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On Rational Bubbles and Fat Tails

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  • Lux, Thomas
  • Sornette, Didier

Abstract

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes follow power-laws (exhibit hyperbolic decline). More precisely, we find that rational bubbles predict a "fat" power tail for both the bubble component and price differences with an exponent mu smaller than 1. The distribution of returns is dominated by the same power-law over an extended range of large returns. Although power-law tails are a pervasive feature of empirical data, these numerical predictions are in disagreement with the usual empirical estimates. It therefore appears that exogenous rational bubbles are hardly reconcilable with some of the stylized facts of financial data at a very elementary level.

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Bibliographic Info

Article provided by Blackwell Publishing in its journal Journal of Money, Credit and Banking.

Volume (Year): 34 (2002)
Issue (Month): 3 (August)
Pages: 589-610

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Handle: RePEc:mcb:jmoncb:v:34:y:2002:i:3:p:589-610

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0022-2879

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References

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Citations

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Cited by:
  1. Wanfeng Yan & Ryan Woodard & Didier Sornette, 2010. "Diagnosis and Prediction of Market Rebounds in Financial Markets," Papers 1003.5926, arXiv.org, revised Mar 2011.
  2. Cristian Valeriu STANCIU & Cristi SPULBAR & Sabin RIZESCU, 2012. "Econophysics - related Remarks in Considering the Necessity of a Distribution Adjustment in the Eurozone Real Economy and Re-modeling its Financial System and Markets. Thermodynamics and Statistical P," Journal of Knowledge Management, Economics and Information Technology, ScientificPapers.org, vol. 2(1), pages 9, February.
  3. Levy, Moshe, 2008. "Stock market crashes as social phase transitions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 137-155, January.
  4. Paul de Grauwe & Roberto Dieci & Marianna Grimaldi, 2005. "Fundamental and Non-Fundamental Equilibria in the Foreign Exchange Market. A Behavioural Finance Framework," CESifo Working Paper Series 1431, CESifo Group Munich.
  5. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, 05.
  6. He, Xue-Zhong & Li, Youwei, 2007. "Power-law behaviour, heterogeneity, and trend chasing," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3396-3426, October.
  7. De Grauwe, Paul & Grimaldi, Maria, 2004. "Bubbles and crashes in a behavioural finance model," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/119667, Katholieke Universiteit Leuven.
  8. Andrea Morone, 2008. "Financial markets in the laboratory: an experimental analysis of some stylized facts," Quantitative Finance, Taylor and Francis Journals, vol. 8(5), pages 513-532.
  9. Paul De Grauwe & Marianna Grimaldi, 2005. "Bubbles and crashes in a Behavioural Finance Model," Working Papers de Economia (Economics Working Papers) 25, Departamento de Economia, Gestão e Engenharia Industrial, Universidade de Aveiro.
  10. De Grauwe, Paul & Grimaldi, Maria, 2003. "Bubbling and crashing exchange rates," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/119410, Katholieke Universiteit Leuven.
  11. Makoto Nirei & Theodoros Stamatiou & Vladyslav Sushko, 2012. "Stochastic Herding in Financial Markets Evidence from Institutional Investor Equity Portfolios," BIS Working Papers 371, Bank for International Settlements.
  12. Sergio Da Silva, 2004. "International Finance, Levy Distributions, and the Econophysics of Exchange Rates," International Finance 0405018, EconWPA.
  13. Li Lin & Didier Sornette, 2009. "Diagnostics of Rational Expectation Financial Bubbles with Stochastic Mean-Reverting Termination Times," Papers 0911.1921, arXiv.org.
  14. Sheri Markose & Amadeo Alentorn, 2005. "Option Pricing and the Implied Tail Index with the Generalized Extreme Value (GEV) Distribution," Computing in Economics and Finance 2005 397, Society for Computational Economics.
  15. Leipus, Remigijus & Paulauskas, Vygantas & Surgailis, Donatas, 2005. "Renewal regime switching and stable limit laws," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 299-327.
  16. D. Sornette & R. Woodard, . "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Working Papers CCSS-09-003, ETH Zurich, Chair of Systems Design.
  17. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.
  18. Prasad Bidarkota, 2003. "Intrinsic Bubbles and Fat Tails in Stock Prices," Working Papers 0306, Florida International University, Department of Economics.
  19. Didier Sornette & Ryan Woodard, 2009. "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Papers 0905.0220, arXiv.org.
  20. Paul De Grauwe & Marianna Grimaldi, 2004. "Bubbles and Crashes in a Behavioural Finance Model," CESifo Working Paper Series 1194, CESifo Group Munich.
  21. Marianna Grimaldi & Paul De Grauwe, 2003. "Bubbling and Crashing Exchange Rates," CESifo Working Paper Series 1045, CESifo Group Munich.
  22. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.

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