Testing Continuous-Time Models of the Spot Interest Rate

Posted: 10 Oct 1994

See all articles by Yacine Ait-Sahalia

Yacine Ait-Sahalia

Princeton University - Department of Economics

Multiple version iconThere are 3 versions of this paper

Date Written: August 1994

Abstract

Many models of the term structure of interest rates rely on a continuous-time specification of the short rate process as one of their factors. Different parametric specifications for this process, often arbitrary and mutually exclusive, coexist in the literature. It is important to specify this process correctly, because it is the input of most interest rate derivative pricing models. This paper proposes a simple testing procedure designed to assess the fit of any given specification of the drift and diffusion of a continuous- time model. The test is based on a comparison of the distribution of the interest rate data implied by the particular parametric model and the distribution estimated nonparametrically. The nonparametric estimate is robust to misspecification of the parametric model and will, therefore, be consistent under both the null and the alternative hypotheses, while the parametric density estimate is consistent under the null and inconsistent under the alternative. The basic idea is that a parametric model for the spot rate process is not rejected if its implied distribution is sufficiently close to the estimated nonparametric distribution, and conversely. The results suggest that the drift of the interest rate process tends to mean-revert more strongly when far away from the mean than predicted by commonly used parametrizations. This reflects a credible commitment by the Federal Reserve to return the short-term interest rate to less extreme levels. Moreover, the interest rate process behaves likes a random walk when close to its mean, with the drift being close to zero in that region. The diffusion function is larger when the interest rate is away from the central region, signaling a higher level of volatility.

JEL Classification: G12, G13, C13, C22

Suggested Citation

Ait-Sahalia, Yacine, Testing Continuous-Time Models of the Spot Interest Rate (August 1994). Available at SSRN: https://ssrn.com/abstract=5573

Yacine Ait-Sahalia (Contact Author)

Princeton University - Department of Economics ( email )

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