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

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  • Markus Junker
  • Alexander Szimayer
  • Niklas Wagner

Abstract

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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File URL: http://128.118.178.162/eps/em/papers/0401/0401007.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0401007.

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Length: 50 pages
Date of creation: 30 Jan 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0401007

Note: Type of Document - pdf; prepared on win00; to print on laserjet; pages: 50
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Web page: http://128.118.178.162

Related research

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

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References

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  1. Simon Babbs & K. Nowman, 1998. "Econometric Analysis of a Continuous Time Multi-Factor Generalized Vasicek Term Structure Model: International Evidence," Asia-Pacific Financial Markets, Springer, vol. 5(2), pages 159-183, May.
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  4. Duan, Jin-Chuan & Simonato, Jean-Guy, 1999. " Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter," Review of Quantitative Finance and Accounting, Springer, vol. 13(2), pages 111-35, September.
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  7. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
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  13. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 115-130, March.
  14. Patton, Andrew J, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series qt01q7j1s2, Department of Economics, UC San Diego.
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Citations

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Cited by:
  1. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
  2. 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.
  3. Cem Çakmakli, 2012. "Bayesian Semiparametric Dynamic Nelson-Siegel Model," Working Paper Series 59_12, The Rimini Centre for Economic Analysis, revised Sep 2012.
  4. Viviana Fernandez, 2006. "Copula-based measures of dependence structure in assets returns," Documentos de Trabajo 228, Centro de Economía Aplicada, Universidad de Chile.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
  10. 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.
  11. repec:asi:joabsj:2013:p:59-68 is not listed on IDEAS
  12. 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.
  13. Viviana Fernández, 2007. "Multi-period hedge ratios for a multi-asset portfolio when accounting for returns comovement," Documentos de Trabajo 242, Centro de Economía Aplicada, Universidad de Chile.
  14. 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.

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