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Bubbles and crashes in finance: A phase transition from random to deterministic behaviour in prices

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  • Fry, J. M.

Abstract

We develop a rational expectations model of financial bubbles and study ways in which a generic risk-return interplay is incorporated into prices. We retain the interpretation of the leading Johansen-Ledoit-Sornette model, namely, that the price must rise prior to a crash in order to compensate a representative investor for the level of risk. This is accompanied, in our stochastic model, by an illusion of certainty as described by a decreasing volatility function. As the volatility function goes to zero, crashes can be seen to represent a phase transition from stochastic to deterministic behaviour in prices.

Suggested Citation

  • Fry, J. M., 2010. "Bubbles and crashes in finance: A phase transition from random to deterministic behaviour in prices," MPRA Paper 24778, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:24778
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    References listed on IDEAS

    as
    1. Sornette, D & Malevergne, Y, 2001. "From rational bubbles to crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 40-59.
    2. George Chang & James Feigenbaum, 2006. "A Bayesian analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 15-36.
    3. Angela Black & Patricia Fraser & Martin Hoesli, 2006. "House Prices, Fundamentals and Bubbles," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9‐10), pages 1535-1555, November.
    4. Zhou, Wei-Xing & Sornette, Didier, 2003. "2000–2003 real estate bubble in the UK but not in the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 249-263.
    5. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    6. Angela Black & Patricia Fraser & Martin Hoesli, 2006. "House Prices, Fundamentals and Bubbles," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9‐10), pages 1535-1555, November.
    7. Anders Johansen, 2004. "Origin of Crashes in 3 US stock markets: Shocks and Bubbles," Papers cond-mat/0401210, arXiv.org.
    8. D. Sornette & J. V. Andersen, 2001. "A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles," Papers cond-mat/0104341, arXiv.org, revised Apr 2002.
    9. George Chang & James Feigenbaum, 2008. "Detecting log-periodicity in a regime-switching model of stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 723-738.
    10. 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.
    11. 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.
    12. D. Sornette & J. V. Andersen, 2002. "A Nonlinear Super-Exponential Rational Model Of Speculative Financial Bubbles," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 171-187.
    13. J. A. Feigenbaum, 2001. "More on a statistical analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 527-532.
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    15. Andersen, J.V. & Sornette, D., 2004. "Fearless versus fearful speculative financial bubbles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 565-585.
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    Cited by:

    1. 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.
    2. 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.

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    More about this item

    Keywords

    financial crashes; super-exponential growth; illusion of certainty; housing-bubble;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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