IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1608.07752.html
   My bibliography  Save this paper

Financial Market Dynamics: Superdiffusive or not?

Author

Listed:
  • Sandhya Devi

Abstract

The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are non-Gaussian. They have fat tails indicating that the stock returns do not follow a random walk model. In this work, a good fit to a Tsallis q-Gaussian distribution is obtained for the distributions of all the returns using the method of Maximum Likelihood Estimate. For all the regions of data considered, the values of the scaling parameter q, estimated from one day returns, lie in the range 1.4 to 1.65. The estimated inverse mean square deviations (beta) show a power law behavior in time with exponent values between -0.91 and -1.1 indicating normal to mildly subdiffusive behavior. Quite often, the dynamics of market return distributions is modelled by a Fokker-Plank (FP) equation either with a linear drift and a nonlinear diffusion term or with just a nonlinear diffusion term. Both of these cases support a q-Gaussian distribution as a solution. The distributions obtained from current estimated parameters are compared with the solutions of the FP equations. For negligible drift term, the inverse mean square deviations (betaFP) from the FP model follow a power law with exponent values between -1.25 and -1.48 indicating superdiffusion. When the drift term is non-negligible, the corresponding betaFP do not follow a power law and become stationary after certain characteristic times that depend on the values of the drift parameter and q. Neither of these behaviors is supported by the results of the empirical fit.

Suggested Citation

  • Sandhya Devi, 2016. "Financial Market Dynamics: Superdiffusive or not?," Papers 1608.07752, arXiv.org, revised Sep 2017.
    • Handle: RePEc:arx:papers:1608.07752
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1608.07752
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cortines, A.A.G. & Riera, R., 2007. "Non-extensive behavior of a stock market index at microscopic time scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 181-192.
    2. D. Sornette, 2003. "Critical Market Crashes," Papers cond-mat/0301543, arXiv.org.
    3. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    4. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    5. V. Schwämmle & E. M.F. Curado & F. D. Nobre, 2009. "Dynamics of normal and anomalous diffusion in nonlinear Fokker-Planck equations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 107-116, July.
    6. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Sarafopoulos, D. & Pavlos, E.G., 2012. "Tsallis statistics and magnetospheric self-organization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3069-3080.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
    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. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Nonextensive triplets in cryptocurrency exchanges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1069-1074.
    2. Chernyshov, A.A. & Kozelov, B.V. & Mogilevsky, M.M., 2024. "Non-extensive (Tsallis) q-statistics and auroral glow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    3. Sandhya Devi, 2019. "Financial Portfolios based on Tsallis Relative Entropy as the Risk Measure," Papers 1901.04945, arXiv.org, revised Mar 2019.
    4. Sandhya Devi, 2021. "Asymmetric Tsallis distributions for modelling financial market dynamics," Papers 2102.04532, arXiv.org.
    5. Devi, Sandhya, 2018. "Financial Portfolios based on Tsallis Relative Entropy as the Risk Measure," MPRA Paper 91614, University Library of Munich, Germany.
    6. Devi, Sandhya, 2021. "Asymmetric Tsallis distributions for modeling financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).

    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. Devi, Sandhya, 2016. "Financial Market Dynamics: Superdiffusive or not?," MPRA Paper 73327, University Library of Munich, Germany, revised 24 Aug 2016.
    2. Devi, Sandhya, 2021. "Asymmetric Tsallis distributions for modeling financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    3. Sandhya Devi, 2021. "Asymmetric Tsallis distributions for modelling financial market dynamics," Papers 2102.04532, arXiv.org.
    4. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Potirakis, Stelios M. & Zitis, Pavlos I. & Eftaxias, Konstantinos, 2013. "Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2940-2954.
    6. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    7. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    8. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    9. Rodrigues, Ana Flávia P. & Cavalcante, Charles C. & Crisóstomo, Vicente L., 2019. "A projection pricing model for non-Gaussian financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    10. Sandhya Devi & Sherman Page, 2022. "Tsallis Relative entropy from asymmetric distributions as a risk measure for financial portfolios," Papers 2205.13625, arXiv.org.
    11. Marian Gidea & Yuri Katz, 2017. "Topological Data Analysis of Financial Time Series: Landscapes of Crashes," Papers 1703.04385, arXiv.org, revised Apr 2017.
    12. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Nonextensive triplets in cryptocurrency exchanges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1069-1074.
    13. Sosa-Correa, William O. & Ramos, Antônio M.T. & Vasconcelos, Giovani L., 2018. "Investigation of non-Gaussian effects in the Brazilian option market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 525-539.
    14. Gottschalk, Sylvia, 2017. "Entropy measure of credit risk in highly correlated markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 11-19.
    15. S. M. Duarte Queiros, 2005. "On non-Gaussianity and dependence in financial time series: a nonextensive approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 475-487.
    16. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
    17. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
    18. Marco Airoldi & Vito Antonelli & Bruno Bassetti & Andrea Martinelli & Marco Picariello, 2004. "Long Range Interaction Generating Fat-Tails in Finance," GE, Growth, Math methods 0404006, University Library of Munich, Germany, revised 27 Apr 2004.
    19. Qin, Guyue & Shang, Pengjian, 2021. "Analysis of time series using a new entropy plane based on past entropy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    20. Diks, Cees & Hommes, Cars & Zeppini, Paolo, 2013. "More memory under evolutionary learning may lead to chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 808-812.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:1608.07752. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.