Bond Duration and Convexity under Stochastic Interest Rates and Credit Spreads

We investigate the impact of credit spreads on the stochastic duration and convexity of corporate bonds with respect to the very metrics for equivalent Treasury bonds. We show that the credit spread has two interacting effects on both the duration and convexity of a corporate coupon bond compared to those of an equivalent Treasury coupon bond. For bond convexity, we newly uncover that the first effect originates from the duration of the Treasuries; from both the duration and convexity of the coupon bonds’ conditional survival probability; and from the covariance between the default-free short rate and the credit spread. The second driver stems from the weighting of the convexities of the zero-coupon bonds. We provide necessary and sufficient conditions for the duration and convexity of defaultable corporate coupon bonds to be smaller than those of equivalent Treasury bonds. Since interest rates and credit spreads are, by and large, negatively correlated, our numerical results support the notion that not only durations but also convexities of defaultable corporate bonds may be smaller than those of equivalent Treasuries.