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Optimal split of orders across liquidity pools: a stochastic algorithm approach

Author

Listed:
  • Sophie Laruelle

    () (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Charles-Albert Lehalle

    () (Head of Quantitative Research - CALYON group)

  • Gilles Pagès

    () (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas. Both procedures are investigated from a theoretical point of view: we prove a.s. convergence of the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. we show that the convergence rate is ruled by a Central Limit Theorem. Finally, the mutual performances of both algorithms are compared on simulated and real data with respect to an "oracle" strategy devised by an "insider" who knows a priori the executed quantities by every venues.

Suggested Citation

  • Sophie Laruelle & Charles-Albert Lehalle & Gilles Pagès, 2010. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Working Papers hal-00422427, HAL.
  • Handle: RePEc:hal:wpaper:hal-00422427
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00422427v3
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    References listed on IDEAS

    as
    1. Thierry Foucault & Albert J. Menkveld, 2008. "Competition for Order Flow and Smart Order Routing Systems," Journal of Finance, American Finance Association, vol. 63(1), pages 119-158, February.
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    Cited by:

    1. Charles-Albert Lehalle, 2013. "Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process," Papers 1302.4592, arXiv.org.
    2. repec:dau:papers:123456789/7390 is not listed on IDEAS
    3. Florian Klock & Alexander Schied & Yuemeng Sun, 2012. "Price manipulation in a market impact model with dark pool," Papers 1205.4008, arXiv.org, revised May 2014.
    4. Aim'e Lachapelle & Jean-Michel Lasry & Charles-Albert Lehalle & Pierre-Louis Lions, 2013. "Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis," Papers 1305.6323, arXiv.org, revised Aug 2015.
    5. Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
    6. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    7. Qing-Qing Yang & Wai-Ki Ching & Jia-Wen Gu & Tak-Kuen Siu, 2016. "Generalized Optimal Liquidation Problems Across Multiple Trading Venues," Papers 1607.04553, arXiv.org, revised Aug 2017.
    8. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Papers 1210.1625, arXiv.org, revised Nov 2014.
    9. R. Azencott & A. Beri & Y. Gadhyan & N. Joseph & C.-A. Lehalle & M. Rowley, 2014. "Real-time market microstructure analysis: online transaction cost analysis," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1167-1185, July.
    10. Mauricio Labadie & Charles-Albert Lehalle, 2012. "Optimal starting times, stopping times and risk measures for algorithmic trading," Working Papers hal-00705056, HAL.
    11. 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.
    12. Bruno Bouchard & Ngoc-Minh Dang, 2013. "Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation," Finance and Stochastics, Springer, vol. 17(1), pages 31-72, January.
    13. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Working Papers hal-00737491, HAL.
    14. Marc Hoffmann & Mauricio Labadie & Charles-Albert Lehalle & Gilles Pagès & Huyên Pham & Mathieu Rosenbaum, 2013. "Optimization And Statistical Methods For High Frequency Finance," Post-Print hal-01102785, HAL.
    15. repec:dau:papers:123456789/7391 is not listed on IDEAS
    16. Mauricio Labadie & Charles-Albert Lehalle, 2012. "Optimal starting times, stopping times and risk measures for algorithmic trading: Target Close and Implementation Shortfall," Papers 1205.3482, arXiv.org, revised Dec 2013.

    More about this item

    Keywords

    Asset allocation; Stochastic Lagrangian algorithm; reinforcement principle; monotone dynamic system;

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