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

Aimé Lachapelle, Jean-Michel Lasry, Charles-Albert Lehalle () and Pierre-Louis Lions ()
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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

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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.

Keywords: Price formation process; Market microstructure; High frequency trading; Liquidity equilibrium; Waiting cost; Order-driven market; Mean field games; Orderbook modeling (search for similar items in EconPapers)
Date: 2016-06
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Published in Mathematics and Financial Economics, 2016, 10 (3), pp.223-262. ⟨10.1007/s11579-015-0157-1⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05313886

DOI: 10.1007/s11579-015-0157-1

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