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Finance and Economics Discussion Series
The Finance and Economics Discussion Series logo links to FEDS home page Around and Around: The Expectations Hypothesis
Mark Fisher and Christian Gilles

Abstract: We show how to construct arbitrage-free models of he term structure of interest rates in which various expectations hypotheses can hold. McCulloch (1993) provided a Gaussian non-Markovian example of the unbiased expectations hypothesis (U--EH), thereby contradicting the assertion by Cox, Ingersoll, and Ross (CIR, 1981) that only the so-called local expectations hypothesis could hold. We generalize that example in three ways: (i) We characterize the U--EH in terms of forward rates; (ii) we extend this characterization to a class of expectations hypotheses that includes all of those considered by CIR; and (iii) we construct stationary Markovian and non-Gaussian economies. The building block is a maturity-dependent vector that travels around a circle at a constant speed as maturity increases.

Keywords: Expectations hypothesis, yield curve, arbitrage

Full paper (330 KB PDF) | Full paper (267 KB Postscript)

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