Estimating the Probabilities of Default for Callable Bonds: A Duffie-Singleton Approach

This paper presents a model for estimating the default risks implicit in the prices of callable corporate bonds. The model considers three essential ingredients in the pricing of callable corporate bonds: stochastic interest rate, default risk, and call provision. The stochastic interest rate is modeled as a square-root diffusion process. The default risk is modeled as a constant spread, with the magnitude of this spread impacting the probability of a Poisson process governing the arrival of the default event. The call provision is modeled as a constraint on the value of the bond in the finite difference scheme. The empirical results are encouraging. First, the estimated default probabilities are consistent with Moody¡¦s ratings. The estimated default probabilities rise with lower ratings and fall with higher ratings. Second, the relationship between the estimated default probabilities and other bond characteristics is consistent with the intuition. The estimated default probabilities are negatively correlated with maturity and positively correlated with coupon payment, age, and issue size. This paper can be used both as a benchmark for models for estimating the default risks associated with callable corporate bonds and as a direction for future research.