Since the seminal work of Merton (1974), many structural credit risk models have been proposed, including Longstaff and Schwartz (1995), Leland and Toft (1996), and Collin-Dufresne and Goldstein (2001), among others. In this type of models, both the equity and the debt of a firm are modeled as contingent claims over the asset value of the issuing firm, and as a result, option pricing theory can be applied.
Defaults occur when the firm asset value, which is usually modeled as a diffusion process, reaches a certain barrier either during the life of the debt or at the maturity of the debt. This type of models establish the relationships between the returns of the firm’s equity and debt, as well as the yield spreads and the firm’s balance sheet information such as leverage ratio.
Structural models can also be used to estimate the default probabilities of the issuing firms. For banks and regulators, timely and accurate predictions of borrowers default probabilities are essential to developing responsive and effective risk management tools. Moreover, the newly adopted Basel II specifically requires financial institutions to use credit risk models that are conceptually sound and empirically validated. Our main aim in this study is to empirically analyze the performance of structural models, including the Merton model, Longstaff and Schwartz (LS) model, Leland and Toft (LT) model, and the Collins-Dufresne and Goldstein (CDG) model, when they are used to estimate the default probabilities of the debt issuing firms.
Many studies have been taken to investigate if structural models can explain yield spreads. They include Jones et al. (1984), Wei and Guo (1997), Anderson et al. (2000), Lyden and Saraniti (2000), Collin-Dufresne et al. (2001), Elton et al. (2001), Cooper and Devydenko (2003), Delianedis and Geske (2003), Huang and Huang (2003), Eom et al (2004), Leland (2004), and Ericsson and Reneby (2005), among others. Huang and Huang (2003) and Eom et al. (2004) provide the most comprehensive comparison among various structural models. By calibrating different models to default probabilities and historical equity premium, Huang and Huang (2003) find that the spread implied by structural models are too low for investment grade bonds. Eom et al (2004) show that the Merton (1974) model and the Geske (1977) model under-predict while the LT model over predicts the yield spreads. With stochastic interest rate, it is found that the LS model and the CDG model do relatively better than the other models. However, they are sensitive to the choice of interest rate parameters.
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