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The Vasicek and CIR Models and the Expectation Hypothesis of the Interest Rate Term Structure

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Patrick Georges

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Abstract

A good understanding of the theories of the interest rate term structure is important when elaborating a debt management strategy and, in particular, when choosing the maturity structure of the public debt. “Best practises” of debt management suggest the use of modern theories of the term structures based on the seminal papers by Vasicek (1977) and Cox, Ingersoll and Ross (1985). These models have been used to analyse the maturity structure of the public debt both at the Bank of Canada and at the Department of Finance, and in other countries [e.g., Danish Nationalbank (2001)]. This paper documents the Vasicek and CIR term structure of the interest rates that has been introduced into a macro-economic stochastic simulation model (SSM) developed at the Department of Finance. The final aim will be to use the SSM with alternative term structures of interest rates to gauge the robustness of our earlier results described in Georges (2003), which suggests that a shorter debt maturity structure is less expensive on average and also less risky from the point of view of the overall budget balance if demand shocks prevail over the business cycle.

Une bonne connaissance des théories de la structure à terme des taux d’intérêts est une condition nécessaire à l’élaboration d’une stratégie de la gestion de la dette publique y comprit du choix de la maturité de cette dette. Les pratiques de rigueur en gestion de la dette utilisent les théories modernes de la gamme des taux basées sur les études de Vasicek (1977) et Cox, Ingersoll et Ross (1985). Ces modèles ont été utilisés à la Banque du Canada et au Ministère des Finances, ainsi que dans d’autres pays [e.g., Banque Nationale du Danemark (2001)] afin d’analyser la maturité de la dette publique. Ce papier documente les structures à terme des modèles de Vasicek et CIR introduits dans un modèle macro-économique de simulation stochastique (MSS) développé au Ministère des Finances. L’objectif ultime sera d’utiliser le MSS avec des structures à terme alternatives afin d’examiner la sensibilité de nos résultats antérieurs (Georges 2003) selon lesquels une structure de dette à plus court terme est moins coûteuse en moyenne et moins risquée du point de vue du solde budgétaire si les chocs de demande dominent au cours du cycle des affaires.

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Paper provided by Department of Finance Canada in its series Working Papers-Department of Finance Canada with number 2003-17.

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Handle: RePEc:fca:wpfnca:2003-17

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