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Optimal Execution with Dynamic Order Flow Imbalance

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  • Kyle Bechler
  • Mike Ludkovski

Abstract

We examine optimal execution models that take into account both market microstructure impact and informational costs. Informational footprint is related to order flow and is represented by the trader's influence on the flow imbalance process, while microstructure influence is captured by instantaneous price impact. We propose a continuous-time stochastic control problem that balances between these two costs. Incorporating order flow imbalance leads to the consideration of the current market state and specifically whether one's orders lean with or against the prevailing order flow, key components often ignored by execution models in the literature. In particular, to react to changing order flow, we endogenize the trading horizon $T$. After developing the general indefinite-horizon formulation, we investigate several tractable approximations that sequentially optimize over price impact and over $T$. These approximations, especially a dynamic version based on receding horizon control, are shown to be very accurate and connect to the prevailing Almgren-Chriss framework. We also discuss features of empirical order flow and links between our model and "Optimal Execution Horizon" by Easley et al (Mathematical Finance, 2013).

Suggested Citation

  • Kyle Bechler & Mike Ludkovski, 2014. "Optimal Execution with Dynamic Order Flow Imbalance," Papers 1409.2618, arXiv.org, revised Oct 2014.
    • Handle: RePEc:arx:papers:1409.2618
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    References listed on IDEAS

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    1. Alfonsi Aurélien & Alexander Schied & Alla Slynko, 2012. "Order Book Resilience, Price Manipulation, and the Positive Portfolio Problem," Post-Print hal-00941333, HAL.
    2. Fabien Guilbaud & Huyên Pham, 2013. "Optimal high-frequency trading with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 79-94, January.
    3. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    4. Rama Cont & Arseniy Kukanov & Sasha Stoikov, 2013. "The Price Impact of Order Book Events," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 47-88, December.
    5. Rene Carmona & Kevin Webster, 2013. "The Self-Financing Equation in High Frequency Markets," Papers 1312.2302, arXiv.org.
    6. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    7. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    8. Easley, David & López de Prado, Marcos M. & O'Hara, Maureen, 2014. "VPIN and the Flash Crash: A rejoinder," Journal of Financial Markets, Elsevier, vol. 17(C), pages 47-52.
    9. David A. Harville, 2014. "Rejoinder," The American Statistician, Taylor & Francis Journals, vol. 68(2), pages 89-92, May.
    10. David Easley & Marcos M. López de Prado & Maureen O'Hara, 2012. "Flow Toxicity and Liquidity in a High-frequency World," The Review of Financial Studies, Society for Financial Studies, vol. 25(5), pages 1457-1493.
    11. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
    12. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    13. Erhan Bayraktar & Mike Ludkovski, 2009. "Optimal Trade Execution in Illiquid Markets," Papers 0902.2516, arXiv.org.
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    Cited by:

    1. Phillip Monin, 2014. "Hedging Market Risk in Optimal Liquidation," Working Papers 14-08, Office of Financial Research, US Department of the Treasury.
    2. 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.

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