Fundamental Properties of Bond Prices in Models of the Short-Term Rate

Abstract

This paper develops restrictions that arbitrage-constrained bond prices impose on the short-term rate process in order to be consistent with given dynamic properties of the term-structure of interest rates. The central focus is the relationship between bond prices and the short-term rate volatility. In both scalar and multidimensional diffusion settings, typical relationships between bond prices and volatility are generated by joint restrictions on the risk-neutralized drift functions of the state variables and convexity of bond prices with respect to the short-term rate. The theory is illustrated by several examples and is partially extended to accommodate the occurrence of jumps and default.