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Optimal High Frequency Trading with limit and market orders

  • Fabien Guilbaud

    ()

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie - Paris VI - Université Paris Diderot - Paris 7)

  • Huyen Pham

    ()

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie - Paris VI - Université Paris Diderot - Paris 7, 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 for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders and submits market orders at discrete dates. The objective of the market maker is to maximize her expected utility from revenue over a short term horizon by a tradeoff between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/ impulse control problem that we characterize in terms of quasi-variational system by dynamic programming methods. In the case of a mean-variance criterion with martingale reference price or when the asset price follows a Levy process and with exponential utility criterion, the dynamic programming system can be reduced to a system of simple equations involving only the inventory and spread variables. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market orders

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    Paper provided by HAL in its series Working Papers with number hal-00603385.

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    Date of creation: 24 Jun 2011
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    Handle: RePEc:hal:wpaper:hal-00603385
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    1. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    2. Luc Bauwens & David Veredas & Winfried Pohlmeier, 2005. "High frequency finance," ULB Institutional Repository 2013/136220, ULB -- Universite Libre de Bruxelles.
    3. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    4. Sasha Stoikov & Mehmet Sağlam, 2009. "Option market making under inventory risk," Review of Derivatives Research, Springer, vol. 12(1), pages 55-79, April.
    5. 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.
    6. Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    7. Erhan Bayraktar & Michael Ludkovski, 2011. "Liquidation in Limit Order Books with Controlled Intensity," Papers 1105.0247, arXiv.org, revised Jan 2012.
    8. Terrence Hendershott & Charles M. Jones & Albert J. Menkveld, 2011. "Does Algorithmic Trading Improve Liquidity?," Journal of Finance, American Finance Association, vol. 66(1), pages 1-33, 02.
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