ABSTRACT
To preclude arbitrage, nominal interest rates must remain non-negative. Models of the term structure have attempted to incorporate this feature by modeling spot rate processes with volatility structures that vanish as the spot rate tends to zero. However, such volatility structures are in conflict with empirical evidence; volatility can remain relatively large even at low interest rates. In this paper, we investigate the term structure of interest rates of one-factor models for spot rate processes subject to reflecting and absorbing boundaries. Such models preclude negative rates, are consistent with large volatility atlow rates, and admit closed form bond price formula. Below, appropriate boundary conditions are derived for spot rates processes that are subject to reflecting and absorbing boundaries. Although it can be demonstrated that spot rate processes with reflecting boundaries can be supported within a general equilibrium framework, we show that reflecting boundaries cannot be placed upon forward rate dynamics without generating arbitrage opportunities. Closed form bond price solutions for select models are obtained.

Download the paper (Acrobat .pdf file) . Download Acrobat Reader.
Download the paper (Postscript .ps file) .

E-mail the dice center