Significance of log-periodic precursors to financial crashes
AbstractWe clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's  criticism and show how it can be rebuked. Feigenbaum's main result is as follows: ``the hypothesis that the log-periodic component is present in the data cannot be rejected at the 95% confidence level when using all the data prior to the 1987 crash; however, it can be rejected by removing the last year of data.'' (e.g., by removing 15% of the data closest to the critical point). We stress that it is naive to analyze a critical point phenomenon, i.e., a power law divergence, reliably by removing the most important part of the data closest to the critical point. We also present the history of log-periodicity in the present context explaining its essential features and why it may be important. We offer an extension of the rational expectation bubble model for general and arbitrary risk-aversion within the general stochastic discount factor theory. We suggest guidelines for using log-periodicity and explain how to develop and interpret statistical tests of log-periodicity. We discuss the issue of prediction based on our results and the evidence of outliers in the distribution of drawdowns. New statistical tests demonstrate that the 1% to 10% quantile of the largest events of the population of drawdowns of the Nasdaq composite index and of the Dow Jones Industrial Average index belong to a distribution significantly different from the rest of the population. This suggests that very large drawdowns result from an amplification mechanism that may make them more predictable than smaller market moves.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number cond-mat/0106520.
Date of creation: Jun 2001
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Publication status: Published in Quantitative Finance 1 (4), 452-471 (2001)
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- Laurent Laloux & Marc Potters & Rama Cont & Jean-Pierre Aguilar & Jean-Philippe Bouchaud, 1998.
"Are Financial Crashes Predictable?,"
- Sornette, Didier & Johansen, Anders, 1998. "A hierarchical model of financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 581-598.
- D. Sornette & Y. Malevergne, 2001.
"From Rational Bubbles to Crashes,"
- Sornette, D & Malevergne, Y, 2001. "From rational bubbles to crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 40-59.
- Marie Christine Adam & Ariane Szafarz, 1993.
"Speculative Bubbles and Financial Markets,"
ULB Institutional Repository
2013/665, ULB -- Universite Libre de Bruxelles.
- A. Johansen & D. Sornette, 1998. "Stock market crashes are outliers," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 1(2), pages 141-143, January.
- Camerer, Colin, 1989. " Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
- S. Gluzman & V. I. Yukalov, 1998. "Booms and Crashes in Self-Similar Markets," Papers cond-mat/9810092, arXiv.org.
- Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-30, September.
- Kirill Ilinski, 1999. "Critical Crashes?," Papers cond-mat/9903142, arXiv.org.
- Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
- Woo, Wing Thye, 1987. "Some Evidence of Speculative Bubbles in the Foreign Exchange Markets," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 19(4), pages 499-514, November.
- 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.
- A. Johansen & D. Sornette, 1999. "Financial ``Anti-Bubbles'': Log-Periodicity in Gold and Nikkei collapses," Papers cond-mat/9901268, arXiv.org.
- J. A. Feigenbaum, 2001. "A statistical analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 346-360.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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