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

Fry, J. M. (2009): Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: financial crashes; super-exponential growth; illusion of certainty; contagion
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C00 - General; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E30 - General; G - Financial Economics > G1 - General Financial Markets > G10 - General

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