Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Economics and Econometrics Research Institute (EERI), Brussels in its series EERI Research Paper Series with number EERI_RP_2009_10.
Length: 18 pages
Date of creation: 08 Oct 2009
Date of revision:
Financial crashes; super-exponential growth; illusion of certainty; contagion; housing-bubble.;
Other versions of this item:
- Fry, J. M., 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," MPRA Paper 16027, University Library of Munich, Germany.
- 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)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-08-30 (All new papers)
- NEP-FDG-2009-08-30 (Financial Development & Growth)
- NEP-FMK-2009-08-30 (Financial Markets)
- NEP-UPT-2009-08-30 (Utility Models & Prospect Theory)
- NEP-URE-2009-08-30 (Urban & Real Estate Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- D. Sornette & Y. Malevergne, 2001.
"From Rational Bubbles to Crashes,"
- Sornette, D & Malevergne, Y, 2001. "From rational bubbles to crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 40-59.
- 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.
- 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.
- Laurent Laloux & Marc Potters & Rama Cont & Jean-Pierre Aguilar & Jean-Philippe Bouchaud, 1998.
"Are Financial Crashes Predictable?,"
- 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.
- 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.
- Anders Johansen, 2004. "Origin of Crashes in 3 US stock markets: Shocks and Bubbles," Papers cond-mat/0401210, arXiv.org.
- 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.
- Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Julia van Hove).
If references are entirely missing, you can add them using this form.