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"Slimming" of power law tails by increasing market returns

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  • D. Sornette

    (Univ. Nice/CNRS and UCLA)

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    Abstract

    We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by [Lux and Sornette, 1999] that the distribution of returns is a power law with exponent less than 1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles must on average grow with the mean market return r. When r is larger than the discount rate r_delta, the distribution of returns of the observable price, sum of the bubble component and of the fundamental price, exhibits an intermediate tail with an exponent which can be larger than 1. This regime r>r_delta corresponds to a generalization of the rational bubble model in which the fundamental price is no more given by the discounted value of future dividends. We explain how this is possible. Our model predicts that, the higher is the market remuneration r above the discount rate, the larger is the power law exponent and thus the thinner is the tail of the distribution of price returns.

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    File URL: http://arxiv.org/pdf/cond-mat/0010112
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0010112.

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    Date of creation: Oct 2000
    Date of revision: Sep 2001
    Publication status: Published in Physica A 309, 403--418 (2002)
    Handle: RePEc:arx:papers:cond-mat/0010112

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    Web page: http://arxiv.org/

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    References

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    1. D. Sornette, 2000. "Stock Market Speculation: Spontaneous Symmetry Breaking of Economic Valuation," Papers cond-mat/0004001, arXiv.org.
    2. Adam, M C & Szafarz, A, 1992. "Speculative Bubbles and Financial Markets," Oxford Economic Papers, Oxford University Press, vol. 44(4), pages 626-40, October.
    3. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
    4. Camerer, Colin, 1989. " Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
    5. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    6. Sornette, Didier, 1998. "Linear stochastic dynamics with nonlinear fractal properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 295-314.
    7. 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.
    8. Mehra, Rajnish & Prescott, Edward C., 1988. "The equity risk premium: A solution?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 133-136, July.
    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.
    10. Sornette, D & Malevergne, Y, 2001. "From rational bubbles to crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 40-59.
    11. 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.
    12. 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.
    13. Y. Malevergne & D. Sornette, 2001. "Multi-dimensional rational bubbles and fat tails," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 533-541.
    14. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    15. Burke, Jonathan L., 2000. "General Equilibrium When Economic Growth Exceeds Discounting," Journal of Economic Theory, Elsevier, vol. 94(2), pages 141-162, October.
    16. 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).
    17. Sornette, Didier, 2000. "Stock market speculation: Spontaneous symmetry breaking of economic valuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 355-375.
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    Cited by:
    1. D. Sornette & Y. Malevergne, 2001. "From Rational Bubbles to Crashes," Papers cond-mat/0102305, arXiv.org.
    2. Y. Malevergne & D. Sornette, 2001. "Multi-dimensional Rational Bubbles and fat tails: application of stochastic regression equations to financial speculation," Papers cond-mat/0101371, arXiv.org.

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