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.
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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)
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