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Gaussian and non-Gaussian models for financial bubbles via econophysics

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  • Fry, J. M.

Abstract

We develop a rational expectations model of financial bubbles and study how the 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 decreases crashes can be seen to represent a phase transition from stochastic to deterministic behaviour in prices. Our approach is first illustrated by a benchmark Gaussian model - subsequently extended to a heavy-tailed model based on the Normal Inverse Gaussian distribution. Our model is illustrated by an empirical application to the London Stock Exchange. Results suggest that the aftermath of the Bank of England's process of quantitative easing has coincided with a bubble in the FTSE 100.

Suggested Citation

  • Fry, J. M., 2010. "Gaussian and non-Gaussian models for financial bubbles via econophysics," MPRA Paper 27307, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:27307
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    File URL: https://mpra.ub.uni-muenchen.de/27307/1/MPRA_paper_27307.pdf
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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. 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.
    4. W. -X. Zhou & D. Sornette, 2003. "2000-2003 Real Estate Bubble in the UK but not in the USA," Papers physics/0303028, arXiv.org, revised Jul 2003.
    5. Laurent Laloux & Marc Potters & Rama Cont & Jean-Pierre Aguilar & Jean-Philippe Bouchaud, 1998. "Are Financial Crashes Predictable?," Papers cond-mat/9804111, arXiv.org.
    6. 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.
    7. 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.
    8. Fabrizio Lillo & Rosario N. Mantegna, 2001. "Power law relaxation in a complex system: Omori law after a financial market crash," Papers cond-mat/0111257, arXiv.org, revised Jun 2003.
    9. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    10. J.A. Feigenbaum, 2001. "A statistical analysis of log-periodic precursors to financial crashes-super-," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 346-360, March.
    11. Anders Johansen, 2004. "Origin of Crashes in 3 US stock markets: Shocks and Bubbles," Papers cond-mat/0401210, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    financial crashes; super-exponential growth; illusion of certainty; bubbles; heavy tails;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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