A Semiparametric Single-Factor Model of the Term Structure∗

We propose a semiparametric single-factor diffusion model for the term structure of interest rate. The This model is highly flexible and encompasses most parametric single-factor models proposed in the literature. We fit the semiparametric model to a proxy of the Eurodollar short term interst rate and compare it with the most flexible parametric model found in the literature: First directly, by testing the fully parametric model against the semiparametric one. Secondly, we look at how much the bond prices predicted by the competing models differ; this yields an alternative measure of the performance of the models. The fitted semiparametric model picks up nonlinearities which the fully parameteric model cannot capture. This leads to a rejection of the parametric model in favour of the semiparametric model in the direct comparison of the two fitted models. Moreover, the calculated bond prices implied by the two competing models are shown to be significantly different. ∗This paper is part of my PhD-thesis at the LSE. I would like to thank my supervisor, Oliver Linton, for valuable suggestions and comments. †E-mail: [email protected] Address: R4z19C, FMG, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom