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Characterization of large price variations in financial markets

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  • Johansen, Anders

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.

Suggested Citation

  • Johansen, Anders, 2003. "Characterization of large price variations in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 157-166.
  • Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:157-166
    DOI: 10.1016/S0378-4371(02)01843-5
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    References listed on IDEAS

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    1. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    2. Fabrizio Lillo & Rosario N. Mantegna, 2000. "Symmetry alteration of ensemble return distribution in crash and rally days of financial markets," Papers cond-mat/0002438, arXiv.org.
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    7. Anders Johansen & Didier Sornette, 2000. "The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash," Papers cond-mat/0004263, arXiv.org, revised May 2000.
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    Cited by:

    1. 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.
    2. D. Sornette & W. -X. Zhou, 2003. "Predictability of large future changes in major financial indices," Papers cond-mat/0304601, arXiv.org, revised Aug 2004.
    3. 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.
    4. Fantazzini, Dean, 2016. "The oil price crash in 2014/15: Was there a (negative) financial bubble?," Energy Policy, Elsevier, vol. 96(C), pages 383-396.
    5. 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.
    6. Fantazzini, Dean & Nigmatullin, Erik & Sukhanovskaya, Vera & Ivliev, Sergey, 2016. "Everything you always wanted to know about bitcoin modelling but were afraid to ask. I," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 44, pages 5-24.
    7. 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.
    8. Didier Sornette & Ryan Woodard, 2009. "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Papers 0905.0220, arXiv.org.
    9. 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.
    10. D. Sornette & W. -X. Zhou, 2003. "The US 2000-2003 Market Descent: Clarifications," Papers cond-mat/0305004, arXiv.org.
    11. 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.
    12. 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.
    13. Fantazzini, Dean & Nigmatullin, Erik & Sukhanovskaya, Vera & Ivliev, Sergey, 2017. "Everything you always wanted to know about bitcoin modelling but were afraid to ask. Part 2," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 45, pages 5-28.
    14. Zhang, Qunzhi & Sornette, Didier & Balcilar, Mehmet & Gupta, Rangan & Ozdemir, Zeynel Abidin & Yetkiner, Hakan, 2016. "LPPLS bubble indicators over two centuries of the S&P 500 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 126-139.
    15. Vinicius Ratton Brandi & Beatriz Vaz de Melo Mendes, 2004. "Assessing Drawdown-at-Risk in Brazilian Real Foreign Exchange Rates," Brazilian Review of Finance, Brazilian Society of Finance, vol. 2(2), pages 207-223.
    16. Caetano, Marco Antonio Leonel & Yoneyama, Takashi, 2015. "Boolean network representation of contagion dynamics during a financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 1-6.
    17. 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.
    18. 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.
    19. 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.
    20. D. Sornette & R. Woodard, "undated". "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers CCSS-09-003, ETH Zurich, Chair of Systems Design.
    21. 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.

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