A Type of HJM Based Affine Model: Theory and Empirical Evidence

51 Pages Posted: 18 May 2010

See all articles by Haitao Li

Haitao Li

University of Michigan - Stephen M. Ross School of Business; Cheung Kong Graduate School of Business; Cheung Kong Graduate School of Business

Xiaoxia Ye

University of Liverpool Management School

Date Written: May 17, 2010

Abstract

In this paper a type of Heath, Jarrow and Morton (1992) (HJM) based affine model is derived theoretically. This type of affine model is obtained by applying Linear Realization Theory to construct Finite Dimensional Realizations (FDRs) of the Gaussian HJM model. The algorithms of constructing Standard Observable Canonical Realization and Jordan Canonical Realization are introduced sequentially. And it is shown that the commonly adopted FDR is actually Jordan Canonical Realization. The empirical results show that a two-factor model of this type provides great fit to the term structure of interest rates data. The resulting state variables have clear economic interpretations. And it is found that the short end of the term structure can be precisely considered as a “medium-run factor” which uniformly shifts the yield curve. This finding has an important implication for bond portfolios management, and also helps us better understand the interactions between macro-economy and term structure dynamics.

Keywords: Affine Term Structure Model, HJM, Finite Dimensional Realization, Linear Realization Theory, State Space Framework, Macro-economy

JEL Classification: C61, E43, E44, G12

Suggested Citation

Li, Haitao and Ye, Xiaoxia, A Type of HJM Based Affine Model: Theory and Empirical Evidence (May 17, 2010). Available at SSRN: https://ssrn.com/abstract=1609945 or http://dx.doi.org/10.2139/ssrn.1609945

Haitao Li

University of Michigan - Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States
734-615-5475 (Phone)

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Xiaoxia Ye (Contact Author)

University of Liverpool Management School ( email )

Chatham Street
Liverpool, L69 7ZH
United Kingdom

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