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General Intensity Shapes In Optimal Liquidation

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  • Olivier Guéant
  • Charles-Albert Lehalle

Abstract

The classical literature on optimal liquidation, rooted in Almgren-Chriss models, tackles the optimal liquidation problem using a trade-off between market impact and price risk. Therefore, it only answers the general question of the optimal liquidation rhythm. The very question of the actual way to proceed with liquidation is then rarely dealt with. Our model, that incorporates both price risk and non-execution risk, is an attempt to tackle this question using limit orders. The very general framework we propose to model liquidation generalizes the existing literature on optimal posting of limit orders. We consider a risk-adverse agent whereas the model of Bayraktar and Ludkovski only tackles the case of a risk-neutral one. We consider very general functional forms for the execution process intensity, whereas Gu\'eant et al. is restricted to exponential intensity. Eventually, we link the execution cost function of Almgren-Chriss models to the intensity function in our model, providing then a way to see Almgren-Chriss models as a limit of ours.
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Suggested Citation

  • Olivier Guéant & Charles-Albert Lehalle, 2015. "General Intensity Shapes In Optimal Liquidation," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 457-495, July.
  • Handle: RePEc:bla:mathfi:v:25:y:2015:i:3:p:457-495
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    File URL: http://hdl.handle.net/10.1111/mafi.2015.25.issue-3
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    References listed on IDEAS

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    1. Erhan Bayraktar & Michael Ludkovski, 2014. "Liquidation In Limit Order Books With Controlled Intensity," Mathematical Finance, Wiley Blackwell, vol. 24(4), pages 627-650, October.
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    11. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
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    Citations

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    Cited by:

    1. Pierre Cardaliaguet & Charles-Albert Lehalle, 2016. "Mean Field Game of Controls and An Application To Trade Crowding," Papers 1610.09904, arXiv.org, revised Sep 2017.
    2. Alvaro Cartea & Luhui Gan & Sebastian Jaimungal, 2018. "Trading Cointegrated Assets with Price Impact," Papers 1807.01428, arXiv.org.
    3. Philippe Bergault & Olivier Gu'eant, 2019. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Papers 1907.01225, arXiv.org, revised Jul 2020.
    4. 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 2020.
    5. Bastien Baldacci & Philippe Bergault & Olivier Gu'eant, 2019. "Algorithmic market making for options," Papers 1907.12433, arXiv.org, revised Jul 2020.
    6. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Papers 1210.1625, arXiv.org, revised Nov 2014.
    7. 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.
    8. Rossella Agliardi & Ramazan Gençay, 2017. "Optimal Trading Strategies With Limit Orders," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-16, February.
    9. Jean-David Fermanian & Olivier Gu'eant & Jiang Pu, 2015. "The behavior of dealers and clients on the European corporate bond market: the case of Multi-Dealer-to-Client platforms," Papers 1511.07773, arXiv.org, revised Mar 2017.
    10. Jean-David Fermanian & Olivier Guéant & Arnaud Rachez, 2015. "Agents' Behavior on Multi-Dealer-to-Client Bond Trading Platforms," Working Papers 2015-11, Center for Research in Economics and Statistics.
    11. Brian Ning & Franco Ho Ting Lin & Sebastian Jaimungal, 2018. "Double Deep Q-Learning for Optimal Execution," Papers 1812.06600, arXiv.org, revised Jun 2020.
    12. Álvaro Cartea & Sebastian Jaimungal & Damir Kinzebulatov, 2016. "Algorithmic Trading With Learning," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-30, June.
    13. Philippe Bergault & Olivier Guéant, 2020. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Working Papers hal-02987894, HAL.
    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. Etienne Chevalier & Vathana Ly Vath & Simone Scotti & Alexandre Roch, 2016. "Optimal Execution Cost For Liquidation Through A Limit Order Market," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-26, February.
    17. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    18. Xiaofei Lu & Fr'ed'eric Abergel, 2018. "Order-book modelling and market making strategies," Papers 1806.05101, arXiv.org.
    19. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
    20. Roman Gayduk & Sergey Nadtochiy, 2016. "Endogenous Formation of Limit Order Books: Dynamics Between Trades," Papers 1605.09720, arXiv.org, revised Jun 2017.
    21. Philippe Bergault & Olivier Guéant, 2020. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02987894, HAL.
    22. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Working Papers hal-00737491, HAL.
    23. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.

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