IDEAS home Printed from https://ideas.repec.org/p/arx/papers/cond-mat-0203166.html
   My bibliography  Save this paper

Investigating Extreme Dependences: Concepts and Tools

Author

Listed:
  • Y. Malevergne

    (Univ. Nice and Univ. Lyon I)

  • D. Sornette

    (CNRS and Univ. Nice and UCLA)

Abstract

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.

Suggested Citation

  • Y. Malevergne & D. Sornette, 2002. "Investigating Extreme Dependences: Concepts and Tools," Papers cond-mat/0203166, arXiv.org.
  • Handle: RePEc:arx:papers:cond-mat/0203166
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/cond-mat/0203166
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    2. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. 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.
    5. King, Mervyn A & Wadhwani, Sushil, 1990. "Transmission of Volatility between Stock Markets," The Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 5-33.
    6. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    7. 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.
    8. D. Sornette & J. V. Andersen & P. Simonetti, 2000. "Portfolio Theory For "Fat Tails"," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 523-535.
    9. Vineer Bhansali & Mark B. Wise, 2001. "Forecasting Portfolio Risk in Normal and Stressed Markets," Papers nlin/0108022, arXiv.org, revised Sep 2001.
    10. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    11. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    12. 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.
    13. 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.
    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. 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.
    16. R. Mansilla, 2001. "Algorithmic Complexity in Real Financial Markets," Papers cond-mat/0104472, arXiv.org.
    17. Starica, Catalin, 1999. "Multivariate extremes for models with constant conditional correlations," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 515-553, December.
    18. 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.).
    19. Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 633-663.
    20. 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.
    21. Y. Malevergne & D. Sornette, 2002. "Tail Dependence of Factor Models," Papers cond-mat/0202356, arXiv.org.
    22. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Harry. M Kat, 2002. "The Dangers of Using Correlation to Measure Dependence," ICMA Centre Discussion Papers in Finance icma-dp2002-23, Henley Business School, University of Reading.
    2. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    3. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.
    4. Y. Malevergne & D. Sornette, 2002. "Hedging Extreme Co-Movements," Papers cond-mat/0205636, arXiv.org.
    5. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Shocks in financial markets, price expectation, and damped harmonic oscillators," Papers 1103.1992, arXiv.org, revised Sep 2011.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gonzalez-Hermosillo Gonzalez, B.M., 2008. "Transmission of shocks across global financial markets : The role of contagion and investors' risk appetite," Other publications TiSEM d684f3c7-7ad8-4e93-88cf-a, Tilburg University, School of Economics and Management.
    2. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    3. Ozer-Imer, Itir & Ozkan, Ibrahim, 2014. "An empirical analysis of currency volatilities during the recent global financial crisis," Economic Modelling, Elsevier, vol. 43(C), pages 394-406.
    4. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    5. De Vries, C.G., 2005. "The simple economics of bank fragility," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 803-825, April.
    6. Dalkir, Mehmet, 2009. "Revisiting stock market index correlations," Finance Research Letters, Elsevier, vol. 6(1), pages 23-33, March.
    7. Simone Manganelli & Lorenzo Cappiello & Bruno Gerard, 2004. "The Contagion Box: Measuring Co-Movements in Financial Markets by Regression Quantiles," Econometric Society 2004 Latin American Meetings 77, Econometric Society.
    8. Y. Malevergne & D. Sornette, 2002. "Tail Dependence of Factor Models," Papers cond-mat/0202356, arXiv.org.
    9. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    10. Gagnon, Louis & Karolyi, G. Andrew, 2006. "Price and Volatility Transmission across Borders," Working Paper Series 2006-5, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    11. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Shocks in financial markets, price expectation, and damped harmonic oscillators," Papers 1103.1992, arXiv.org, revised Sep 2011.
    12. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    13. Guesmi, Khaled & Nguyen, Duc Khuong, 2011. "How strong is the global integration of emerging market regions? An empirical assessment," Economic Modelling, Elsevier, vol. 28(6), pages 2517-2527.
    14. Zied Ftiti & Aviral Tiwari & Amél Belanès & Khaled Guesmi, 2015. "Tests of Financial Market Contagion: Evolutionary Cospectral Analysis Versus Wavelet Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 575-611, December.
    15. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    16. L. Bauwens & E. Otranto, 2013. "Modeling the Dependence of Conditional Correlations on Volatility," Working Paper CRENoS 201304, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    17. Hans Manner & Bertrand Candelon, 2010. "Testing For Asset Market Linkages: A New Approach Based On Time‐Varying Copulas," Pacific Economic Review, Wiley Blackwell, vol. 15(3), pages 364-384, August.
    18. Degryse, H.A. & Elahi, M.A. & Penas, M.F., 2012. "Determinants of Banking System Fragility : A Regional Perspective," Discussion Paper 2012-015, Tilburg University, Center for Economic Research.
    19. Chen, Wang & Wei, Yu & Lang, Qiaoqi & Lin, Yu & Liu, Maojuan, 2014. "Financial market volatility and contagion effect: A copula–multifractal volatility approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 289-300.
    20. Kang, Sang Hoon & Uddin, Gazi Salah & Troster, Victor & Yoon, Seong-Min, 2019. "Directional spillover effects between ASEAN and world stock markets," Journal of Multinational Financial Management, Elsevier, vol. 52.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:cond-mat/0203166. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.