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An Empirical Study of Corporate Bond Pricing with Unobserved Capital Structure Dynamics

by Iain Campbell Maclachlan of the University of Melbourne

May 2007

Abstract: This work empirically examines six structural models of the term structure of credit risk spreads: Merton (1974), Longstaff & Schwartz (1995) (with and without stochastic interest rates), Leland & Toft (1996), Collin-Dufresne & Goldstein (2001), and a constant elasticity of variance model. The conventional approach to testing structural models has involved the use of observable data to proxy the latent capital structure process, which may introduce additional specification error. This study extends Jones, Mason & Rosenfeld (1983) and Eom, Helwege & Huang (2004) by using implicit estimation of key model parameters resulting in an improved level of model fit. Unlike prior studies, the models are fitted from the observed dynamic term structure of firm-specific credit spreads, thereby providing a pure test of model specification. The models are implemented by adapting the method of Duffee (1999) to structural credit models, thereby treating the capital structure process is truly latent, and simultaneously enforcing crosssectional and time-series model constraints. Quasi-maximum likelihood parameter estimates of the capital structure process are obtained via the extended Kalman filter applied to actual market trade prices on 32 firms and 200 bonds for the period 1994 to 2000.

We find that including an allowance for time-variation in the market liquidity premium improves model specification. A simple extension of the Merton (1974) model is found to have the greatest prediction accuracy, although all models performed with similar prediction errors. At between 28.8 to 34.4 percent, the root mean squared error of the credit spread prediction is comparable with reduced-form models. Unlike Eom, Helwege & Huang (2004) we do not find a wide dispersion in model prediction errors, as evidenced by an across model average mean absolute percentage error of 22 percent. However, in support of prior studies we find an overall tendency for slight underprediction, with the mean percentage prediction error of between -6.2 and -8.7 percent. Underprediction is greatest with short remaining bond tenor and low rating. Credit spread prediction errors across all models are non-normal, and fatter tailed than expected, with autocorrelation evident in their time series.

More complex models did not outperform the extended Merton (1974) model; in particular stochastic interest-rate and early default accompanied by an exogenous write-down rate appear to add little to model accuracy. However, the inclusion of solvency ratio mean-reversion in the Collin-Dufresne & Goldstein (2001) model results in the most realistic latent solvency dynamics as measured by its implied levels of asset volatility, default boundary level, and mean-reversion rate. The extended Merton (1974) is found to imply asset volatility levels that are too high on average when compared to observed firm equity volatility.

We find that the extended Merton (1974) and the Collin-Dufresne & Goldstein (2001) models account for approximately 43 percent of the credit spread on average. For BB rated trades, the explained proportion rises to 55 to 60 percent. For investment grade trades, our results suggest that the amount of the credit spread that is default related is approximately double the previous estimate of Huang & Huang (2003).

Finally, we find evidence that the prediction errors are related to market-wide factors exogenous to the models. The percentage prediction errors are positively related to the VIX and change in GDP, and negatively related to the Refcorp-Treasury spread.

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