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

11 Pages Posted: 8 Jun 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: 2008-09

Abstract

Dai and Singleton (2000) study a class of term structure models for interest rates that specify the short rate as an affine combination of the components of an N-dimensional affine diffusion process. Observable quantities in such models are invariant under regular affine transformations of the underlying diffusion process. 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+ × RN−m for integers 0 ≤ m ≤ N satisfying m ≤ 1 or m ≥ N − 1, there exists a regular affine transformation of D onto itself that diagonalizes the diffusion matrix. So in this case, the Dai–Singleton canonical representation is exhaustive. On the other hand, we provide examples of affine diffusion processes with state spaceR2+ × R2 whose diffusion matrices cannot be diagonalized through regular affine transformation. This shows that for 2 ≤ m ≤ (N − 2)), the assumption of diagonal diffusion matrices may impose unnecessary restrictions and result in an avoidable loss of generality.

Suggested Citation

Cheridito, Patrick and Filipovic, Damir and Kimmel, Robert L., A Note on the Dai–Singleton Canonical Representation of Affine Term Structure Models (2008-09). Mathematical Finance, Vol. 20, Issue 3, pp. 509-519, July 2010. Available at SSRN: https://ssrn.com/abstract=1622002 or http://dx.doi.org/10.1111/j.1467-9965.2010.00408.x

Patrick Cheridito (Contact Author)

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

Independent

No Address Available
United States

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