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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.
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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. As the volatility function goes to zero, crashes can be seen to represent a phase transition from stochastic to deterministic behaviour in prices.

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File URL: http://mpra.ub.uni-muenchen.de/24778/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 24778.

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Date of creation: 03 Sep 2010
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Handle: RePEc:pra:mprapa:24778

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

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  1. George Chang & James Feigenbaum, 2006. "A Bayesian analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 6(1), pages 15-36.
  2. Sornette, D & Malevergne, Y, 2001. "From rational bubbles to crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 40-59.
  3. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
  4. J. A. Feigenbaum, 2001. "A statistical analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(3), pages 346-360.
  5. J. A. Feigenbaum, 2001. "More on a statistical analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(5), pages 527-532.
  6. Laurent Laloux & Marc Potters & Rama Cont & Jean-Pierre Aguilar & Jean-Philippe Bouchaud, 1998. "Are Financial Crashes Predictable?," Papers cond-mat/9804111, arXiv.org.
  7. 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.
  8. George Chang & James Feigenbaum, 2008. "Detecting log-periodicity in a regime-switching model of stock returns," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(7), pages 723-738.
  9. 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.
  10. Anders Johansen, 2004. "Origin of Crashes in 3 US stock markets: Shocks and Bubbles," Papers cond-mat/0401210, arXiv.org.
  11. 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.
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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.

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