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

Author

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  • Pietro Fodra
  • Mauricio Labadie

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.

Suggested Citation

  • Pietro Fodra & Mauricio Labadie, 2012. "High-frequency market-making with inventory constraints and directional bets," Papers 1206.4810, arXiv.org.
  • Handle: RePEc:arx:papers:1206.4810
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    File URL: http://arxiv.org/pdf/1206.4810
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    References listed on IDEAS

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    1. Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Working Papers hal-00603385, HAL.
    2. Stoll, Hans R, 1978. "The Supply of Dealer Services in Securities Markets," Journal of Finance, American Finance Association, vol. 33(4), pages 1133-1151, September.
    3. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    4. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    5. Fabien Guilbaud & Huyen Pham, 2011. "Optimal High Frequency Trading with limit and market orders," Papers 1106.5040, arXiv.org.
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    Cited by:

    1. Marc Hoffmann & Mauricio Labadie & Charles-Albert Lehalle & Gilles Pagès & Huyên Pham & Mathieu Rosenbaum, 2013. "Optimization And Statistical Methods For High Frequency Finance," Post-Print hal-01102785, HAL.
    2. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.

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