A New Approach to Estimation of the Term Structure of Interest Rates

Abstract

The purpose of this study is to extend the analysis of estimation of the term structure. The ability of the exponential/polynomial present-value function of equation (5) to approximate the theoretical present-value function is analyzed empirically. This study confirms previous results that indicate that the function does not provide an acceptable fit using least squares regression. In most samples, the near end of the estimated term structure appears substantially in error. Lengthening the polynomial tends to improve the fit only at the far end. Since the data appear to be subject to maturity-related heteroschedasticity, we have generalized the disturbance variance specification to allow for this possibility.Our correction permits determination of sample-specific degrees of heteroschedasticity. The reason is that the intensity of the heteroschedasticity appears to change from period to period. Although previous studies have attempted heteroschedasticity corrections (see [4]), the same specification was imposed on each sample in such studies. Maximum likelihood estimation was proposed and implemented in this paper. The results indicate that the difficulties of providing a good fit using the exponential/polynomial function are substantially eliminated.Recent literature regarding term structure estimation emphasizes the selection of more sophisticated estimating functions to provide a reasonable fit throughout the entire maturity range. This study emphasizes more careful modeling of the pricing disturbances. The prior approach involves somewhat complicated estimating functions and a potential loss of efficiency due to the lack of influence that each portion of the term structure is able to exert on other portions (with spline functions, for example.) Our maximum likelihood approach is somewhat difficult to implement and computationally burdensome. Nevertheless, it appears to provide a useful term structure estimation procedure.