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 same metrics for equivalent Treasury bonds. We show that the credit spread has two interacting effects on both the duration and the convexity of a corporate coupon bond as compared to those of an equivalent Treasury coupon bond. For bond convexity, we newly uncover that the first impact originates from the duration of the Treasuries and from both duration and convexity of the coupon bonds conditional survival probability, and the covariance between the default-free short rate and the credit spread. The second driving factor 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. The numerical experiments confirm our theoretical results. Given the empirical evidence that interest rates and credit spreads are, by and large, negatively correlated, our results support the notion that not only durations but also convexities of defaultable corporate bonds may be smaller than those of equivalent Treasuries