IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2306.13378.html
   My bibliography  Save this paper

Exact solution to a generalised Lillo-Mike-Farmer model with heterogeneous order-splitting strategies

Author

Listed:
  • Yuki Sato
  • Kiyoshi Kanazawa

Abstract

The Lillo-Mike-Farmer (LMF) model is an established econophysics model describing the order-splitting behaviour of institutional investors in financial markets. In the original article (LMF, Physical Review E 71, 066122 (2005)), LMF assumed the homogeneity of the traders' order-splitting strategy and derived a power-law asymptotic solution to the order-sign autocorrelation function (ACF) based on several heuristic reasonings. This report proposes a generalised LMF model by incorporating the heterogeneity of traders' order-splitting behaviour that is exactly solved without heuristics. We find that the power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous intensity distributions. On the other hand, the prefactor in the ACF is very sensitive to heterogeneity in trading strategies and is shown to be systematically underestimated in the original homogeneous LMF model. Our work highlights that the ACF prefactor should be more carefully interpreted than the ACF power-law exponent in data analyses.

Suggested Citation

  • Yuki Sato & Kiyoshi Kanazawa, 2023. "Exact solution to a generalised Lillo-Mike-Farmer model with heterogeneous order-splitting strategies," Papers 2306.13378, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2306.13378
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2306.13378
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    2. J. Donier & J. Bonart & I. Mastromatteo & J.-P. Bouchaud, 2015. "A fully consistent, minimal model for non-linear market impact," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1109-1121, July.
    3. Jonathan Donier & Julius Bonart & Iacopo Mastromatteo & Jean-Philippe Bouchaud, 2014. "A fully consistent, minimal model for non-linear market impact," Papers 1412.0141, arXiv.org, revised Mar 2015.
    4. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    5. Yamamoto, Ryuichi, 2011. "Order aggressiveness, pre-trade transparency, and long memory in an order-driven market," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1938-1963.
    6. Yuki Sato & Kiyoshi Kanazawa, 2023. "Can we infer microscopic financial information from the long memory in market-order flow?: a quantitative test of the Lillo-Mike-Farmer model," Papers 2301.13505, arXiv.org, revised Aug 2023.
    7. F. Lillo & Szabolcs Mike & J. Doyne Farmer, 2004. "A theory for long-memory in supply and demand," Papers cond-mat/0412708, arXiv.org, revised Mar 2005.
    8. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    9. Tóth, Bence & Palit, Imon & Lillo, Fabrizio & Farmer, J. Doyne, 2015. "Why is equity order flow so persistent?," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 218-239.
    10. Kiyoshi Kanazawa & Takumi Sueshige & Hideki Takayasu & Misako Takayasu, 2017. "Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders," Papers 1703.06739, arXiv.org, revised Mar 2018.
    11. Sato, Aki-Hiro & Takayasu, Hideki, 1998. "Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 231-252.
    12. Blake LeBaron & Ryuichi Yamamoto, 2008. "The Impact of Imitation on Long Memory in an Order-Driven Market," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 34(4), pages 504-517.
    13. LeBaron, Blake & Yamamoto, Ryuichi, 2007. "Long-memory in an order-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 85-89.
    14. Kiyoshi Kanazawa & Takumi Sueshige & Hideki Takayasu & Misako Takayasu, 2018. "Kinetic Theory for Finance Brownian Motion from Microscopic Dynamics," Papers 1802.05993, arXiv.org.
    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. Ioanna-Yvonni Tsaknaki & Fabrizio Lillo & Piero Mazzarisi, 2023. "Online Learning of Order Flow and Market Impact with Bayesian Change-Point Detection Methods," Papers 2307.02375, arXiv.org.

    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. Takumi Sueshige & Kiyoshi Kanazawa & Hideki Takayasu & Misako Takayasu, 2018. "Ecology of trading strategies in a forex market for limit and market orders," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-14, December.
    2. Ioanna-Yvonni Tsaknaki & Fabrizio Lillo & Piero Mazzarisi, 2023. "Online Learning of Order Flow and Market Impact with Bayesian Change-Point Detection Methods," Papers 2307.02375, arXiv.org.
    3. Erdinc Akyildirim & Shaen Corbet & Guzhan Gulay & Duc Khuong Nguyen & Ahmet Sensoy, 2019. "Order Flow Persistence in Equity Spot and Futures Markets: Evidence from a Dynamic Emerging Market," Working Papers 2019-011, Department of Research, Ipag Business School.
    4. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    5. Mohammed Salek & Damien Challet & Ioane Muni Toke, 2023. "Price impact in equity auctions: zero, then linear," Working Papers hal-03938660, HAL.
    6. Christopher J. Cho & Timothy J. Norman & Manuel Nunes, 2023. "PRIME: A Price-Reverting Impact Model of a cryptocurrency Exchange," Papers 2305.07559, arXiv.org.
    7. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    8. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Toth, 2016. "Linear models for the impact of order flow on prices II. The Mixture Transition Distribution model," Papers 1604.07556, arXiv.org.
    9. Kiyoshi Kanazawa & Hideki Takayasu & Misako Takayasu, 2022. "Exact solution to two-body financial dealer model: revisited from the viewpoint of kinetic theory," Papers 2205.15558, arXiv.org.
    10. Tóth, Bence & Palit, Imon & Lillo, Fabrizio & Farmer, J. Doyne, 2015. "Why is equity order flow so persistent?," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 218-239.
    11. Martin D. Gould & Mason A. Porter & Sam D. Howison, 2015. "Quasi-Centralized Limit Order Books," Papers 1502.00680, arXiv.org, revised Oct 2016.
    12. Ke Xu & Martin D. Gould & Sam D. Howison, 2019. "Multi-Level Order-Flow Imbalance in a Limit Order Book," Papers 1907.06230, arXiv.org, revised Oct 2019.
    13. Martin D. Gould & Mason A. Porter & Sam D. Howison, 2015. "The Long Memory of Order Flow in the Foreign Exchange Spot Market," Papers 1504.04354, arXiv.org, revised Oct 2015.
    14. Marvin S. Mueller, 2016. "A stochastic Stefan-type problem under first-order boundary conditions," Papers 1601.03968, arXiv.org, revised Oct 2018.
    15. M. Derksen & B. Kleijn & R. de Vilder, 2019. "Clearing price distributions in call auctions," Papers 1904.07583, arXiv.org, revised Nov 2019.
    16. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Toth, 2016. "Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact," Papers 1602.02735, arXiv.org.
    17. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    18. Juan C. Henao-Londono & Sebastian M. Krause & Thomas Guhr, 2021. "Price response functions and spread impact in correlated financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(4), pages 1-20, April.
    19. Yamamoto, Ryuichi, 2019. "Dynamic Predictor Selection And Order Splitting In A Limit Order Market," Macroeconomic Dynamics, Cambridge University Press, vol. 23(5), pages 1757-1792, July.
    20. Svitlana Vyetrenko & David Byrd & Nick Petosa & Mahmoud Mahfouz & Danial Dervovic & Manuela Veloso & Tucker Hybinette Balch, 2019. "Get Real: Realism Metrics for Robust Limit Order Book Market Simulations," Papers 1912.04941, 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:2306.13378. 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.