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

Economics

Further details

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 the scalar diffusion setting, bond prices are negatively related to volatility at short maturity dates when the market risk is positively priced. In the setting of diffusion processes with random volatility, bond prices are still decreasing in volatility at short maturity dates when 1) the risk-neutralized drift function of the short-term rate is increasing in volatility; if 1) fails, bond prices are always increasing in volatility when they are 2) decreasing and 3) convex in the short-term rate.