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Stochastic resonance as a model for financial market crashes and bubbles

Author

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  • Krawiecki, A.
  • Hołyst, J.A.

Abstract

A bistable model of a financial market is considered, aimed at modelling financial crashes and bubbles, based on the Ising model with thermal-bath dynamics and long-range interactions, subject to a weak external information-carrying signal and noise. In the ordered phase, opposite stable orientations of magnetization correspond to the growing and declining market before and after the crash or bubble, and jumps of magnetization direction correspond to crashes and bubbles. It is shown that the influence of an information-carrying signal, assumed to be too weak to induce magnetization jumps, can be enhanced by the external noise via the effect of stochastic resonance. It is argued that in real stock markets the arrival of a piece of information, considered a posteriori to be the cause for a crash or bubble, can be enhanced in a similar way, thus leading to price return whose value is unexpectedly large in comparison with relatively weak importance of this piece of information.

Suggested Citation

  • Krawiecki, A. & Hołyst, J.A., 2003. "Stochastic resonance as a model for financial market crashes and bubbles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(3), pages 597-608.
    • Handle: RePEc:eee:phsmap:v:317:y:2003:i:3:p:597-608
    DOI: 10.1016/S0378-4371(02)01375-4
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    Citations

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    Cited by:

    1. Quanbo Zha & Gang Kou & Hengjie Zhang & Haiming Liang & Xia Chen & Cong-Cong Li & Yucheng Dong, 2020. "Opinion dynamics in finance and business: a literature review and research opportunities," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-22, December.
    2. Cross, Rod & Grinfeld, Michael & Lamba, Harbir & Seaman, Tim, 2005. "A threshold model of investor psychology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 463-478.
    3. Kyrylo Shmatov & Mikhail Smirnov, 2005. "On Some Processes and Distributions in a Collective Model of Investors' Behavior," Papers nlin/0506015, arXiv.org.
    4. Kim, Jun Sik & Ryu, Doojin, 2014. "Intraday price dynamics in spot and derivatives markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 247-253.
    5. Sato, Aki-Hiro, 2007. "Frequency analysis of tick quotes on the foreign exchange market and agent-based modeling: A spectral distance approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 258-270.
    6. Dror Y Kenett & Yoash Shapira & Asaf Madi & Sharron Bransburg-Zabary & Gitit Gur-Gershgoren & Eshel Ben-Jacob, 2011. "Index Cohesive Force Analysis Reveals That the US Market Became Prone to Systemic Collapses Since 2002," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-8, April.
    7. Chen, Zhiping & Duan, Qihong, 2011. "New models of trader beliefs and their application for explaining financial bubbles," Economic Modelling, Elsevier, vol. 28(5), pages 2215-2227, September.
    8. Ditian Zhang & Yangyang Zhuang & Pan Tang & Hongjuan Peng & Qingying Han, 2023. "Financial price dynamics and phase transitions in the stock markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(3), pages 1-21, March.
    9. 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.
    10. Silver, Steven D. & Raseta, Marko & Bazarova, Alina, 2023. "Stochastic resonance in the recovery of signal from agent price expectations," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    11. A. Christian Silva & Ju-Yi Yen, 2010. "Stochastic resonance and the trade arrival rate of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 461-466.
    12. Tao, Chen & Zhong, Guang-Yan & Li, Jiang-Cheng, 2023. "Dynamic correlation and risk resonance among industries of Chinese stock market: New evidence from time–frequency domain and complex network perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    13. Aki-Hiro Sato, 2005. "A characteristic time scale of tick quotes on foreign currency markets," Papers physics/0509142, arXiv.org.
    14. Mbakob Yonkeu, R. & David, Afungchui, 2022. "Coherence and stochastic resonance in the fractional-birhythmic self-sustained system subjected to fractional time-delay feedback and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    15. Cajueiro, Daniel O. & Tabak, Benjamin M., 2006. "Testing for rational bubbles in banking indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 365-376.

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