This paper first reviews empirical evidence and estimation methods of structural credit risk models. Next, an empirical investigation of the performance of default prediction under the down-and-out barrier option framework is provided. In the literature review, a brief overview of the structural credit risk models is provided. Empirical investigations in extant literature papers are described in some detail, and their results are summarized in terms of subject and estimation method adopted in each paper. Current estimation methods and their drawbacks are discussed in detail. In our empirical investigation, we adopt the Maximum Likelihood Estimation method proposed by Duan [Mathematical Finance 10 (1994) 461-462]. This method has been shown by Ericsson and Reneby [Journal of Business 78 (2005) 707-735] through simulation experiments to be superior to the volatility restriction approach commonly adopted in the literature. Our empirical results surprisingly show that the simple Merton model outperforms the Brockman and Turtle [Journal of Financial Economics 67 (2003) 511-529] model in default prediction. The inferior performance of the Brockman and Turtle model may be the result of its unreasonable assumption of the flat barrier.
We study defaultable bond prices in the Black-Cox model with jumps in the asset value. The jump-size distribution is arbitrary, and following Longstaff and Schwartz (1995) and Zhou (2001) we assume that, if default occurs, the recovery at maturity depends on the 'severity of default'. Under this general setting, the vehicle for our analysis is an integral equation. With the aid of this, we prove some properties of the bond price which are consistent numerically and empirically with earlier works. In particular, the limiting credit spread as time to maturity tends to 0 is nonzero. As a byproduct, we show that the integral equation implies an infinite-series expansion for the bond price.
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