On Rational Bubbles and Fat Tails
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.
|Date of creation:||Oct 1999|
|Date of revision:|
|Publication status:||Published in Journal of Money, Credit and Banking, Part 1, vol. 34, No. 3, 589-610 (August 2002)|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Ikeda, Shinsuke & Shibata, Akihisa, 1992. "Fundamentals-dependent bubbles in stock prices," Journal of Monetary Economics, Elsevier, vol. 30(1), pages 143-168, October.
- Hamilton, James D. & Whiteman, Charles H., 1985. "The observable implications of self-fulfilling expectations," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 353-373, November.
- 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).
- 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.
- 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.
- Kenneth A. Froot & Maurice Obstfeld, 1989.
"Intrinsic Bubbles: The Case of Stock Prices,"
NBER Working Papers
3091, National Bureau of Economic Research, Inc.
- Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
- Adam, M C & Szafarz, A, 1992.
"Speculative Bubbles and Financial Markets,"
Oxford Economic Papers,
Oxford University Press, vol. 44(4), pages 626-40, October.
- Marie Christine Adam & Ariane Szafarz, 1993. "Speculative Bubbles and Financial Markets," ULB Institutional Repository 2013/665, ULB -- Universite Libre de Bruxelles.
- Marie Christine Adam & Ariane Szafarz, 1992. "Speculative Bubbles and Financial Markets," ULB Institutional Repository 2013/689, ULB -- Universite Libre de Bruxelles.
- 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.
- P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 3(2), pages 139-140, July.
- 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.
- Sornette, Didier, 1998. "Linear stochastic dynamics with nonlinear fractal properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 295-314.
- 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.
- 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.
- Camerer, Colin, 1989. " Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
- 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.
- Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
- de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
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