Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion
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 considered fixed does volatility increase prior to a crash.
|Date of creation:||08 Oct 2009|
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- Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
- Anders Johansen, 2004. "Origin of Crashes in 3 US stock markets: Shocks and Bubbles," Papers cond-mat/0401210, arXiv.org.
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"From rational bubbles to crashes,"
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Elsevier, vol. 299(1), pages 40-59.
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- 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.
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Science & Finance (CFM) working paper archive
9804111, Science & Finance, Capital Fund Management.
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