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A learning market-maker in the Glosten-Milgrom model

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  • Sanmay Das

Abstract

This paper develops a model of a learning market-maker by extending the Glosten-Milgrom model of dealer markets. The market-maker tracks the changing true value of a stock in settings with informed traders (with noisy signals) and liquidity traders, and sets bid and ask prices based on its estimate of the true value. We empirically evaluate the performance of the market-maker in markets with different parameter values to demonstrate the effectiveness of the algorithm, and then use the algorithm to derive properties of price processes in simulated markets. When the true value is governed by a jump process, there is a two regime behaviour marked by significant heterogeneity of information and large spreads immediately following a price jump, which is quickly resolved by the market-maker, leading to a rapid return to homogeneity of information and small spreads. We also discuss the similarities and differences between our model and real stock market data in terms of distributional and time series properties of returns.

Suggested Citation

  • Sanmay Das, 2005. "A learning market-maker in the Glosten-Milgrom model," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 169-180.
    • Handle: RePEc:taf:quantf:v:5:y:2005:i:2:p:169-180
    DOI: 10.1080/14697680500148067
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    Cited by:

    1. Pankaj Kumar, 2021. "Deep Hawkes Process for High-Frequency Market Making," Papers 2109.15110, arXiv.org.
    2. van Bruggen, G.H. & Spann, M. & Lilien, G.L. & Skiera, B., 2006. "Institutional Forecasting: The Performance of Thin Virtual Stock Markets," ERIM Report Series Research in Management ERS-2006-028-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Ivan Jericevich & Patrick Chang & Tim Gebbie, 2021. "Simulation and estimation of an agent-based market-model with a matching engine," Papers 2108.07806, arXiv.org, revised Aug 2021.
    4. Nelson Vadori & Leo Ardon & Sumitra Ganesh & Thomas Spooner & Selim Amrouni & Jared Vann & Mengda Xu & Zeyu Zheng & Tucker Balch & Manuela Veloso, 2022. "Towards Multi-Agent Reinforcement Learning driven Over-The-Counter Market Simulations," Papers 2210.07184, arXiv.org, revised Aug 2023.
    5. Zhang, Wei & Huang, Ke & Feng, Xu & Zhang, Yongjie, 2017. "Market maker competition and price efficiency: Evidence from China," Economic Modelling, Elsevier, vol. 66(C), pages 121-131.
    6. Aseem Brahma & Sanmay Das & Malik Magdon-Ismail, 2010. "Comparing Prediction Market Structures, With an Application to Market Making," Papers 1009.1446, arXiv.org.
    7. Alexandru Mandes, 2015. "Impact of inventory-based electronic liquidity providers within a high-frequency event- and agent-based modeling framework," MAGKS Papers on Economics 201515, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    8. Sumitra Ganesh & Nelson Vadori & Mengda Xu & Hua Zheng & Prashant Reddy & Manuela Veloso, 2019. "Reinforcement Learning for Market Making in a Multi-agent Dealer Market," Papers 1911.05892, arXiv.org.
    9. Gelman, Sergey & Lushchikov, Roman, 2015. "Stock liquidity in forefront of anticipated announcements," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113176, Verein für Socialpolitik / German Economic Association.
    10. Alexandru Mandes, 2016. "Algorithmic and High-Frequency Trading Strategies: A Literature Review," MAGKS Papers on Economics 201625, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    11. Hugh L. Christensen, 2015. "Algorithmic arbitrage of open-end funds using variational Bayes," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-38, December.
    12. Ren, F. & Zheng, B. & Chen, P., 2010. "Modeling interactions of trading volumes in financial dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2744-2750.
    13. Boer-Sorban, K. & Kaymak, U. & Spiering, J., 2006. "From Discrete-Time Models to Continuous-Time, Asynchronous Models of Financial Markets," ERIM Report Series Research in Management ERS-2006-009-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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