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Universal Behavior of Extreme Price Movements in Stock Markets

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  • Miguel A. Fuentes
  • Austin Gerig
  • Javier Vicente

Abstract

Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model -- adding a slow, but significant, fluctuation to the standard deviation of the process -- accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we show that this process is similar across stocks so that their price fluctuations can be characterized by a single curve. Because the behavior of price fluctuations is rooted in the characteristics of volatility, we expect our results to bring increased interest to stochastic volatility models, and especially to those that can produce the properties of volatility reported here.

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  • Miguel A. Fuentes & Austin Gerig & Javier Vicente, 2009. "Universal Behavior of Extreme Price Movements in Stock Markets," Papers 0912.5448, arXiv.org.
    • Handle: RePEc:arx:papers:0912.5448
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    References listed on IDEAS

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    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    2. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, June.
    3. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, Decembrie.
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    Cited by:

    1. Dashti Moghaddam, M. & Serota, R.A., 2021. "Combined multiplicative–Heston model for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Hamed Farahani & R. A. Serota, 2025. "Asymmetry in Distributions of Accumulated Gains and Losses in Stock Returns," Papers 2503.24241, arXiv.org.
    3. Wei, J.R. & Huang, J.P. & Hui, P.M., 2013. "An agent-based model of stock markets incorporating momentum investors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2728-2735.
    4. M. Dashti Moghaddam & R. A. Serota, 2018. "Combined Mutiplicative-Heston Model for Stochastic Volatility," Papers 1807.10793, arXiv.org.
    5. Jiong Liu & R. A. Serota, 2022. "Rethinking Generalized Beta Family of Distributions," Papers 2209.05225, arXiv.org.
    6. M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2018. "Distributions of Historic Market Data -- Implied and Realized Volatility," Papers 1804.05279, arXiv.org.
    7. Jianrong Wei & Jiping Huang, 2012. "An Exotic Long-Term Pattern in Stock Price Dynamics," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-5, December.
    8. Lu Liu & Jianrong Wei & Jiping Huang, 2013. "Scaling and Volatility of Breakouts and Breakdowns in Stock Price Dynamics," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-6, December.
    9. Wu, Liang & Liu, Hengzhi & Liu, Chang & Long, Yunshen, 2020. "Determining the information share of liquidity and order flows in extreme price movements," Economic Modelling, Elsevier, vol. 93(C), pages 559-575.
    10. Dashti Moghaddam, M. & Mills, Jeffrey & Serota, R.A., 2020. "From a stochastic model of economic exchange to measures of inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    11. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.

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