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

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  • Fry, J. M.
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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 fixed does volatility increase prior to a crash.

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File URL: http://mpra.ub.uni-muenchen.de/16027/
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16027.

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Date of creation: 2009
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Handle: RePEc:pra:mprapa:16027

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Keywords: financial crashes; super-exponential growth; illusion of certainty; contagion;

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  1. 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.
  2. 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.
  3. 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.
  4. J. A. Feigenbaum, 2001. "A statistical analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 346-360.
  5. 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.
  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. Anders Johansen, 2004. "Origin of Crashes in 3 US stock markets: Shocks and Bubbles," Papers cond-mat/0401210, arXiv.org.
  8. 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.
  9. D. Sornette & Y. Malevergne, 2001. "From Rational Bubbles to Crashes," Papers cond-mat/0102305, arXiv.org.
  10. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
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