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

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  • Pietro Fodra
  • Mauricio Labadie
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    Abstract

    In this paper 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. In order to achieve this, the marker-maker places non-symmetric limit orders that favour market orders to hit her bid (resp. ask) quotes if she expects that prices will go up (resp. down). 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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    File URL: http://arxiv.org/pdf/1206.4810
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1206.4810.

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    Date of creation: Jun 2012
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    Handle: RePEc:arx:papers:1206.4810

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    1. Thomas Ho & Hans Stoll, . "Optimal Dealer Pricing Under Transactions and Return Uncertainty," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 27-79, Wharton School Rodney L. White Center for Financial Research.
    2. Stoll, Hans R, 1978. "The Supply of Dealer Services in Securities Markets," Journal of Finance, American Finance Association, American Finance Association, vol. 33(4), pages 1133-51, September.
    3. 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.
    4. Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Working Papers hal-00603385, HAL.
    5. Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Papers 1106.5040, arXiv.org.
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