Assessing Default Probabilities from Structural Credit Risk Models

Abstract

In this paper, we study the empirical performance of structural credit risk models by examining the default probabilities calculated from these models with different time horizons. The parameters of the models are estimated from firm's bond and equity prices. The models studied include Merton (1974), Merton model with stochastic interest rate, Longstaff and Schwartz (1995), Leland and Toft (1996) and Collin-Dufresne and Goldstein (2001). The sample firms chosen are those that have only one bond outstanding when bond prices are observed. We first find that when the Maximum Likelihood estimation, introduced in Duan (1994), is used to estimate the Merton model from bond prices, the estimated volatility is unreasonable high and the estimation process does not converge for most of the firms in our sample. This shows that the Merton (1974) is not able to generate high yields to match the empirical observations. On the other hand, when equity prices are used as input we find that the default probabilities predicted for investment-grade firms by Merton (1974) are all close to zero. When stochastic interest rates are assumed in Merton model, the model performance is improved. The models of Longstaff and Schwartz (1995) with constant interest rate as well as the Leland and Toft (1996) provide quite reasonable predictions on real default probabilities when compared with those reported by Moody's and S&P. However, Collin-Dufresnce and Goldstein (2001) predict unreasonably high default probabilities for longer time horizons.