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Optimal liquidation in a Level-I limit order book for large tick stocks

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  • Antoine Jacquier
  • Hao Liu

Abstract

We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to independent Poisson processes, with parameters depending on price move directions. Our goal is to maximise the expected terminal wealth of an agent who needs to liquidate her positions within a fixed time horizon. Assuming that the agent trades (through sell limit order or/and sell market order) only when the price moves, we model her liquidation procedure as a semi-Markov decision process, and compute the semi-Markov kernel using Laplace method in the language of queueing theory. The optimal liquidation policy is then solved by dynamic programming, and illustrated numerically.

Suggested Citation

  • Antoine Jacquier & Hao Liu, 2017. "Optimal liquidation in a Level-I limit order book for large tick stocks," Papers 1701.01327, arXiv.org, revised Nov 2017.
    • Handle: RePEc:arx:papers:1701.01327
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    References listed on IDEAS

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    Cited by:

    1. Frédéric Abergel & Côme Huré & Huyên Pham, 2019. "Algorithmic trading in a microstructural limit order book model," Working Papers hal-01514987, HAL.
    2. Fr'ed'eric Abergel & C^ome Hur'e & Huy^en Pham, 2017. "Algorithmic trading in a microstructural limit order book model," Papers 1705.01446, arXiv.org, revised Feb 2020.
    3. Hyoeun Lee & Kiseop Lee, 2020. "Optimal execution with liquidity risk in a diffusive order book market," Papers 2004.10951, arXiv.org.
    4. Jos'e E. Figueroa-L'opez & Hyoeun Lee & Raghu Pasupathy, 2017. "Optimal placement of a small order in a diffusive limit order book," Papers 1708.04337, arXiv.org.
    5. Federico Gonzalez & Mark Schervish, 2017. "Instantaneous order impact and high-frequency strategy optimization in limit order books," Papers 1707.01167, arXiv.org, revised Oct 2017.

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