Around and Around: The Expectations Hypothesis

Abstract

We show how to construct models of the term structure of interest rates in which the expectations hypothesis holds. McCulloch (1993) presents such a model, thereby contradicting an assertion by Cox, Ingersoll, and Ross (1981), but his example is Gaussian and falls outside the class of finite-dimensional Markovian models. We generalize McCulloch's model in three ways: (i) We provide an arbitrage-free characterization of the unbiased expectations hypothesis in terms of forward rates; (ii) we extend this characterization to a whole class of expectations hypotheses; and (iii) we show how to construct finite-dimensional Markovian and non-Gaussian examples.