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High frequency trading in a Markov renewal model

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  • Pietro Fodra

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

  • Huyen Pham

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

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    Abstract

    We study an optimal high frequency trading problem within a market microstructure model aiming at a good compromise between accuracy and tractability. The stock price is modeled by a Markov Renewal Process (MRP), while market orders arrive in the limit order book via a point process correlated with the stock price, and taking into account the adverse selection risk. We apply stochastic control methods in this semi-Markov framework, and show how to reduce remarkably the complexity of the associated Hamilton-Jacobi-Bellman equation by suitable change of variables that exploits the specific symmetry of the problem. We then handle numerically the remaining part of the HJB equation, simplified into an integro-ordinary differential equation, by a bidimensional Euler scheme. Statistical procedures and numerical tests for computing the optimal limit order strategies illustrate our results.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/86/71/13/PDF/MarketMakingMRP-FodraPham.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00867113.

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    Date of creation: 27 Sep 2013
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    Handle: RePEc:hal:wpaper:hal-00867113

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00867113
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    Related research

    Keywords: High frequency trading; Markov renewal process; Marked Cox process; adverse selection; integro-ordinary differential equation.;

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    1. Christian Y. Robert & Mathieu Rosenbaum, 2011. "A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 344-366, Spring.
    2. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2011. "Modeling microstructure noise with mutually exciting point processes," Papers 1101.3422, arXiv.org.
    3. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    4. Rene Carmona & Kevin Webster, 2012. "High Frequency Market Making," Papers 1210.5781, arXiv.org.
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