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On Rational Bubbles and Fat Tails

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Author Info
Thomas Lux (Bonn University)
D. Sornette (CNRS/Univ. Nice and UCLA)
Abstract

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982), corresponding to multiplicative maps, whose study has recently be revived recently in physics as a mechanism of intermittent dynamics generating power law distributions. 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 smaller than 1, implying absence of convergence of the mean. 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 of an exponent between 2 and 4. 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: http://arxiv.org/abs/cond-mat/9910141
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number cond-mat/9910141.

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Date of creation: Oct 1999
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Publication status: Published in Journal of Money, Credit and Banking, Part 1, vol. 34, No. 3, 589-610 (August 2002)
Handle: RePEc:arx:papers:cond-mat/9910141

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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. 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)
  2. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May. [Downloadable!] (restricted)
  3. 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)
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  4. 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)
  5. 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)
  6. De Vries, C.G. & Leuven, K.U., 1994. "Stylized Facts of Nominal Exchange Rate Returns," Papers 94-002, Purdue University, Krannert School of Management - Center for International Business Education and Research (CIBER).
  7. 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)
  8. 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)
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  9. Camerer, Colin, 1989. " Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Blackwell Publishing, vol. 3(1), pages 3-41.
  10. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389. [Downloadable!] (restricted)
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  1. Prasad Bidarkota, 2003. "Intrinsic Bubbles and Fat Tails in Stock Prices," Working Papers 0306, Florida International University, Department of Economics. [Downloadable!]
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