Abstract
We compare the durations of corporate and Treasury bonds in the reduced-form, intensity based credit risk modeling framework. In the case where default risk is independent of default-free interest rates, we provide in each of the three most popular recovery regimes a sufficient condition under which the duration of the corporate bond is smaller than the duration of a similar Treasury bond. In the case where the default intensity and the recovery rate may depend on the default-free interest rate, we also provide a sufficient condition for the duration of a corporate bond to be smaller than the duration of the corresponding Treasury bond, assuming that recovery of market value applies. We illustrate our findings and offer more details in a specific setting in which default-free interest rates follow a Vasicek model and recovery of market value applies with a constant loss rate and a default intensity which is affine in the default-free short rate. While the unanimous conclusion of earlier papers is that the corporate bond has a smaller duration than the corresponding Treasury bond, we demonstrate in this setting that the duration of a corporate coupon bond can very well be greater than that of the similar Treasury bond.
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