rδ 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."> rδ 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.">
[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v309y2002i3p403-418.html
   My bibliography  Save this article

“Slimming” of power-law tails by increasing market returns

Author

Listed:
  • Sornette, D.
Abstract
We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by Lux and Sornette (J. Money, Credit and Banking, preprint at http://xxx.lanl.gov/abs/cond-mat/9910141) that the distribution of returns is a power law with exponent <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 rδ, 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>rδ 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.

Suggested Citation

  • Sornette, D., 2002. "“Slimming” of power-law tails by increasing market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 403-418.
    • Handle: RePEc:eee:phsmap:v:309:y:2002:i:3:p:403-418
    DOI: 10.1016/S0378-4371(02)00614-3
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437102006143
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(02)00614-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sornette, D & Malevergne, Y, 2001. "From rational bubbles to crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 40-59.
    2. Burke, Jonathan L., 2000. "General Equilibrium When Economic Growth Exceeds Discounting," Journal of Economic Theory, Elsevier, vol. 94(2), pages 141-162, October.
    3. Lux, Thomas & Sornette, Didier, 2002. "On Rational Bubbles and Fat Tails," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(3), pages 589-610, August.
    4. Adam, M C & Szafarz, A, 1992. "Speculative Bubbles and Financial Markets," Oxford Economic Papers, Oxford University Press, vol. 44(4), pages 626-640, October.
    5. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    6. 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.
    7. Y. Malevergne & D. Sornette, 2001. "Multi-dimensional rational bubbles and fat tails," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 533-541.
    8. Giulia Iori, 1999. "Avalanche Dynamics And Trading Friction Effects On Stock Market Returns," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(06), pages 1149-1162.
    9. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    10. D. Sornette, 2000. "Stock Market Speculation: Spontaneous Symmetry Breaking of Economic Valuation," Papers cond-mat/0004001, arXiv.org.
    11. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    12. 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;EDP Sciences, vol. 3(2), pages 139-140, July.
    13. Olivier J. Blanchard & Mark W. Watson, 1982. "Bubbles, Rational Expectations and Financial Markets," NBER Working Papers 0945, National Bureau of Economic Research, Inc.
    14. Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
    15. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    16. Camerer, Colin, 1989. "Bubbles and Fads in Asset Prices," Journal of Economic Surveys, Wiley Blackwell, vol. 3(1), pages 3-41.
    17. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
    18. Sornette, Didier, 1998. "Linear stochastic dynamics with nonlinear fractal properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 295-314.
    19. D. Sornette & J. V. Andersen, 2001. "A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles," Papers cond-mat/0104341, arXiv.org, revised Apr 2002.
    20. Behzad T. Diba & Herschel I. Grossman, 1987. "On the Inception of Rational Bubbles," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(3), pages 697-700.
    21. Mehra, Rajnish & Prescott, Edward C., 1988. "The equity risk premium: A solution?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 133-136, July.
    22. D. Sornette & J. V. Andersen, 2002. "A Nonlinear Super-Exponential Rational Model Of Speculative Financial Bubbles," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 171-187.
    23. Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374, arXiv.org, revised May 1998.
    24. 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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jerome L Kreuser & Didier Sornette, 2017. "Super-Exponential RE Bubble Model with Efficient Crashes," Swiss Finance Institute Research Paper Series 17-33, Swiss Finance Institute.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. D. Sornette, 2000. ""Slimming" of power law tails by increasing market returns," Papers cond-mat/0010112, arXiv.org, revised Sep 2001.
    2. Lux, Thomas & Sornette, Didier, 2002. "On Rational Bubbles and Fat Tails," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(3), pages 589-610, August.
    3. Zhou, Wei-Xing & Sornette, Didier, 2003. "Evidence of a worldwide stock market log-periodic anti-bubble since mid-2000," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 543-583.
    4. 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.
    5. Jerome L Kreuser & Didier Sornette, 2017. "Super-Exponential RE Bubble Model with Efficient Crashes," Swiss Finance Institute Research Paper Series 17-33, Swiss Finance Institute.
    6. Harras, Georges & Sornette, Didier, 2011. "How to grow a bubble: A model of myopic adapting agents," Journal of Economic Behavior & Organization, Elsevier, vol. 80(1), pages 137-152.
    7. Li Lin & Didier Sornette, 2009. "Diagnostics of Rational Expectation Financial Bubbles with Stochastic Mean-Reverting Termination Times," Papers 0911.1921, arXiv.org.
    8. Li Lin & Didier Sornette, 2023. "The inverse Cox-Ingersoll-Ross process for parsimonious financial price modeling," Papers 2302.11423, arXiv.org, revised Jun 2023.
    9. Leiss, Matthias & Nax, Heinrich H. & Sornette, Didier, 2015. "Super-exponential growth expectations and the global financial crisis," Journal of Economic Dynamics and Control, Elsevier, vol. 55(C), pages 1-13.
    10. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Papers cond-mat/0106520, arXiv.org.
    11. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    12. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.
    13. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    14. Anders Johansen & Didier Sornette, 2000. "The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash," Papers cond-mat/0004263, arXiv.org, revised May 2000.
    15. Michael Demmler & Amilcar Orlian Fernández Domínguez, 2021. "Bitcoin and the South Sea Company: A comparative analysis," Revista Finanzas y Politica Economica, Universidad Católica de Colombia, vol. 13(1), pages 197-224, March.
    16. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    17. Lin, L. & Ren, R.E. & Sornette, D., 2014. "The volatility-confined LPPL model: A consistent model of ‘explosive’ financial bubbles with mean-reverting residuals," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 210-225.
    18. Luis Goncalves de Faria, 2022. "An Agent-Based Model With Realistic Financial Time Series: A Method for Agent-Based Models Validation," Papers 2206.09772, arXiv.org.
    19. Kaizoji, Taisei & Leiss, Matthias & Saichev, Alexander & Sornette, Didier, 2015. "Super-exponential endogenous bubbles in an equilibrium model of fundamentalist and chartist traders," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 289-310.
    20. Vladimir Filimonov & Didier Sornette, 2014. "Power law scaling and "Dragon-Kings" in distributions of intraday financial drawdowns," Papers 1407.5037, arXiv.org, revised Apr 2015.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:309:y:2002:i:3:p:403-418. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.