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High-frequency market-making with inventory constraints and directional bets

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  • Pietro Fodra

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

  • Mauricio Labadie

    ()
    (EXQIM - EXclusive Quantitative Investment Management - EXQIM)

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    Abstract

    We extend the market-making models with inventory constraints of Avellaneda and Stoikov ("High-frequency trading in a limit-order book", Quantitative Finance Vol.8 No.3 2008) and Gueant, Lehalle and Fernandez-Tapia ("Dealing with inventory risk", Preprint 2011) to the case of a rather general class of mid-price processes, under either exponential or linear PnL utility functions, and we add an inventory-risk-aversion parameter that penalises the marker-maker if she finishes her day with a non-zero inventory. This general, non-martingale framework allows a market-maker to make directional bets on market trends whilst keeping under control her inventory risk. With this inventory-risk-aversion parameter, the market-maker has not only direct control on her inventory risk but she also has indirect control on the moments of her PnL distribution. Therefore, this parameter can be seen as a fine-tuning of the marker-maker's risk-reward profile. In the case of a mean-reverting mid-price, we show numerically that the inventory-risk-aversion parameter gives the market-maker enough room to tailor her risk-reward profile, depending on her risk budgets in inventory and PnL distribution (especially variance, skewness, kurtosis and VaR). For example, when compared to the martingale benchmark, a market can choose to either increase her average PNL by more than 15\% and carry a huge risk, on inventory and PNL, or either give up 5\% of her benchmark PNL to increase her control on inventory and PNL, as well as increasing her Sharpe ratio by a factor bigger than 2.

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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00675925.

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    Date of creation: 02 Mar 2012
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    Handle: RePEc:hal:wpaper:hal-00675925

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00675925
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    Related research

    Keywords: Quantitative Finance; high-frequency trading; market-making; limit-order book; inventory risk; optimisation; stochastic control; Hamilton-Jacobi-Bellman; PnL distribution;

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    1. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 324(1), pages 133-140.
    2. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, Elsevier, vol. 9(1), pages 47-73, March.
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