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Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis

Author

Listed:
  • Aimé Lachapelle

    (ORFE - Department of Operations Research and Financial Engineering - Princeton University)

  • Jean-Michel Lasry

    (Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres)

  • Charles-Albert Lehalle

    (X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Pierre-Louis Lions

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, Collège de France - Chaire Équations aux dérivées partielles et applications - CdF (institution) - Collège de France)

Abstract

This paper deals with a stochastic order-driven market model with waiting costs, for orderbooks with heterogenous traders. Offer and demand of liquidity drives price formation and traders anticipate future evolutions of the orderbook. 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: orderbook 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

  • Aimé Lachapelle & Jean-Michel Lasry & Charles-Albert Lehalle & Pierre-Louis Lions, 2016. "Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis," Post-Print hal-05313886, HAL.
    • Handle: RePEc:hal:journl:hal-05313886
    DOI: 10.1007/s11579-015-0157-1
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    Cited by:

    1. is not listed on IDEAS
    2. Elias Strehle, 2016. "Optimal Execution in a Multiplayer Model of Transient Price Impact," Papers 1609.00599, arXiv.org, revised Mar 2019.
    3. Weibing Huang & Mathieu Rosenbaum, 2015. "Ergodicity and diffusivity of Markovian order book models: a general framework," Papers 1505.04936, arXiv.org.
    4. 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.
    5. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    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. 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.
    8. 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 Mar 2018.

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