This article uses a Kalman filter to fit yields of investment-grade corporate bonds to the model of instantaneous default risk, based on Duffee (1999. Review of Financial Studies. 12. PP. 197-226). The first part of this article fits the term structure of default-free interest rates to a translated two-factor square-root diffusion model. The parameters in the two-factor model are estimated by using a quasi-maxirnum-likelihood estimator in a state-space model in the Korean treasury bond market. A Kalman filter is used to estimate the unobservable factors.
The two-factor model successfully incorporates random variations in the slope of the term structure and the level of interest rates‘ After estimating the default-free term structure of interest rates, the second part of this article extends the model to noncallable corporate bonds‘ This is done by assuming that the probability of default follows a translated square-root diffusion process with the possibility of being correlated with default-free interest rates. The parameters of the process are estimated for investment-grade corporate bonds including AM. AA, A. and BBB. Empirical results show that the default risk is negatively correlated with default-free interest rates and confirm that the default risk is greater for lower grades. In addition, the estimated model successfully produces the term structures of credit spreads for corporate bonds and show that the credit spreads for lower grade bonds are more steeply sloped than those for higher grade bonds. These results show that Duffee's model can reasonably account for the observed corporate bond prices in the Korean bond market.
