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Characterization of large price variations in financial markets

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  • Johansen, Anders
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    Abstract

    Statistics of drawdowns (loss from the last local maximum to the next local minimum) plays an important role in risk assessment of investment strategies. As they incorporate higher (> two) order correlations, they offer a better measure of real market risks than the variance or other cumulants of daily (or some other fixed time scale) of returns. Previous results have shown that the vast majority of drawdowns occurring on the major financial markets have a distribution which is well represented by a stretched exponential, while the largest drawdowns are occurring with a significantly larger rate than predicted by the bulk of the distribution and should thus be characterized as outliers (Eur. Phys. J. B 1 (1998) 141; J. Risk 2001). In the present analysis, the definition of drawdowns is generalized to coarse-grained drawdowns or so-called ε-drawdowns and a link between such ε-outliers and preceding log-periodic power law bubbles previously identified (Quantitative Finance 1 (2001) 452) is established.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 324 (2003)
    Issue (Month): 1 ()
    Pages: 157-166

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    Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:157-166

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Financial markets; Bubbles and crashes; Outliers;

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    Cited by:
    1. Caetano, Marco Antonio Leonel & Yoneyama, Takashi, 2009. "A new indicator of imminent occurrence of drawdown in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3563-3571.
    2. Brée, David S. & Joseph, Nathan Lael, 2013. "Testing for financial crashes using the Log Periodic Power Law model," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 287-297.
    3. Zhang, Hongzhong & Leung, Tim & Hadjiliadis, Olympia, 2013. "Stochastic modeling and fair valuation of drawdown insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 840-850.
    4. Petr Geraskin & Dean Fantazzini, 2013. "Everything you always wanted to know about log-periodic power laws for bubble modeling but were afraid to ask," The European Journal of Finance, Taylor & Francis Journals, vol. 19(5), pages 366-391, May.
    5. Doney, Ron & Maller, Ross & Savov, Mladen, 2009. "Renewal theorems and stability for the reflected process," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1270-1297, April.
    6. Caetano, Marco Antonio Leonel & Yoneyama, Takashi, 2012. "A method for detection of abrupt changes in the financial market combining wavelet decomposition and correlation graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4877-4882.
    7. D. Sornette & R. Woodard, . "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers CCSS-09-003, ETH Zurich, Chair of Systems Design.
    8. D. Sornette & W. -X. Zhou, 2003. "The US 2000-2003 Market Descent: Clarifications," Papers cond-mat/0305004, arXiv.org.
    9. D. Sornette & W. -X. Zhou, 2003. "Predictability of large future changes in major financial indices," Papers cond-mat/0304601, arXiv.org, revised Aug 2004.
    10. Gee Kwang Randolph Tan & Xiao Qin, 2005. "Bubbles, Can We Spot Them? Crashes, Can We Predict Them?," Computing in Economics and Finance 2005 206, Society for Computational Economics.
    11. Didier Sornette & Ryan Woodard, 2009. "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Papers 0905.0220, arXiv.org.
    12. Sornette, Didier & Zhou, Wei-Xing, 2006. "Predictability of large future changes in major financial indices," International Journal of Forecasting, Elsevier, vol. 22(1), pages 153-168.
    13. Zhou, Wei-Xing & Sornette, Didier, 2009. "A case study of speculative financial bubbles in the South African stock market 2003–2006," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 869-880.
    14. Qian, Xi-Yuan & Song, Fu-Tie & Zhou, Wei-Xing, 2008. "Nonlinear behaviour of the Chinese SSEC index with a unit root: Evidence from threshold unit root tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 503-510.
    15. Miśkiewicz, Janusz & Ausloos, Marcel, 2008. "Correlation measure to detect time series distances, whence economy globalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6584-6594.

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