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Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis

Author

Listed:
  • Aim'e Lachapelle
  • Jean-Michel Lasry
  • Charles-Albert Lehalle
  • Pierre-Louis Lions

Abstract

This paper deals with a stochastic order-driven market model with waiting costs, for order books with heterogenous traders. Offer and demand of liquidity drives price formation and traders anticipate future evolutions of the order book. The natural framework we use is mean field game theory, a class of stochastic differential games with a continuum of anonymous players. Several sources of heterogeneity are considered including the mean size of orders. Thus we are able to consider the coexistence of Institutional Investors and High Frequency Traders (HFT). We provide both analytical solutions and numerical experiments. Implications on classical quantities are explored: order book size, prices, and effective bid/ask spread. According to the model, in markets with Institutional Investors only we show the existence of inefficient liquidity imbalances in equilibrium, with two symmetrical situations corresponding to what we call liquidity calls for liquidity. During these situations the transaction price significantly moves away from the fair price. However this macro phenomenon disappears in markets with both Institutional Investors and HFT, although a more precise study shows that the benefits of the new situation go to HFT only, leaving Institutional Investors even with higher trading costs.

Suggested Citation

  • 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.
  • Handle: RePEc:arx:papers:1305.6323
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    File URL: http://arxiv.org/pdf/1305.6323
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    References listed on IDEAS

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    1. Charles-Albert Lehalle & Sophie Laruelle (ed.), 2013. "Market Microstructure in Practice," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8967.
    2. Thierry Foucault & Ohad Kadan & Eugene Kandel, 2005. "Limit Order Book as a Market for Liquidity," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1171-1217.
    3. Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag`es, 2009. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Papers 0910.1166, arXiv.org, revised May 2010.
    4. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    5. 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.
    6. A. Gareche & G. Disdier & J. Kockelkoren & J. -P. Bouchaud, 2013. "A Fokker-Planck description for the queue dynamics of large tick stocks," Papers 1304.6819, arXiv.org.
    7. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    8. Ho, Thomas S Y & Stoll, Hans R, 1983. " The Dynamics of Dealer Markets under Competition," Journal of Finance, American Finance Association, vol. 38(4), pages 1053-1074, September.
    9. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    10. Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4601-4641, November.
    11. Christian Y. Robert & Mathieu Rosenbaum, 2011. "A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 344-366, Spring.
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    Citations

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    Cited by:

    1. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    2. 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.
    3. Charles-Albert Lehalle & Othmane Mounjid, 2016. "Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency," Papers 1610.00261, arXiv.org, revised Dec 2016.
    4. Weibing Huang & Mathieu Rosenbaum, 2015. "Ergodicity and diffusivity of Markovian order book models: a general framework," Papers 1505.04936, arXiv.org.
    5. Frank Kelly & Elena Yudovina, 2015. "A Markov model of a limit order book: thresholds, recurrence, and trading strategies," Papers 1504.00579, arXiv.org, revised Mar 2017.
    6. Donovan Platt & Tim Gebbie, 2016. "The Problem of Calibrating an Agent-Based Model of High-Frequency Trading," Papers 1606.01495, arXiv.org, revised Mar 2017.
    7. Elias Strehle, 2016. "Are Order Anticipation Strategies Harmful? A Theoretical Approach," Papers 1609.00599, arXiv.org, revised Sep 2017.

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