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A two-mean reverting-factor model of the term structure of interest rates

✍ Scribed by Manuel Moreno

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
261 KB
Volume
23
Category
Article
ISSN
0270-7314

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✦ Synopsis

Abstract

This article presents a two‐factor model of the term structure of interest rates. It is assumed that default‐free discount bond
prices are determined by the time to maturity and two factors, the long‐term interest rate, and the spread (i.e., the difference)
between the short‐term (instantaneous) risk‐free rate of interest and the long‐term rate. Assuming that both factors
follow a joint Ornstein‐Uhlenbeck process, a general bond pricing equation is derived. Closed‐form expressions for prices of bonds and
interest rate derivatives are obtained. The analytical formula for derivatives is applied to price European options on discount bonds and more
complex types of options. Finally, empirical evidence of the model's performance in comparison with an alternative two‐factor
(Vasicek‐CIR) model is presented. The findings show that both models exhibit a similar behavior for the shortest maturities.
However, importantly, the results demonstrate that modeling the volatility in the long‐term rate process can help to fit the observed data,
and can improve the prediction of the future movements in medium‐ and long‐term interest rates. So it is not so clear which is the best
model to be used. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23: 1075–1105, 2003

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