The short-term riskless interest rate is one of the most fundamental and important prices determined in financial markets. More models have been put forward to explain its behavior than for any other issue in finance. Many of the more popular models currently used by academic researchers and practitioners have been developed in a continuous-time setting, which provides a rich framework for specifying the dynamic behavior of the short-term riskless rate. A partial listing of these interest rate models includes those by Merton (1973), Brennan and Schwartz (1977, 1979, 1980), Vasicek (1977), Dothan (1978), Cox, Ingersoll, and Ross (1980, 1985), Constantinides and Ingersoll (1984), Schaefer and Schwartz (1984), Sundaresan (1984), Feldman (1989), Longstaff (1989a), Hull and White (1990), Black and Karasinski (1991), and Longstaff and Schwartz (1992).

Despite a bewildering array of models, relatively little is known about how these models compare in terms of their ability to capture the actual behavior of the short-term riskless rate. The primary reason for this has probably been the lack of a common framework in which different models could be nested and their performance benchmarked. Without a common framework, it is difficult to evaluate relative performance in a consistent way.^{1} The issue of how these models compare with each other is particularly important, however, since each model differs fundamentally in its implications for valuing contingent claims and hedging interest rate risk.

This paper uses a simple econometric framework to compare the performance of a wide variety of well-known models in capturing the stochastic behavior of the short-term rate. Our approach exploits the fact that many term structure models—both single-factor and multifactor—imply dynamics for the short-term riskless rate *r* that can be nested within the following stochastic differential equation:

These dynamics imply that the conditional mean and variance of changes in the short-term rate depend on the level of *r*. We estimate the parameters of this process in discrete time using the Generalized Method of Moments technique of Hansen (1982). As in Marsh and Rosenfeld (1983), we test the restrictions imposed by the alternative short-term interest rate models nested within equation (1). In addition, we compare the ability of each model to capture the volatility of the term structure. This property is of primary importance since the volatility of the riskless rate is a key variable governing the value of contingent claims such as interest rate options. In addition, optimal hedging strategies for risk-averse investors depend critically on the level of term structure volatility.

The empirical analysis provides a number of important results. Using one-month Treasury bill yields, we find that the value of *γ* is the most important feature differentiating interest rate models. In particular, we show that models which allow *r*; the unconstrained estimate of *γ* is 1.50. We also show that the models differ significantly in their ability to capture the volatility of the short-term interest rate. We find no evidence of a structural shift in the interest rate process in October 1979 for the models that allow

We show that these interest rate models differ significantly in their implications for valuing interest-rate-contingent securities. Using the estimated parameters for these models from the 1964 to 1989 sample period, we employ numerical procedures to value call options on long-term coupon bonds under different economic conditions. Our findings demonstrate that the range of possible call values varies significantly across the various models.

The remainder of the paper is organized as follows. Section I describes the short-term interest rate models examined in the paper. Section II discusses the econometric approach. Section III describes the data. Section IV presents the empirical results from comparing the models. Section V contrasts the models' implications for valuing options on long-term bonds. Section VI summarizes the paper and makes concluding remarks.