On the Term Structure of Interest Rates in the Presence of Reflecting and Absorbing Boundaries

38 Pages Posted: 21 Aug 1997

See all articles by Robert S. Goldstein

Robert S. Goldstein

University of Minnesota - Twin Cities - Carlson School of Management; National Bureau of Economic Research (NBER)

William P. Keirstead

Goldman Sachs Group, Inc. - Japan Office

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

Goldstein, Robert S. and Keirstead, William P., On the Term Structure of Interest Rates in the Presence of Reflecting and Absorbing Boundaries (June 12, 1997). Available at SSRN: https://ssrn.com/abstract=19840 or http://dx.doi.org/10.2139/ssrn.19840

Robert S. Goldstein (Contact Author)

University of Minnesota - Twin Cities - Carlson School of Management ( email )

19th Avenue South
Minneapolis, MN 55455
United States
612-624-8581 (Phone)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

William P. Keirstead

Goldman Sachs Group, Inc. - Japan Office ( email )

Minato-ku, Tokyo 107
Japan

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