On the Term Structure of Interest Rates in the Presence of Reflecting and Absorbing Boundaries
38 Pages Posted: 21 Aug 1997
Date Written: June 12, 1997
Abstract
To preclude arbitrage, nominal interest rates must remain non-negative. Researchers have captured this feature by modeling the spot rate 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 for spot rate processes subject to reflecting and absorbing boundaries. Such models preclude negative rates, are consistent with large volatility at low rates, and admit closed form solutions for both bond and European-type derivative security prices. 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.
JEL Classification: G13
Suggested Citation: Suggested Citation