A Note on the Dai-Singleton Canonical Representation of Affine Term Structure Models

Fisher College of Business Working Paper No. 2007-03-005

Charles A. Dice Working Paper No. 2007-2

11 Pages Posted: 26 Feb 2007 Last revised: 27 Sep 2010

See all articles by Patrick Cheridito

Patrick Cheridito

ETH Zurich

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Robert L. Kimmel

Independent

Date Written: September 2008

Abstract

Dai and Singleton (2000) study a class of term structure models for interest rates that specify the instantaneous interest rate as an affine combination of the components of an N-dimensional affine diffusion process. Observable quantities of such models are invariant under regular affine transformations of the underlying diffusion process. And in their canonical form, the models in Dai and Singleton (2000) are based on diffusion processes with diagonal diffusion matrices. This motivates the following question: Can the diffusion matrix of an affine diffusion process always be diagonalized by means of a regular affine transformation?

We show that if the state space of the diffusion is of the form D = Rm+ x RN - m for integers 0 <= m <= N satisfying m <= 1 or m >= N - 1, then there exists a regular affine transformation of D onto itself that diagonalizes the diffusion matrix. On the other hand, we provide examples of affine diffusion processes with state space R2+ x R2 whose diffusion matrices cannot be diagonalized through regular affine transformation.

Keywords: affine diffusion processes, affine transformations, diagonal diffusion matrices

JEL Classification: G12, G13

Suggested Citation

Cheridito, Patrick and Filipovic, Damir and Kimmel, Robert L., A Note on the Dai-Singleton Canonical Representation of Affine Term Structure Models (September 2008). Fisher College of Business Working Paper No. 2007-03-005; Charles A. Dice Working Paper No. 2007-2. Available at SSRN: https://ssrn.com/abstract=964956 or http://dx.doi.org/10.2139/ssrn.964956

Patrick Cheridito

ETH Zurich ( email )

Department of Mathematics
8092 Zurich
Switzerland

Damir Filipovic

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Robert L. Kimmel (Contact Author)

Independent

No Address Available

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