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Conditional quantiles and tail dependence

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  • Bernard, Carole
  • Czado, Claudia

Abstract

Conditional quantile estimation is a crucial step in many statistical problems. For example, the recent work on systemic risk relies on estimating risk conditional on an institution being in distress or conditional on being in a crisis (Adrian and Brunnermeier, 2010; Brownlees and Engle, 2011). Specifically, the CoVaR systemic risk measure is based on a conditional quantile when one of the variable is in the tail of the distribution. In this paper, we study properties of conditional quantiles and how they relate to properties of the copula. In particular, we provide a new graphical characterization of tail dependence and intermediate tail dependence from plots of conditional quantiles with normalized marginal distributions (probit scale). A popular method to estimate conditional quantiles is the quantile regression (Koenker, 2005; Koenker and Bassett, 1978). We discuss the properties and pitfalls of this estimation approach.

Suggested Citation

  • Bernard, Carole & Czado, Claudia, 2015. "Conditional quantiles and tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 104-126.
    • Handle: RePEc:eee:jmvana:v:138:y:2015:i:c:p:104-126
    DOI: 10.1016/j.jmva.2015.01.011
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    1. Carole Bernard & Zhenyu Cui & Don Mcleish, 2012. "Nearly Exact Option Price Simulation Using Characteristic Functions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-29.
    2. Eide, Eric & Showalter, Mark H., 1998. "The effect of school quality on student performance: A quantile regression approach," Economics Letters, Elsevier, vol. 58(3), pages 345-350, March.
    3. Eric Bouye & Mark Salmon, 2009. "Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 721-750.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    5. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    6. Chan, Louis K. C. & Lakonishok, Josef, 1992. "Robust Measurement of Beta Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(2), pages 265-282, June.
    7. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    8. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    9. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    11. Buchinsky, Moshe, 1994. "Changes in the U.S. Wage Structure 1963-1987: Application of Quantile Regression," Econometrica, Econometric Society, vol. 62(2), pages 405-458, March.
    12. Gourieroux, C. & Jasiak, J., 2008. "Dynamic quantile models," Journal of Econometrics, Elsevier, vol. 147(1), pages 198-205, November.
    13. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    14. ., 2013. "Population and key macroeconomic variables," Chapters, in: The Political Economy of Iraq, chapter 2, pages 6-24, Edward Elgar Publishing.
    15. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
    16. Härdle, Wolfgang Karl & Spokoiny, Vladimir & Wang, Weining, 2010. "Local quantile regression," SFB 649 Discussion Papers 2011-005, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    17. Embrechts, Paul & Puccetti, Giovanni & Rüschendorf, Ludger, 2013. "Model uncertainty and VaR aggregation," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2750-2764.
    18. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    19. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    20. Katherine Elizabeth Castellano & Andrew Dean Ho, 2013. "Contrasting OLS and Quantile Regression Approaches to Student “Growth†Percentiles," Journal of Educational and Behavioral Statistics, , vol. 38(2), pages 190-215, April.
    21. repec:wyi:journl:002199 is not listed on IDEAS
    22. repec:hum:wpaper:sfb649dp2011-005 is not listed on IDEAS
    23. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
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