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

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  • Fry, J. M.

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.

Suggested Citation

  • Fry, J. M., 2009. "Statistical modelling of financial crashes: Rapid growth, illusion of certainty and contagion," MPRA Paper 16027, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:16027
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    References listed on IDEAS

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    1. Sornette, D & Malevergne, Y, 2001. "From rational bubbles to crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 40-59.
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    More about this item

    Keywords

    financial crashes; super-exponential growth; illusion of certainty; contagion;
    All these keywords.

    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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