IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-00422427.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://hal.archives-ouvertes.fr/hal-00422427v3/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Phuong Pham, Thu & Joakim Westerholm, P., 2013. "An international trend in market design: Endogenous effects of limit order book transparency on volatility, spreads, depth and volume," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 27(C), pages 202-223.
    2. Comerton-Forde, Carole & Grégoire, Vincent & Zhong, Zhuo, 2019. "Inverted fee structures, tick size, and market quality," Journal of Financial Economics, Elsevier, vol. 134(1), pages 141-164.
    3. Kei Kawakami, 2013. "Optimal Market Size," Department of Economics - Working Papers Series 1168, The University of Melbourne.
    4. Garvey, Ryan & Huang, Tao & Wu, Fei, 2016. "Why do traders choose dark markets?," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 12-28.
    5. Friederich, Sylvain & Payne, Richard, 2015. "Order-to-trade ratios and market liquidity," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 214-223.
    6. Brolley, Michael & Cimon, David A., 2020. "Order-Flow Segmentation, Liquidity, and Price Discovery: The Role of Latency Delays," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(8), pages 2555-2587, December.
    7. M. Moses Antony RAJENDRAN, & Alexandru Mircea Nedelea, 2017. "Re - Modeling Of Global Financial Markets, Assets And Services Of Financial Institutions For Public Benefits," EcoForum, "Stefan cel Mare" University of Suceava, Romania, Faculty of Economics and Public Administration - Economy, Business Administration and Tourism Department., vol. 6(1), pages 1-57, January.
    8. Umut c{C}etin & Henri Waelbroeck, 2020. "Informed trading, limit order book and implementation shortfall: equilibrium and asymptotics," Papers 2003.04425, arXiv.org.
    9. Peter Gomber & Satchit Sagade & Erik Theissen & Moritz Christian Weber & Christian Westheide, 2017. "Competition Between Equity Markets: A Review Of The Consolidation Versus Fragmentation Debate," Journal of Economic Surveys, Wiley Blackwell, vol. 31(3), pages 792-814, July.
    10. Clapham, Benjamin & Gomber, Peter & Lausen, Jens & Panz, Sven, 2021. "Liquidity provider incentives in fragmented securities markets," Journal of Empirical Finance, Elsevier, vol. 60(C), pages 16-38.
    11. Buti, Sabrina & Rindi, Barbara & Wen, Yuanji & Werner, Ingrid M., 2013. "Tick Size Regulation and Sub-Penny Trading," Working Paper Series 2013-14, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    12. Thierry Foucault & Ohad Kadan & Eugene Kandel, 2013. "Liquidity Cycles and Make/Take Fees in Electronic Markets," Journal of Finance, American Finance Association, vol. 68(1), pages 299-341, February.
    13. Aitken, Michael & Chen, Haoming & Foley, Sean, 2017. "The impact of fragmentation, exchange fees and liquidity provision on market quality," Journal of Empirical Finance, Elsevier, vol. 41(C), pages 140-160.
    14. Cantillon, Estelle & Yin, Pai-Ling, 2011. "Competition between exchanges: A research agenda," International Journal of Industrial Organization, Elsevier, vol. 29(3), pages 329-336, May.
    15. G. Wuyts, 2007. "Stock Market Liquidity.Determinants and Implications," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 279-316.
    16. Fany Declerck & Laurence Lescourret, 2015. "Dark pools et trading haute fréquence : une évolution utile ?," Revue d'économie financière, Association d'économie financière, vol. 0(4), pages 113-126.
    17. Carole Gresse, 2013. "Effects of Lit and Dark Trading Venue Competition on Liquidity : The MiFID Experience," Post-Print hal-01632517, HAL.
    18. Oliver Linton & Soheil Mahmoodzadeh, 2018. "Implications of High-Frequency Trading for Security Markets," Annual Review of Economics, Annual Reviews, vol. 10(1), pages 237-259, August.
    19. Yildiz, Serhat & Van Ness, Bonnie & Van Ness, Robert, 2020. "VPIN, liquidity, and return volatility in the U.S. equity markets," Global Finance Journal, Elsevier, vol. 45(C).
    20. Hans Degryse & Rudy de Winne & Carole Gresse & Richard Payne, 2018. "Cross-Venue Liquidity Provision: High Frequency Trading and Ghost Liquidity," Post-Print hal-01947824, HAL.

    More about this item

    Keywords

    Asset allocation; Stochastic Lagrangian algorithm; reinforcement principle; monotone dynamic system;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00422427. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.