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

Author

Listed:
  • Pietro Fodra

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Mauricio Labadie

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

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.

Suggested Citation

  • Pietro Fodra & Mauricio Labadie, 2012. "High-frequency market-making with inventory constraints and directional bets," Working Papers hal-00675925, HAL.
  • Handle: RePEc:hal:wpaper:hal-00675925
    Note: View the original document on HAL open archive server: https://hal.science/hal-00675925v5
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    References listed on IDEAS

    as
    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. repec:dau:papers:123456789/7390 is not listed on IDEAS
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Campi, Luciano & Zabaljauregui, Diego, 2020. "Optimal market making under partial information with general intensities," LSE Research Online Documents on Economics 104612, London School of Economics and Political Science, LSE Library.
    2. Pietro Fodra & Huy^en Pham, 2013. "High frequency trading and asymptotics for small risk aversion in a Markov renewal model," Papers 1310.1756, arXiv.org, revised Jan 2015.
    3. Qing-Qing Yang & Wai-Ki Ching & Jiawen Gu & Tak-Kuen Siu, 2020. "Trading strategy with stochastic volatility in a limit order book market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 277-301, June.
    4. Thomas Spooner & Rahul Savani, 2020. "Robust Market Making via Adversarial Reinforcement Learning," Papers 2003.01820, arXiv.org, revised Jul 2020.
    5. Sofiene El Aoud & Frédéric Abergel, 2015. "A stochastic control approach for options market making," Post-Print hal-01061852, HAL.
    6. Pietro Fodra & Huyen Pham, 2013. "High frequency trading in a Markov renewal model," Working Papers hal-00867113, HAL.
    7. L. Ingber, 2020. "Forecasting with importance-sampling and path-integrals: Applications to COVID-19," Lester Ingber Papers 20fi, Lester Ingber.
    8. Lester Ingber, 2020. "Developing Bid-Ask Probabilities for High-Frequency Trading," Virtual Economics, The London Academy of Science and Business, vol. 3(2), pages 7-24, April.
    9. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    10. Burcu Aydoğan & Ömür Uğur & Ümit Aksoy, 2023. "Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 289-324, June.
    11. Philippe Bergault & David Evangelista & Olivier Gu'eant & Douglas Vieira, 2018. "Closed-form approximations in multi-asset market making," Papers 1810.04383, arXiv.org, revised Sep 2022.
    12. Baron Law & Frederi Viens, 2019. "Market Making under a Weakly Consistent Limit Order Book Model," Papers 1903.07222, arXiv.org, revised Jan 2020.
    13. Saran Ahuja & George Papanicolaou & Weiluo Ren & Tzu-Wei Yang, 2016. "Limit order trading with a mean reverting reference price," Papers 1607.00454, arXiv.org, revised Nov 2016.
    14. Diego Zabaljauregui, 2020. "Optimal market making under partial information and numerical methods for impulse control games with applications," Papers 2009.06521, arXiv.org.
    15. Diego Zabaljauregui & Luciano Campi, 2019. "Optimal market making under partial information with general intensities," Papers 1902.01157, arXiv.org, revised Apr 2020.
    16. Pietro Fodra & Mauricio Labadie, 2013. "High-frequency market-making for multi-dimensional Markov processes," Papers 1303.7177, arXiv.org, revised Apr 2013.
    17. 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.

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    More about this item

    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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