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

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  • 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
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    References listed on IDEAS

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    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, revised May 2024.

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