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

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  • 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.

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File URL: http://arxiv.org/pdf/1305.6323
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Paper provided by arXiv.org in its series Papers with number 1305.6323.

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Date of creation: May 2013
Date of revision: Mar 2014
Handle: RePEc:arx:papers:1305.6323

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  2. FOUCAULT, Thierry & KADAN, Ohad & KANDEL, Eugene, 2001. "Limit order book as a market for liquidity," Les Cahiers de Recherche 728, HEC Paris.
  3. Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag├Ęs, 2009. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Working Papers hal-00422427, HAL.
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  8. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
  9. Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 22(11), pages 4601-4641, November.
  10. Ho, Thomas S Y & Stoll, Hans R, 1983. " The Dynamics of Dealer Markets under Competition," Journal of Finance, American Finance Association, American Finance Association, vol. 38(4), pages 1053-74, September.
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