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Quadratic, Affine and Hybrid Gaussian Term Structure Models in Discrete Time: Theory and Evidence

52 Pages Posted: 26 Oct 2009 Last revised: 28 Mar 2013

Grégoire Leblon

University of Rennes I, Graduate School of Management and CREM

Franck Moraux

Université de Rennes I and CREM

Date Written: January 1, 2013

Abstract

This paper explores Affine, Quadratic and Hybrid Term Structure Models in discrete time. Hybrid specification joints ATSM and QTSM with correlated Gaussian state variables. We provide new formulae and a new estimation strategy that make these models implementable. We estimate and extract latent factors of nine specifications (Affine, Quadratic and Hybrid Gaussian types). We analyze the behavior of each model, their capacity to fit moments of data and to reproduce the yield curves shapes. Our empirical results suggest first that Hybrid models with less than two quadratic factors are not worth considering. Second, three-factor Hybrid models have to be favored over ATSMs or QTSMs. Third, all models tend to have similar performance as the number of state factors increases. Fourth, given a number of state factors, Affine, Quadratic or Hybrid models have state factors that vehicle similar information about the level, the slope and the curvature of the yield curve. As an exception, three-factor model Hybrid specifications do not exhibit curvature effect. Finally, only three-factor models have their dynamic performance structurally uncorrelated to the level, the slope and the curvature. However, no model can absorb corresponding huge squared first-order variations.

JEL Classification: G10, G11

Suggested Citation

Leblon, Grégoire and Moraux, Franck, Quadratic, Affine and Hybrid Gaussian Term Structure Models in Discrete Time: Theory and Evidence (January 1, 2013). Paris December 2009 Finance International Meeting AFFI - EUROFIDAI. Available at SSRN: https://ssrn.com/abstract=1494243 or http://dx.doi.org/10.2139/ssrn.1494243

Grégoire Leblon (Contact Author)

University of Rennes I, Graduate School of Management and CREM ( email )

IGR - IAE de Rennes
11, rue Jean Macé
Rennes, 35000
France

Franck Moraux

Université de Rennes I and CREM ( email )

IAE de Rennes
11, rue Jean Macé
Rennes, 35000
France
+33 (0)2 23 23 78 08 (Phone)
+33 (0)2 23 23 78 00 (Fax)

HOME PAGE: http://perso.univ-rennes1.fr/franck.moraux/

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