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Estimating Discrete-Time Gaussian Term Structure Models in Canonical Companion Form

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This article proposes a convenient parametrization for the popular class of (discrete-time)

essentially-affine term structure models of Duffee (2002), and Ang and Piazzesi (2003). First, I

show that if bond prices are determined by N latent state variables, all their pricing information

must be present in the short end of the term structure, i.e., one can rotate the model to an observationally

equivalent form with exactly N short maturity forward rates as factors. Second, the

risk-neutral transition of the rotated model is conveniently parametrized by N unrestricted real

numbers (contained in a companion matrix), and only one additional parameter is needed to specify

the risk neutral drift. Third, the resulting state-space representation makes it easy to estimate the

model either by the Kalman filter (in one step), or treating N linear combinations of observable

bond prices (or yields) as observable factors. Finally, I interpret some difficulties in fitting the

essentially-affine term structure models to the data, using the standard set of Fama-Bliss discount

bonds as example. The problem is the existence of (spanned) factors that significantly predict term

structure movements but are virtually impossible to detect from the shortest-maturity forward

rates, which is (by the results of this paper) inconsistent with no arbitrage within the discussed

class of models.

Author(s):

Juliusz Radwanski

HU Berlin

Germany