AN INTEGRAL-EQUATION APPROACH FOR DEFAULTABLE BOND PRICES WITH APPLICATION TO CREDIT SPREADS

Abstract

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 by product, we show that the integral equation implies an infinite-series expansion for the bond price.