IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v20y2017i06ns0219024917500388.html
   My bibliography  Save this article

Logistic Model For Stock Market Bubbles And Anti-Bubbles

Author

Listed:
  • CHRISTOPHER LYNCH

    (School of Mathematics & Statistics, The Open University, Milton Keynes, MK7 6AA, UK)

  • BENJAMIN MESTEL

    (School of Mathematics & Statistics, The Open University, Milton Keynes, MK7 6AA, UK)

Abstract

Log-periodic power laws often occur as signatures of impending criticality of hierarchical systems in the physical sciences. It has been proposed that similar signatures may be apparent in the price evolution of financial markets as bubbles and the associated crashes develop. The features of such market bubbles have been extensively studied over the past 20 years, and models derived from an initial discrete scale invariance assumption have been developed and tested against the wealth of financial data with varying degrees of success. In this paper, the equations that form the basis for the standard log-periodic power law model and its higher extensions are compared to a logistic model derived from the solution of the Schröder equation for the renormalization group with nonlinear scaling function. Results for the S&P 500 and Nikkei 225 indices studied previously in the literature are presented and compared to established models, including a discussion of the apparent frequency shifting observed in the S&P 500 index in the 1980s. In the particular case of the Nikkei 225 anti-bubble between 1990 and 2003, the logistic model appears to provide a better description of the large-scale observed features over the whole 13-year period, particularly near the end of the anti-bubble.

Suggested Citation

  • Christopher Lynch & Benjamin Mestel, 2017. "Logistic Model For Stock Market Bubbles And Anti-Bubbles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-24, September.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:06:n:s0219024917500388
    DOI: 10.1142/S0219024917500388
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024917500388
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024917500388?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. D. Sornette, "undated". "Dragon-Kings, Black Swans and the Prediction of Crises," Working Papers CCSS-09-005, ETH Zurich, Chair of Systems Design.
    2. 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.
    3. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    4. Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
    5. Laurent Laloux & Marc Potters & Rama Cont & Jean-Pierre Aguilar & Jean-Philippe Bouchaud, 1998. "Are financial crashes predictable?," Science & Finance (CFM) working paper archive 9804111, Science & Finance, Capital Fund Management.
    6. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    7. 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.
    8. David S. Br�e & Damien Challet & Pier Paolo Peirano, 2013. "Prediction accuracy and sloppiness of log-periodic functions," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 275-280, January.
    9. Sornette, Didier & Woodard, Ryan & Yan, Wanfeng & Zhou, Wei-Xing, 2013. "Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4417-4428.
    10. Anders Johansen & Didier Sornette, 2000. "Evaluation Of The Quantitative Prediction Of A Trend Reversal On The Japanese Stock Market In 1999," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 359-364.
    11. David S. Bree & Nathan Lael Joseph, 2010. "Testing for financial crashes using the Log Periodic Power Law mode," Papers 1002.1010, arXiv.org, revised Apr 2013.
    12. Didier SORNETTE, 2009. "Dragon-Kings, Black Swans and the Prediction of Crises," Swiss Finance Institute Research Paper Series 09-36, Swiss Finance Institute.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Papastamatiou, Konstantinos & Karakasidis, Theodoros, 2022. "Bubble detection in Greek Stock Market: A DS-LPPLS model approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    2. V. Filimonov & G. Demos & D. Sornette, 2017. "Modified profile likelihood inference and interval forecast of the burst of financial bubbles," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1167-1186, August.
    3. 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.
    4. John Fry & McMillan David, 2015. "Stochastic modelling for financial bubbles and policy," Cogent Economics & Finance, Taylor & Francis Journals, vol. 3(1), pages 1002152-100, December.
    5. Martin Herdegen & Sebastian Herrmann, 2017. "Strict Local Martingales and Optimal Investment in a Black-Scholes Model with a Bubble," Papers 1711.06679, arXiv.org.
    6. Sornette, Didier & Woodard, Ryan & Yan, Wanfeng & Zhou, Wei-Xing, 2013. "Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4417-4428.
    7. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    8. 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.
    9. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Can log-periodic power law structures arise from random fluctuations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 228-250.
    10. Riza Demirer & Guilherme Demos & Rangan Gupta & Didier Sornette, 2019. "On the predictability of stock market bubbles: evidence from LPPLS confidence multi-scale indicators," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 843-858, May.
    11. John Fry, 2014. "Bubbles, shocks and elementary technical trading strategies," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(1), pages 1-13, January.
    12. Fry, John & Cheah, Eng-Tuck, 2016. "Negative bubbles and shocks in cryptocurrency markets," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 343-352.
    13. Hideyuki Takagi, 2021. "Exploring the Endogenous Nature of Meme Stocks Using the Log-Periodic Power Law Model and Confidence Indicator," Papers 2110.06190, arXiv.org.
    14. Zhou, Wei & Huang, Yang & Chen, Jin, 2018. "The bubble and anti-bubble risk resistance analysis on the metal futures in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 947-957.
    15. Daniel Traian Pele & Miruna Mazurencu-Marinescu & Peter Nijkamp, 2013. "Herding Behaviour, Bubbles and Log Periodic Power Laws in Illiquid Stock Markets. A Case Study on the Bucharest Stock Exchange," Tinbergen Institute Discussion Papers 13-109/VIII, Tinbergen Institute.
    16. Kristoffer Pons Bertelsen, 2019. "Comparing Tests for Identification of Bubbles," CREATES Research Papers 2019-16, Department of Economics and Business Economics, Aarhus University.
    17. Min Shu & Ruiqiang Song & Wei Zhu, 2021. "The 'COVID' Crash of the 2020 U.S. Stock Market," Papers 2101.03625, arXiv.org.
    18. Hanwool Jang & Yena Song & Sungbin Sohn & Kwangwon Ahn, 2018. "Real Estate Soars and Financial Crises: Recent Stories," Sustainability, MDPI, vol. 10(12), pages 1-12, December.
    19. Grobys, Klaus, 2023. "A finite-time singularity in the dynamics of the US equity market: Will the US equity market eventually collapse?," International Review of Financial Analysis, Elsevier, vol. 89(C).
    20. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:20:y:2017:i:06:n:s0219024917500388. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.