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

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Author Info
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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Publisher Info
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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Related research
Keywords: financial crashes; super-exponential growth; illusion of certainty; contagion;

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Find related papers by 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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  1. D. Sornette & J. V. Andersen, 2001. "A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles," Quantitative Finance Papers cond-mat/0104341, arXiv.org, revised Apr 2002. [Downloadable!]
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This page was last updated on 2009-12-1.


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