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On Rational Bubbles and Fat Tails

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Author Info
Thomas Lux
Didier Sornette

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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 m 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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File URL: ftp://web.bgse.uni-bonn.de/pub/RePEc/bon/bonsfb/bonsfb458.pdf
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Publisher Info
Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 458.

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Date of creation: Oct 1999
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Handle: RePEc:bon:bonsfb:458

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 9221
Web page: http://www.bgse.uni-bonn.de/index.php?id=517

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Related research
Keywords: rational bubbles; random difference equations; multiplicative processes; rational bubbles; random difference equations; multiplicative processes; fat tails.;

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Meese, Richard A, 1986. "Testing for Bubbles in Exchange Markets: A Case of Sparkling Rates?," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 345-73, April. [Downloadable!] (restricted)
  2. Ikeda, Shinsuke & Shibata, Akihisa, 1995. "Fundamentals uncertainty, bubbles, and exchange rate dynamics," Journal of International Economics, Elsevier, vol. 38(3-4), pages 199-222, May. [Downloadable!] (restricted)
  3. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
  4. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-30, September. [Downloadable!] (restricted)
  5. Froot, Kenneth A & Obstfeld, Maurice, 1991. "Intrinsic Bubbles: The Case of Stock Prices," American Economic Review, American Economic Association, vol. 81(5), pages 1189-214, December. [Downloadable!] (restricted)
    Other versions:
  6. Camerer, Colin, 1989. " Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Blackwell Publishing, vol. 3(1), pages 3-41.
  7. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389. [Downloadable!] (restricted)
  8. Ikeda, Shinsuke & Shibata, Akihisa, 1992. "Fundamentals-dependent bubbles in stock prices," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 143-168, October. [Downloadable!] (restricted)
  9. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129. [Downloadable!] (restricted)
  10. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May. [Downloadable!] (restricted)
  11. Adam, M C & Szafarz, A, 1992. "Speculative Bubbles and Financial Markets," Oxford Economic Papers, Oxford University Press, vol. 44(4), pages 626-40, October. [Downloadable!] (restricted)
    Other versions:
  12. Fukuta, Yuichi, 1998. "A simple discrete-time approximation of continuous-time bubbles," Journal of Economic Dynamics and Control, Elsevier, vol. 22(6), pages 937-954, June. [Downloadable!] (restricted)
  13. Diba, Behzad T & Grossman, Herschel I, 1987. "On the Inception of Rational Bubbles," The Quarterly Journal of Economics, MIT Press, vol. 102(3), pages 697-700, August. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Paul De Grauwe & Marianna Grimaldi, 2004. "Bubbles and Crashes in a Behavioural Finance Model," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  2. 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 CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  3. Sheri M. Markose, 2004. "Computability and Evolutionary Complexity: Markets As Complex Adaptive Systems (CAS)," Economics Discussion Papers 574, University of Essex, Department of Economics. [Downloadable!]
    Other versions:
  4. Sergio Da Silva, 2004. "International Finance, Levy Distributions, and the Econophysics of Exchange Rates," International Finance 0405018, EconWPA. [Downloadable!]
  5. 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. [Downloadable!]
  6. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Quantitative Finance Papers physics/0305089, arXiv.org. [Downloadable!]
  7. Prasad Bidarkota, 2003. "Intrinsic Bubbles and Fat Tails in Stock Prices," Working Papers 0306, Florida International University, Department of Economics. [Downloadable!]
  8. Andrea Morone, 2005. "Financial Market in the Laboratory, an Experimental Analysis of some Stylized Facts," Papers on Strategic Interaction 2005-27, Max Planck Institute of Economics, Strategic Interaction Group. [Downloadable!]
    Other versions:
  9. Marianna Grimaldi & Paul De Grauwe, 2003. "Bubbling and Crashing Exchange Rates," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  10. Sheri Markose & Amadeo Alentorn, 2005. "The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing," Economics Discussion Papers 594, University of Essex, Department of Economics. [Downloadable!]
  11. Didier Sornette & Ryan Woodard, 2009. "Financial Bubbles, Real Estate bubbles, Derivative Bubbles, and the Financial and Economic Crisis," Quantitative Finance Papers 0905.0220, arXiv.org. [Downloadable!]
  12. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical Mechanics of Money, Wealth, and Income," Quantitative Finance Papers 0905.1518, arXiv.org. [Downloadable!]
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