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Optimal High Frequency Trading in a Pro-Rata Microstructure with Predictive Information

  • Fabien Guilbaud

    ()

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Paris VI - Pierre et Marie Curie - Université Paris VII - Paris Diderot)

  • Huyên Pham

    ()

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Paris VI - Pierre et Marie Curie - Université Paris VII - Paris Diderot, CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique)

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    We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically arises in short-term interest rate futures contracts. The high-frequency trader has the choice to trade via market orders or limit orders, which are represented respectively by impulse controls and regular controls. We model and discuss the consequences of the two main features of this particular microstructure: first, the limit orders sent by the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For this purpose, cumulative executed volumes are modelled by compound Poisson processes. Second, the high frequency trader faces the overtrading risk, which is the risk of brutal variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. The optimal trading problem is studied by stochastic control and dynamic progra\-mming methods, which lead to a characterization of the value function in terms of an integro quasi-variational inequality. We then provide the associated numerical resolution procedure, and convergence of this computational scheme is proved. Next, we examine several situations where we can on one hand simplify the numerical procedure by reducing the number of state variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where the mid-price process is a martingale. We also detail a high frequency trading strategy in the case where a (predictive) directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests.

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    Paper provided by HAL in its series Working Papers with number hal-00697125.

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    Date of creation: 14 May 2012
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    Handle: RePEc:hal:wpaper:hal-00697125
    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00697125
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    1. Field, Jonathan & Large, Jeremy, 2008. "Pro-rata matching and one-tick futures markets," CFS Working Paper Series 2008/40, Center for Financial Studies (CFS).
    2. Guéant, Olivier & Lehalle, Charles-Albert & Tapia, Joaquin Fernandez, 2011. "Dealing with the Inventory Risk," Economics Papers from University Paris Dauphine 123456789/7390, Paris Dauphine University.
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