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Optimal Execution with Identity Optionality

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  • René Carmona
  • Claire Zeng

Abstract

This paper investigates the impact of anonymous trading on the agents' strategy in an optimal execution framework. It mainly explores the specificity of order attribution on the Toronto Stock Exchange, where brokers can choose to either trade with their own identity or under a generic anonymous code that is common to all the brokers. We formulate a stochastic differential game for the optimal execution problem of a population of N brokers and incorporate permanent and temporary price impacts for both the identity-revealed and anonymous trading processes. We then formulate the limiting mean-field game of controls with common noise and obtain a solution in closed-form via the probablistic approach for the Almgren-Chris price impact framework. Finally, we perform a sensitivity analysis to explore the impact of the model parameters on the optimal strategy.

Suggested Citation

  • René Carmona & Claire Zeng, 2022. "Optimal Execution with Identity Optionality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 29(4), pages 261-287, July.
    • Handle: RePEc:taf:apmtfi:v:29:y:2022:i:4:p:261-287
    DOI: 10.1080/1350486X.2023.2193343
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    References listed on IDEAS

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    1. Rene Carmona & Laura Leal, 2021. "Optimal Execution with Quadratic Variation Inventories," Papers 2104.14615, arXiv.org.
    2. Comerton-Forde, Carole & Putniņš, Tālis J. & Tang, Kar Mei, 2011. "Why Do Traders Choose to Trade Anonymously?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(4), pages 1025-1049, August.
    3. Peter C. Reiss, 2005. "Anonymity, Adverse Selection, and the Sorting of Interdealer Trades," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 599-636.
    4. Pierre Cardaliaguet & Charles-Albert Lehalle, 2016. "Mean Field Game of Controls and An Application To Trade Crowding," Papers 1610.09904, arXiv.org, revised Sep 2017.
    5. Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October.
    6. Rene Carmona & Kevin Webster, 2019. "Applications of a New Self-Financing Equation," Papers 1905.04137, arXiv.org.
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