This paper empirically tests five structural models of corporate bond pricing: those of Merton (1974), Geske (1977), Leland and Toft (1996), Longsta# and Schwartz (1995), and Collin-Dufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capital structures during the period 1986-1997. The conventional wisdom is that structural models do not generate spreads as high as those seen in the bond market, and true to expectations we find that the predicted spreads in our implementation of the Merton model are too low. However, most of the other structural models predict spreads that are too high on average. Nevertheless, accuracy is a problem, as the newer models tend to severely overstate the credit risk of firms with high leverage or volatility and yet su#er from a spread underprediction problem with safer bonds. The Leland and Toft model is an exception in that it overpredicts spreads on most bonds, particularly those with high coupons. More accurate structural models must avoid features that increase the credit risk on the riskier bonds while scarcely a#ecting the spreads of the safest bonds.

We show that a simple structural model of credit risk is able to generate credit yield spreads for the low-rated bonds close to the historical spreads once the recent trends in the stock volatility are taken into account. We study the idiosyncratic and market volatility of stock returns in the cross-section of credit ratings. We find that the increase in the level of the firm-specific volatility, demonstrated recently by Campbell et al. (2001), refers only to the low-rated stocks. A time-varying deterministic volatility process is used to imply the asset volatilities, the asset risk premia and the default boundaries from the historical default rates. Stock volatility is modeled as an autoregressive process. Physical default probability of an investment-grade bond is primarily linked to the drift of the firm value process and default probability of a low-rated bond to the total asset volatility. We confirm this by finding that an increase in the firm-specific volatility affects credit spreads of the low-rated bonds and does not have an observable impact on the investment-grade bonds.

No consensus has yet emerged from the existing credit risk literature on how much of the observed corporate-Treasury yield spreads can be explained by credit risk. In this paper, we propose a new calibration approach based on historical default data and show that one can indeed obtain consistent estimate of the credit spread across many different economic considerations within the structural framework of credit risk valuation. We find that credit risk accounts for only a small fraction of the observed corporate-Treasury yield spreads for investment grade bonds of all maturities, with the fraction smaller for bonds of shorter maturities; and that it accounts for a much higher fraction of yield spreads for junk bonds. We obtain these results by calibrating each of the models – both existing and new ones – to be consistent with data on historical default loss experience. Different structural models, which in theory can still generate a very large range of credit spreads, are shown to predict fairly similar credit spreads under empirically reasonable parameter

We show that credit risk accounts for only a small fraction of the observed corporate-Treasury yield spreads for investment grade bonds of all maturities, with the fraction smaller for bonds of shorter maturities; and that it accounts for a much higher fraction of yield spreads for junk bonds. This conclusion is shown to be robust across a wide class of structural models—both existing and new ones—that incorporate many different economic considerations. We obtain such consistent results by calibrating each of the models to be consistent with data on historical default loss experience. Different models, which in theory can still generate a very large range of credit risk premia, are shown to predict fairly similar credit risk premia under empirically reasonable parameter choices, Corporate bonds typically trade at higher yields than Treasury bonds of comparable maturities. The yield spread is partly due to the credit risk of corporate bonds, and is thus frequently referred to as the “credit spread. ” Credit risk, however, is only one of the factors contributing towards the corporate-Treasury yield spread; other factors include illiquidity,