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A Precursor of Market Crashes

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  • Taisei Kaizoji

Abstract

In this paper, we quantitatively investigate the properties of a statistical ensemble of stock prices. We focus attention on the relative price defined as $ X(t) = S(t)/S(0) $, where $ S(0) $ is the initial price. We selected approximately 3200 stocks traded on the Japanese Stock Exchange and formed a statistical ensemble of daily relative prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corresponding to the period in which the {\it internet Bubble} formed and {\it crashes} in the Japanese stock market. We found that the upper tail of the complementary cumulative distribution function of the ensemble of the relative prices in the high value of the price is well described by a power-law distribution, $ P(S>x) \sim x^{-\alpha} $, with an exponent that moves over time. Furthermore, we found that as the power-law exponents $ \alpha $ approached {\it two}, the bubble burst. It is reasonable to assume that when the power-law exponents approached {\it two}, it indicates the bubble is about to burst. PACS: 89.65.Gh; Keywords: Market crashes, Power law, Precursor

Suggested Citation

  • Taisei Kaizoji, 2005. "A Precursor of Market Crashes," Papers physics/0510055, arXiv.org, revised Mar 2006.
    • Handle: RePEc:arx:papers:physics/0510055
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    Citations

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    Cited by:

    1. Todorova, Lora & Vogt, Bodo, 2011. "Power law distribution in high frequency financial data? An econometric analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4433-4444.
    2. Frederic Abergel & Nicolas Huth & Ioane Muni Toke, 2009. "Financial bubbles analysis with a cross-sectional estimator," Papers 0909.2885, arXiv.org.
    3. Rutledge, John, 2015. "Economics as energy framework: Complexity, turbulence, financial crises, and protectionism," Review of Financial Economics, Elsevier, vol. 25(C), pages 10-18.
    4. Blackwell, Calvin, 2018. "Power Laws in Real Estate Prices? Some Evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 69(C), pages 90-98.
    5. Esteban Guevara Hidalgo, 2015. "Bin Size Independence in Intra-day Seasonalities for Relative Prices," Papers 1501.05176, arXiv.org, revised Dec 2016.
    6. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    7. Li Lin & Didier Sornette, 2023. "The inverse Cox-Ingersoll-Ross process for parsimonious financial price modeling," Papers 2302.11423, arXiv.org, revised Jun 2023.
    8. Kerim Eser AFÞAR & Zakayo S. KISAVA, 2018. "The analysis of bubbles and crashes on financial markets for emerging economies: Evidenced From BRICS," Turkish Economic Review, KSP Journals, vol. 5(1), pages 1-11, March.
    9. David Vidal-Tomás & Simone Alfarano, 2020. "An agent-based early warning indicator for financial market instability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(1), pages 49-87, January.
    10. Cajueiro, Daniel O. & Tabak, Benjamin M. & Werneck, Filipe K., 2009. "Can we predict crashes? The case of the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1603-1609.
    11. Bikramaditya Ghosh & Spyros Papathanasiou & Georgios Pergeris, 2022. "Did cryptocurrencies exhibit log‐periodic power law signature during the second wave of COVID‐19?," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(3), November.
    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. John Rutledge, 2015. "Economics as energy framework: Complexity, turbulence, financial crises, and protectionism," Review of Financial Economics, John Wiley & Sons, vol. 25(1), pages 10-18, April.
    14. Graham Bird & Wenti Du & Thomas Willett, 2017. "Behavioral Finance and Efficient Markets: What does the Euro Crisis Tell us?," Open Economies Review, Springer, vol. 28(2), pages 273-295, April.
    15. Kaizoji, Taisei & Miyano, Michiko, 2016. "Why does the power law for stock price hold?," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 19-23.
    16. Guevara Hidalgo, Esteban, 2017. "Bin size independence in intra-day seasonalities for relative prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 722-732.

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