IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v45y2012i6p899-908.html
   My bibliography  Save this article

An adaptive stochastic model for financial markets

Author

Listed:
  • Hernández, Juan Antonio
  • Benito, Rosa Marı´a
  • Losada, Juan Carlos

Abstract

An adaptive stochastic model is introduced to simulate the behavior of real asset markets. The model adapts itself by changing its parameters automatically on the basis of the recent historical data. The basic idea underlying the model is that a random variable uniformly distributed within an interval with variable extremes can replicate the histograms of asset returns. These extremes are calculated according to the arrival of new market information. This adaptive model is applied to the daily returns of three well-known indices: Ibex35, Dow Jones and Nikkei, for three complete years. The model reproduces the histograms of the studied indices as well as their autocorrelation structures. It produces the same fat tails and the same power laws, with exactly the same exponents, as in the real indices. In addition, the model shows a great adaptation capability, anticipating the volatility evolution and showing the same volatility clusters observed in the assets. This approach provides a novel way to model asset markets with internal dynamics which changes quickly with time, making it impossible to define a fixed model to fit the empirical observations.

Suggested Citation

  • Hernández, Juan Antonio & Benito, Rosa Marı´a & Losada, Juan Carlos, 2012. "An adaptive stochastic model for financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 899-908.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:6:p:899-908
    DOI: 10.1016/j.chaos.2012.03.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077912000781
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2012.03.005?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. Kitt, Robert & Säkki, Maksim & Kalda, Jaan, 2009. "Probability of large movements in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4838-4844.
    2. Kirchler, Michael & Huber, Jurgen, 2007. "Fat tails and volatility clustering in experimental asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1844-1874, June.
    3. M. Cristelli & V. Alfi & L. Pietronero & A. Zaccaria, 2010. "Liquidity crisis, granularity of the order book and price fluctuations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 73(1), pages 41-49, January.
    4. Chiang, Thomas C. & Zheng, Dazhi, 2010. "An empirical analysis of herd behavior in global stock markets," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1911-1921, August.
    5. I. Vodenska-Chitkushev & F. Z. Wang & P. Weber & K. Yamasaki & S. Havlin & H. E. Stanley, 2008. "Comparison between volatility return intervals of the S&P 500 index and two common models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(2), pages 217-223, January.
    6. Dong, Linrong, 2007. "Volatilities and desires of the agent clusters drive together markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 512-518.
    7. Kirchler, Michael & Huber, Jürgen, 2009. "An exploration of commonly observed stylized facts with data from experimental asset markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1631-1658.
    8. Alfarano, Simone & Lux, Thomas, 2007. "A Noise Trader Model As A Generator Of Apparent Financial Power Laws And Long Memory," Macroeconomic Dynamics, Cambridge University Press, vol. 11(S1), pages 80-101, November.
    9. Amilon, Henrik, 2008. "Estimation of an adaptive stock market model with heterogeneous agents," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 342-362, March.
    10. G. Tedeschi & G. Iori & M. Gallegati, 2009. "The role of communication and imitation in limit order markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 489-497, October.
    11. Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2010. "Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 107-116.
    12. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    13. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2008. "Financial market models with Lévy processes and time-varying volatility," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1363-1378, July.
    14. Shimokawa, Tetsuya & Suzuki, Kyoko & Misawa, Tadanobu, 2007. "An agent-based approach to financial stylized facts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 207-225.
    15. G.-F. Gu & W.-X. Zhou, 2009. "On the probability distribution of stock returns in the Mike-Farmer model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(4), pages 585-592, February.
    16. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
    17. Mr. Noureddine Krichene, 2008. "Crude Oil Prices: Trends and Forecast," IMF Working Papers 2008/133, International Monetary Fund.
    18. Chiang, Thomas C. & Yu, Hai-Chin & Wu, Ming-Chya, 2009. "Statistical properties, dynamic conditional correlation and scaling analysis: Evidence from Dow Jones and Nasdaq high-frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1555-1570.
    19. Frantisek Slanina, 2008. "Critical comparison of several order-book models for stock-market fluctuations," Papers 0801.0631, arXiv.org.
    20. Dong, Linrong, 2008. "A self-adapting herding model: The agent judge-abilities influence the dynamic behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5868-5873.
    21. Robert Kitt & Maksim Sakki & Jaan Kalda, 2008. "Probability of Large Movements in Financial Markets," Papers 0812.4455, arXiv.org, revised Sep 2009.
    22. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    23. F. Slanina, 2008. "Critical comparison of several order-book models for stock-market fluctuations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(2), pages 225-240, January.
    24. A. Krawiecki, 2008. "Microscopic Spin Model For The Stock Market With Attractor Bubbling On Regular And Small-World Lattices," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1035-1045.
    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. Lahmiri, Salim & Bekiros, Stelios & Salvi, Antonio, 2018. "Long-range memory, distributional variation and randomness of bitcoin volatility," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 43-48.

    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. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    2. Inoua, Sabiou M. & Smith, Vernon L., 2023. "A classical model of speculative asset price dynamics," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    3. Alexander Lykov & Stepan Muzychka & Kirill Vaninsky, 2016. "Investor'S Sentiment In Multi-Agent Model Of The Continuous Double Auction," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-29, September.
    4. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    5. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    6. Chiarella, Carl & Iori, Giulia, 2009. "The impact of heterogeneous trading rules on the limit order book and order flows," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 525-537.
    7. Alessio Emanuele Biondo, 2018. "Order book microstructure and policies for financial stability," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 35(1), pages 196-218, March.
    8. Ghonghadze, Jaba & Lux, Thomas, 2016. "Bringing an elementary agent-based model to the data: Estimation via GMM and an application to forecasting of asset price volatility," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 1-19.
    9. Andria, Joseph & di Tollo, Giacomo & Kalda, Jaan, 2022. "The predictive power of power-laws: An empirical time-arrow based investigation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    11. Mingjie Ji & Honggang Li, 2016. "Exploring Price Fluctuations in a Double Auction Market," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 189-209, August.
    12. Marco Bartolozzi, 2010. "A Multi Agent Model for the Limit Order Book Dynamics," Papers 1005.0182, arXiv.org, revised Oct 2010.
    13. Weihong Huang & Huanhuan Zheng & Wai-Mun Chia, 2013. "Asymmetric returns, gradual bubbles and sudden crashes," The European Journal of Finance, Taylor & Francis Journals, vol. 19(5), pages 420-437, May.
    14. Sabiou M. Inoua & Vernon L. Smith, 2022. "Perishable goods versus re-tradable assets: A theoretical reappraisal of a fundamental dichotomy," Chapters, in: Sascha Füllbrunn & Ernan Haruvy (ed.), Handbook of Experimental Finance, chapter 15, pages 162-171, Edward Elgar Publishing.
    15. Georges, Christophre, 2008. "Staggered updating in an artificial financial market," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2809-2825, September.
    16. M. Bartolozzi, 2010. "A multi agent model for the limit order book dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 78(2), pages 265-273, November.
    17. T. T. Chen & B. Zheng & Y. Li & X. F. Jiang, 2017. "New approaches in agent-based modeling of complex financial systems," Papers 1703.06840, arXiv.org.
    18. Sandrine Jacob Leal & Mauro Napoletano & Andrea Roventini & Giorgio Fagiolo, 2016. "Rock around the clock: An agent-based model of low- and high-frequency trading," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 49-76, March.
    19. Lux, Thomas, 2008. "Stochastic behavioral asset pricing models and the stylized facts," Economics Working Papers 2008-08, Christian-Albrechts-University of Kiel, Department of Economics.
    20. Lei Tan & Bo Zheng & Jun-Jie Chen & Xiong-Fei Jiang, 2015. "How Volatilities Nonlocal in Time Affect the Price Dynamics in Complex Financial Systems," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-16, February.

    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:eee:chsofr:v:45:y:2012:i:6:p:899-908. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.