maturity is at a similar risk level as a double A bond with a long maturity, and why a single A bond with a long maturity is riskier than a triple B bond with a short maturity. Third, I also obtain a negative relation between cumulative default rates and recovery rates. This relationship is consistent with the negative relation between annual default rates and recovery rates, a relation that has been observed in the historical data for a long time but is rarely considered by previous bond models. In addition, this paper provides an alternative explanation to this negative relation from the firm perspective.

Keywords: credit risk modeling, structural model, default risk, corporate bond pricing, non-Gaussian distribution, jump-diffusion, stochastic volatility

JEL Classification: C51, C52, C53, G12, G13

Suggested Citation

Zhu, Zhongyan, Can the Performance of Structural Corporate Bond Models Be Improved? (November 18, 2008). Available at SSRN: or

Zhongyan Zhu (Contact Author)

Monash University ( email )

Department of Banking and Finance
Caufield East, Victoria 3145
61-3-9903-4546 (Phone)


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