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Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion

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  • John M. Fry

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. The basic model is then extended to incorporate multivariate bubbles and contagion, non-Gaussian models and models based on stochastic volatility. Only in a stochastic volatility model where the mean of the log-returns is considered fixed does volatility increase prior to a crash.

Suggested Citation

  • John M. Fry, 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," EERI Research Paper Series EERI_RP_2009_10, Economics and Econometrics Research Institute (EERI), Brussels.
  • Handle: RePEc:eei:rpaper:eeri_rp_2009_10
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    File URL: http://www.eeri.eu/documents/wp/EERI_RP_2009_10.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. Laurent Laloux & Marc Potters & Rama Cont & Jean-Pierre Aguilar & Jean-Philippe Bouchaud, 1998. "Are Financial Crashes Predictable?," Papers cond-mat/9804111, arXiv.org.
    5. 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.
    6. 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.
    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. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    9. 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.
    10. Anders Johansen, 2004. "Origin of Crashes in 3 US stock markets: Shocks and Bubbles," Papers cond-mat/0401210, arXiv.org.
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    More about this item

    Keywords

    Financial crashes; super-exponential growth; illusion of certainty; contagion; housing-bubble.;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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