Empirical investigation of the unique linear solution to the term structure of interest rates

Abstract

Guo (2000) derived a unique linear solution to the term structure of interest rates, which guarantees the existence of a unique risk-neutral martingale probability measure, as long as the underlying state vector follows Ito process. This solution describes the space of term structures as linearly spanned by a state vector upon a constant basis of exponential functions. Since the state vector is defined relatively to a constant basis, it is critical to investigate empirically whether such a constant basis exists. Since there are only seven benchmark Treasury securities with reliable price quotes, and seven factors are sufficient for representing the entire term structure, this paper specifies a seven-factor version of the linear solution so that the seven state factors can be inverted directly from the seven benchmark prices. This paper has confirmed that the parameters can be kept constant over time, hence, the state factors are well defined. This paper has further found that every state factor in discrete time · follows an AR ( 1) process, which clearly supports the Ito process assumption underlying the unique linear solution.