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Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications


  • Markus Junker
  • Alexander Szimayer
  • Niklas Wagner


This paper documents nonlinear cross-sectional dependence in the term structure of U.S. Treasury yields and points out risk management implications. The analysis is based on a Kalman filter estimation of a two-factor affine model which specifies the yield curve dynamics. We then apply a broad class of copula functions for modeling dependence in factors spanning the yield curve. Our sample of monthly yields in the 1982 to 2001 period provides evidence of upper tail dependence in yield innovations; i.e., large positive interest rate shocks tend to occur under increased dependence. In contrast, the best fitting copula model coincides with zero lower tail dependence. This asymmetry has substantial risk management implications. We give an example in estimating bond portfolio loss quantiles and report the biases which result from an application of the normal dependence model.

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  • Markus Junker & Alexander Szimayer & Niklas Wagner, 2004. "Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications," Econometrics 0401007, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0401007 Note: Type of Document - pdf; prepared on win00; to print on laserjet; pages: 50

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    References listed on IDEAS

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    Cited by:

    1. Fernandez, Viviana, 2008. "Copula-based measures of dependence structure in assets returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3615-3628.
    2. Koziol, Philipp & Schell, Carmen & Eckhardt, Meik, 2015. "Credit risk stress testing and copulas: Is the Gaussian copula better than its reputation?," Discussion Papers 46/2015, Deutsche Bundesbank.
    3. Joe-Ming Lee, 2013. "Measuring the Mutual Fund Industry Risk Management and Performance Sustainability - Quantile Regression Model," Journal of Asian Business Strategy, Asian Economic and Social Society, vol. 3(4), pages 59-68, April.
    4. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    5. Chatrath, Arjun & Christie-David, Rohan A. & Lee, Kiseop & Moore, William T., 2009. "Competitive inventory management in Treasury markets," Journal of Banking & Finance, Elsevier, vol. 33(5), pages 800-809, May.
    6. Äijö, Janne, 2008. "Implied volatility term structure linkages between VDAX, VSMI and VSTOXX volatility indices," Global Finance Journal, Elsevier, vol. 18(3), pages 290-302.
    7. Aloui, Riadh & Gupta, Rangan & Miller, Stephen M., 2016. "Uncertainty and crude oil returns," Energy Economics, Elsevier, vol. 55(C), pages 92-100.
    8. 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.
    9. Joe-Ming Lee, 2013. "The Search of Structural Changes in Mutual Fund Industry-Based On the ARMAX-GJR-GARCH Model," Asian Journal of Empirical Research, Asian Economic and Social Society, vol. 3(3), pages 308-316, March.
    10. Wang, Zong-Run & Chen, Xiao-Hong & Jin, Yan-Bo & Zhou, Yan-Ju, 2010. "Estimating risk of foreign exchange portfolio: Using VaR and CVaR based on GARCH–EVT-Copula model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4918-4928.
    11. Viviana Fernandez, 2008. "Multi‐period hedge ratios for a multi‐asset portfolio when accounting for returns co‐movement," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(2), pages 182-207, February.
    12. Christian M. Hafner & Hans Manner, 2012. "Dynamic stochastic copula models: estimation, inference and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(2), pages 269-295, March.
    13. Marc Gronwald & Janina Ketterer & Stefan Trück, 2011. "The Dependence Structure between Carbon Emission Allowances and Financial Markets - A Copula Analysis," CESifo Working Paper Series 3418, CESifo Group Munich.
    14. Penikas, Henry & Simakova, Varvara, 2009. "Interest Rate Risk Management Based on Copula-GARCH Models," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 13(1), pages 3-36.
    15. Chu, Ba, 2011. "Recovering copulas from limited information and an application to asset allocation," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1824-1842, July.
    16. Cem Çakmakli, 2012. "Bayesian Semiparametric Dynamic Nelson-Siegel Model," Working Paper series 59_12, Rimini Centre for Economic Analysis, revised Sep 2012.
    17. Manner Hans, 2007. "Estimation and Model Selection of Copulas with an Application to Exchange Rates," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    18. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
    19. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modelling Multivariate Interest Rates using Time-Varying Copulas and Reducible Non-Linear Stochastic Differential," Economics Working Papers 09-02, Queen's Management School, Queen's University Belfast.

    More about this item


    affine term structure models; nonlinear dependence; copula functions; tail dependence; value-at-risk;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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