On the form and risk-sensitivity of zero coupon bonds for a class of interest rate models

We consider the form and the comparative static properties of the price of a zero coupon bond with maturity T for a broad class of interest rate models. We first demonstrate that increased volatility increases the price of a T-claim whenever the price is convex as a function of the current short rate. We then present a class of diffusion models (including, for example, the Dothan, the Black–Derman–Toy, and the Merton model of interest rates) for which the positivity of the sign of the relationship between volatility and the price of zero coupon bonds is always unambiguously guaranteed. Consequently, we find that for the considered class of models the price of zero coupon bonds can be completely ordered in terms of the riskiness of the underlying interest rate dynamics. We also show that for the proposed class of interest rate models, increased volatility increases the price of all convex and non-increasing T-claims as well.