Wishart Quadratic Term Structure Models

Les Cahiers du CREF of HEC Montreal Working Paper No. 03-10

35 Pages Posted: 18 Jul 2005

See all articles by Christian Gourieroux

Christian Gourieroux

University of Toronto - Department of Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO); Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE); National Bureau of Economic Research (NBER)

Razvan Sufana

University of Toronto - Department of Economics

Date Written: December 2003

Abstract

This paper reveals that the class of affine term structure models introduced by Duffie and Kan (1996) is much larger than it has been usually considered in the literature. We study fundamental risk factors, which represent multivariate risk aversion of the consumer or the volatility matrix of the technological activity returns, and argue that they can be defined as symmetric positive matrices. For such matrices we introduce a dynamic affine process called the Wishart autoregressive (WAR) process; this process is used to reveal the associated term structure. In this framework:

i) we derive very simple restrictions on the parameters to ensure positive yields at all maturities;

ii) we observe that the usual constraint that the volatility matrix of an affine process be diagonal up to a path independent linear invertible transformation can be considerably relaxed.

The Wishart Quadratic Term Structure Model is the natural extension of the one-dimensional Cox-Ingersoll-Ross model and of the quadratic models introduced in the literature.

Keywords: Affine Term Structure, Quadratic Term Structure, CAR Process, Affine Process, WAR Process

JEL Classification: G13, C51

Suggested Citation

Gourieroux, Christian and Sufana, Razvan, Wishart Quadratic Term Structure Models (December 2003). Les Cahiers du CREF of HEC Montreal Working Paper No. 03-10, Available at SSRN: https://ssrn.com/abstract=757307 or http://dx.doi.org/10.2139/ssrn.757307

Christian Gourieroux (Contact Author)

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Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

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National Bureau of Economic Research (NBER)

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Razvan Sufana

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S 3G7
Canada

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