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Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations

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Author Info

  • Ruijun Bu

    ()
    (Liverpool University - Liverpool University)

  • Ludovic Giet

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

  • Kaddour Hadri

    (Queen's University - Queen's University)

  • Michel Lubrano

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

Abstract

We propose a new approach for modeling non-linear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of non-linear SDEs that are reducible to Ornstein-Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a non-linear transformation function. The main advantage of this approach is that these SDEs can account for non-linear features, observed in short-term interest rate series, while at the same time leading to \emph{exact discretisation } and \emph{closed form likelihood functions. } Although a rich set of specifications may be entertained, our exposition focuses on a couple of non-linear constant elasticity volatility (CEV) processes, denoted OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed form likelihood functions. The statistical properties of the two processes are investigated. In order to obtain more flexible functional form over time, we allow the transformation function to be time-varying. Results from our study of US and UK short term interest rates suggest that the new models outperform existing parametric models with closed form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying Symmetrised Joe-Clayton copula. We find evidence of asymmetric dependencebetween the two rates, and that the level of dependence is positively related to the level of the two rates.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00408014.

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Date of creation: 15 Nov 2009
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Handle: RePEc:hal:wpaper:halshs-00408014

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Related research

Keywords: Interest Rate Models; Reducible Stochastic Differential Equations; Maximum Likelihood Estimation; Constant Elasticity Models; Copula;

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