"Slimming" of power law tails by increasing market returns
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.
|Date of creation:||Oct 2000|
|Date of revision:||Sep 2001|
|Publication status:||Published in Physica A 309, 403--418 (2002)|
|Contact details of provider:|| Web page: http://arxiv.org/|
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.:
- Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
- 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.
- 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.
- Camerer, Colin, 1989. " Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
- Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
- Burke, Jonathan L., 2000. "General Equilibrium When Economic Growth Exceeds Discounting," Journal of Economic Theory, Elsevier, vol. 94(2), pages 141-162, October.
- 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.
- 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.
- Sornette, D & Malevergne, Y, 2001.
"From rational bubbles to crashes,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 299(1), pages 40-59.
- Y. Malevergne & D. Sornette, 2001. "Multi-dimensional rational bubbles and fat tails," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 533-541.
- Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
- Sornette, Didier, 1998. "Linear stochastic dynamics with nonlinear fractal properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 295-314.
- D. Sornette, 2000. "Stock Market Speculation: Spontaneous Symmetry Breaking of Economic Valuation," Papers cond-mat/0004001, arXiv.org.
- Mehra, Rajnish & Prescott, Edward C., 1988. "The equity risk premium: A solution?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 133-136, July.
- 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.
- 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.
- 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).
When requesting a correction, please mention this item's handle: RePEc:arx:papers:cond-mat/0010112. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.