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Estimation of the probability of informed trading models via an expectation-conditional maximization algorithm

Author

Listed:
  • Montasser Ghachem

    (Stockholm University)

  • Oguz Ersan

    (Kadir Has University)

Abstract

The estimation of the probability of informed trading (PIN) model and its extensions poses significant challenges owing to various computational problems. To address these issues, we propose a novel estimation method called the expectation-conditional-maximization (ECM) algorithm, which can serve as an alternative to the existing methods for estimating PIN models. Our method provides optimal estimates for the original PIN model as well as two of its extensions: the multilayer PIN model and the adjusted PIN model, along with its restricted versions. Our results indicate that estimations using the ECM algorithm are generally faster, more accurate, and more memory-efficient than the standard methods used in the literature, making it a robust alternative. More importantly, the ECM algorithm is not limited to the models discussed and can be easily adapted to estimate future extensions of the PIN model.

Suggested Citation

  • Montasser Ghachem & Oguz Ersan, 2025. "Estimation of the probability of informed trading models via an expectation-conditional maximization algorithm," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 11(1), pages 1-37, December.
    • Handle: RePEc:spr:fininn:v:11:y:2025:i:1:d:10.1186_s40854-024-00729-w
    DOI: 10.1186/s40854-024-00729-w
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    References listed on IDEAS

    as
    1. Oguz Ersan & Montasser Ghachem, 2024. "Identifying Information Types in the Estimation of Informed Trading: An Improved Algorithm," JRFM, MDPI, vol. 17(9), pages 1-20, September.
    2. Easley, David & Hvidkjaer, Soeren & O’Hara, Maureen, 2010. "Factoring Information into Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(2), pages 293-309, April.
    3. Duarte, Jefferson & Hu, Edwin & Young, Lance, 2020. "A comparison of some structural models of private information arrival," Journal of Financial Economics, Elsevier, vol. 135(3), pages 795-815.
    4. Quan Gan & Wang Chun Wei & David Johnstone, 2015. "A faster estimation method for the probability of informed trading using hierarchical agglomerative clustering," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1805-1821, November.
    5. Griffin, Jim & Oberoi, Jaideep & Oduro, Samuel D., 2021. "Estimating the probability of informed trading: A Bayesian approach," Journal of Banking & Finance, Elsevier, vol. 125(C).
    6. Yan, Yuxing & Zhang, Shaojun, 2012. "An improved estimation method and empirical properties of the probability of informed trading," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 454-467.
    7. William Lin, Hsiou-Wei & Ke, Wen-Chyan, 2011. "A computing bias in estimating the probability of informed trading," Journal of Financial Markets, Elsevier, vol. 14(4), pages 625-640, November.
    8. Cheng-Few Lee & John C. Lee (ed.), 2015. "Handbook of Financial Econometrics and Statistics," Springer Books, Springer, edition 127, number 978-1-4614-7750-1, March.
    9. Easley, David, et al, 1996. "Liquidity, Information, and Infrequently Traded Stocks," Journal of Finance, American Finance Association, vol. 51(4), pages 1405-1436, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Expectation conditional-maximization algorithm; ECM; PIN model; MPIN; Multilayer probability of informed trading; Adjusted PIN model; Maximum-likelihood estimation; Private information; Information asymmetry;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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