A generalized method of moments comparison of several discrete time stochastic models of the term structure in the Heath-Jarrow-Morton arbitrage-based framework.

Abstract

This paper tests a new methodology; the discrete time no arbitrage-based model of Heath, Jarrow and Morton (HJM). From within Ho and Lee's framework, HJM's model is shown to encompass Ho and Lee's AR model as a special case. Several discrete stochastic models of the term structure based on restrictions placed on the variance of the forward rate process are discussed. These models are tested in HJM's no arbitrage-based framework. For testing, it is necessary to use current bond prices to substitute out for the market price of risk implied in the initial term structure. In this way, additional current bond prices appear in the pricing formulas, but the market price of risk does not. Several sets of forward rate models are tested. To avoid measurement errors associated with fitting splines to coupon-bearing bonds, coupon-free data are used. Weekly T-bill quotes over a twenty-three year period, starting in 1968 are split into two equal sets about the structural break of October 7, 1979 following the shift in the Federal Reserve's monetary policy. These two data sets are split in half for further testing. Hansen's Generalized Method of Moments (GMM) is employed to estimate the models' parameters with a minimum of assumptions. Because the models are not nested, the resulting J statistics are not suitable for model comparisons. As an alternative, "simulated residuals" resulting from the imposition of the parameter values obtained from the GMM estimation are calculated. The model generating the set of simulated residuals with the smallest variance is assumed to have the best fit. The F test is used for pairwise comparisons of the models. The sets of simulated residuals are not normally distributed. However, unless two samples are from radically different distributions, the F test is quite robust to the assumption of sample normality and can still be used to perform an informal comparison of two similar samples.