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Optimal make take fees in a multi market maker environment

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  • Bastien Baldacci
  • Dylan Possamai
  • Mathieu Rosenbaum

Abstract

Following the recent literature on make take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimise their quotes in a Nash equilibrium fashion, providing best response to the contract proposed by the principal (the exchange). This contract aims at attracting liquidity on the platform. This is because the wealth of the exchange depends on the arrival of market orders, which is driven by the spread of market makers. We compute the optimal contract in quasi explicit form and also derive the optimal spread policies for the market makers. Several new phenomena appears in this multi market maker setting. In particular we show that it is not necessarily optimal to have a large number of market makers in the presence of a contracting scheme.

Suggested Citation

  • Bastien Baldacci & Dylan Possamai & Mathieu Rosenbaum, 2019. "Optimal make take fees in a multi market maker environment," Papers 1907.11053, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:1907.11053
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    References listed on IDEAS

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    1. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    3. Madhavan, Ananth & Richardson, Matthew & Roomans, Mark, 1997. "Why Do Security Prices Change? A Transaction-Level Analysis of NYSE Stocks," The Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 1035-1064.
    4. Weibing Huang & Mathieu Rosenbaum & Pamela Saliba, 2019. "From Glosten-Milgrom to the whole limit order book and applications to financial regulation," Papers 1902.10743, arXiv.org.
    5. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    6. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    7. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    8. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
    9. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    10. Othmane Mounjid & Mathieu Rosenbaum & Pamela Saliba, 2019. "From asymptotic properties of general point processes to the ranking of financial agents," Papers 1906.05420, arXiv.org.
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    Citations

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    Cited by:

    1. Roberto Riccó & Barbara Rindi & Duane J. Seppi, 2021. "Optimal Market Asset Pricing," Working Papers 675, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Emma Hubert, 2023. "Continuous-time incentives in hierarchies," Finance and Stochastics, Springer, vol. 27(3), pages 605-661, July.
    3. Daniel Krv{s}ek & Dylan Possamai, 2023. "Randomisation with moral hazard: a path to existence of optimal contracts," Papers 2311.13278, arXiv.org.
    4. Bastien Baldacci & Iuliia Manziuk & Thibaut Mastrolia & Mathieu Rosenbaum, 2019. "Market making and incentives design in the presence of a dark pool: a deep reinforcement learning approach," Papers 1912.01129, arXiv.org.
    5. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.
    6. Bastien Baldacci & Philippe Bergault & Dylan Possamai, 2022. "A mean-field game of market-making against strategic traders," Papers 2203.13053, arXiv.org.
    7. Bingyan Han, 2022. "Can maker-taker fees prevent algorithmic cooperation in market making?," Papers 2211.00496, arXiv.org.
    8. Bastien Baldacci & Paul Jusselin & Mathieu Rosenbaum, 2019. "How to design a derivatives market?," Papers 1909.09257, arXiv.org.
    9. Dylan Possamai & Chiara Rossato, 2023. "Golden parachutes under the threat of accidents," Papers 2312.02101, arXiv.org, revised Sep 2024.
    10. Bingyan Han, 2022. "Cooperation between Independent Market Makers," Papers 2206.05410, arXiv.org.

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