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Investigating Extreme Dependences: Concepts and Tools

  • Y. Malevergne

    (Univ. Nice and Univ. Lyon I)

  • D. Sornette

    (CNRS and Univ. Nice and UCLA)

We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are respectively the linear correlation $\rho^+_v$ and Spearman's rho $\rho_s(v)$ conditioned on signed exceedance of one variable above the threshold $v$, or on both variables ($\rho_u$), the linear correlation $\rho^s_v$ conditioned on absolute value exceedance (or large volatility) of one variable, the so-called asymptotic tail-dependence $\lambda$ and a probability-weighted tail dependence coefficient ${\bar \lambda}$. The models are the bivariate Gaussian distribution, the bivariate Student's distribution, and the factor model for various distributions of the factor. We offer explicit analytical formulas as well as numerical estimations for these six measures of dependence in the limit where $v$ and $u$ go to infinity. This provides a quantitative proof that conditioning on exceedance leads to conditional correlation coefficients that may be very different from the unconditional correlation and gives a straightforward mechanism for fluctuations or changes of correlations, based on fluctuations of volatility or changes of trends. Moreover, these various measures of dependence exhibit different and sometimes opposite behaviors, suggesting that, somewhat similarly to risks whose adequate characterization requires an extension beyond the restricted one-dimensional measure in terms of the variance (volatility) to include all higher order cumulants or more generally the knowledge of the full distribution, tail-dependence has also a multidimensional character.

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File URL: http://arxiv.org/pdf/cond-mat/0203166
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Paper provided by arXiv.org in its series Papers with number cond-mat/0203166.

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Date of creation: Mar 2002
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Publication status: Published in transformed and extended in the book ``Extreme Financial Risks (From dependence to risk management)'' (Springer, Heidelberg, 2006)
Handle: RePEc:arx:papers:cond-mat/0203166
Contact details of provider: Web page: http://arxiv.org/

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  1. P. Hartmann & S. Straetmans & C. G. de Vries, 2004. "Asset Market Linkages in Crisis Periods," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 313-326, February.
  2. P. Cizeau & M. Potters & J-P. Bouchaud, 2001. "Correlation structure of extreme stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 217-222.
  3. Y. Malevergne & D. Sornette, 2001. "Testing the Gaussian Copula Hypothesis for Financial Assets Dependences," Papers cond-mat/0111310, arXiv.org.
  4. Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Correlation structure of extreme stock returns," Science & Finance (CFM) working paper archive 0006034, Science & Finance, Capital Fund Management.
  5. Patton, Andrew J, 2001. "Estimation of Copula Models for Time Series of Possibly Different Length," University of California at San Diego, Economics Working Paper Series qt3fc1c8hw, Department of Economics, UC San Diego.
  6. H. A. Hauksson & M. Dacorogna & T. Domenig & U. Mller & G. Samorodnitsky, 2001. "Multivariate extremes, aggregation and risk estimation," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 79-95.
  7. Longin, Francois & Solnik, Bruno, 1995. "Is the correlation in international equity returns constant: 1960-1990?," Journal of International Money and Finance, Elsevier, vol. 14(1), pages 3-26, February.
  8. Y. Malevergne & D. Sornette, 2002. "Tail Dependence of Factor Models," Papers cond-mat/0202356, arXiv.org.
  9. Vineer Bhansali & Mark B. Wise, 2001. "Forecasting Portfolio Risk in Normal and Stressed Markets," Papers nlin/0108022, arXiv.org, revised Sep 2001.
  10. Mervyn A. King & Sushil Wadhwani, 1989. "Transmission of Volatility Between Stock Markets," NBER Working Papers 2910, National Bureau of Economic Research, Inc.
  11. Brian H. Boyer & Michael S. Gibson & Mico Loretan, 1997. "Pitfalls in tests for changes in correlations," International Finance Discussion Papers 597, Board of Governors of the Federal Reserve System (U.S.).
  12. Ramchand, Latha & Susmel, Raul, 1998. "Volatility and cross correlation across major stock markets," Journal of Empirical Finance, Elsevier, vol. 5(4), pages 397-416, October.
  13. P. Silvapulle & C. W. J. Granger, 2001. "Large returns, conditional correlation and portfolio diversification: a value-at-risk approach," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 542-551.
  14. Mansilla, R., 2001. "Algorithmic complexity of real financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 483-492.
  15. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
  16. Quintos, Carmela & Fan, Zhenhong & Phillips, Peter C B, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," Review of Economic Studies, Wiley Blackwell, vol. 68(3), pages 633-63, July.
  17. Starica, Catalin, 1999. "Multivariate extremes for models with constant conditional correlations," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 515-553, December.
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