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

Author

Listed:
  • Ruijun Bu

    () (Liverpool University - LIVERPOOL UNIVERSITY)

  • Ludovic Giet

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

  • Kaddour Hadri

    (QUB - Queen's University [Belfast])

  • Michel Lubrano

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

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.

Suggested Citation

  • Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations," Working Papers halshs-00408014, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00408014
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00408014
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    References listed on IDEAS

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    Keywords

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

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