IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1809.09273.html
   My bibliography  Save this paper

Asynchronous stochastic price pump

Author

Listed:
  • Misha Perepelitsa
  • Ilya Timofeyev

Abstract

We propose a model for equity trading in a population of agents where each agent acts to achieve his or her target stock-to-bond ratio, and, as a feedback mechanism, follows a market adaptive strategy. In this model only a fraction of agents participates in buying and selling stock during a trading period, while the rest of the group accepts the newly set price. Using numerical simulations we show that the stochastic process settles on a stationary regime for the returns. The mean return can be greater or less than the return on the bond and it is determined by the parameters of the adaptive mechanism. When the number of interacting agents is fixed, the distribution of the returns follows the log-normal density. In this case, we give an analytic formula for the mean rate of return in terms of the rate of change of agents' risk levels and confirm the formula by numerical simulations. However, when the number of interacting agents per period is random, the distribution of returns can significantly deviate from the log-normal, especially as the variance of the distribution for the number of interacting agents increases.

Suggested Citation

  • Misha Perepelitsa & Ilya Timofeyev, 2018. "Asynchronous stochastic price pump," Papers 1809.09273, arXiv.org.
  • Handle: RePEc:arx:papers:1809.09273
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1809.09273
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Egenter, E. & Lux, T. & Stauffer, D., 1999. "Finite-size effects in Monte Carlo simulations of two stock market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 250-256.
    2. Olivier J. Blanchard & Mark W. Watson, 1982. "Bubbles, Rational Expectations and Financial Markets," NBER Working Papers 0945, National Bureau of Economic Research, Inc.
    3. Levy, Moshe & Levy, Haim & Solomon, Sorin, 1994. "A microscopic model of the stock market : Cycles, booms, and crashes," Economics Letters, Elsevier, vol. 45(1), pages 103-111, May.
    4. Levy, Haim & Levy, Moshe & Solomon, Sorin, 2000. "Microscopic Simulation of Financial Markets," Elsevier Monographs, Elsevier, edition 1, number 9780124458901.
    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. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    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. Perepelitsa, Misha & Timofeyev, Ilya, 2019. "Asynchronous stochastic price pump," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 356-364.
    2. A. Corcos & J-P Eckmann & A. Malaspinas & Y. Malevergne & D. Sornette, 2002. "Imitation and contrarian behaviour: hyperbolic bubbles, crashes and chaos," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 264-281.
    3. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    4. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    5. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2018. "Simulation of Stylized Facts in Agent-Based Computational Economic Market Models," Papers 1812.02726, arXiv.org, revised Nov 2019.
    6. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    7. Misha Perepelitsa, 2018. "A model of adaptive, market behavior generating positive returns, volatility and system risk," Papers 1809.09601, arXiv.org.
    8. Torsten Trimborn & Philipp Otte & Simon Cramer & Max Beikirch & Emma Pabich & Martin Frank, 2018. "SABCEMM-A Simulator for Agent-Based Computational Economic Market Models," Papers 1801.01811, arXiv.org, revised Oct 2018.
    9. Misha Perepelitsa & Ilya Timofeyev, 2020. "Self-sustained price bubbles driven by Bitcoin innovations and adaptive behavior," Papers 2012.14860, arXiv.org.
    10. 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.
    11. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    12. 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.
    13. Misha Perepelitsa, 2021. "Psychological dimension of adaptive trading in cryptocurrency markets," Papers 2109.12166, arXiv.org.
    14. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 9, Edward Elgar Publishing.
    15. Misha Perepelitsa, 2021. "Investing in crypto: speculative bubbles and cyclic stochastic price pumps," Papers 2111.11315, arXiv.org, revised Oct 2022.
    16. Misha Perepelitsa & Ilya Timofeyev, 2022. "Self-sustained price bubbles driven by digital currency innovations and adaptive market behavior," SN Business & Economics, Springer, vol. 2(3), pages 1-15, March.
    17. Torsten Trimborn & Lorenzo Pareschi & Martin Frank, 2017. "Portfolio Optimization and Model Predictive Control: A Kinetic Approach," Papers 1711.03291, arXiv.org, revised Feb 2019.
    18. Maximilian Beikirch & Torsten Trimborn, 2020. "Novel Insights in the Levy-Levy-Solomon Agent-Based Economic Market Model," Papers 2002.10222, arXiv.org.
    19. 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.
    20. Baosheng Yuan & Kan Chen, 2005. "Impact of Investor's Varying Risk Aversion on the Dynamics of Asset Price Fluctuations," Papers physics/0506224, arXiv.org.

    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:1809.09273. 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.