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An Optimal Execution Problem with a Geometric Ornstein-Uhlenbeck Price Process

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  • Takashi Kato
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    Abstract

    We study an optimal execution problem in the presence of market impact where the security price follows a geometric Ornstein-Uhlenbeck process, which implies the mean-reverting property, and show that the optimal strategy is a mixture of initial/terminal block liquidation and gradual intermediate liquidation. The mean-reverting property describes a price recovery effect that is strongly related to the resilience of market impact, as described in several papers that have studied optimal execution in a limit order book (LOB) model. It is interesting that despite the fact that the model in this paper is different from the LOB model, the form of our optimal strategy is quite similar to those obtained for an LOB model. Moreover, we discuss what properties cause gradual liquidation as an optimal strategy by studying various cases and find out that not only "convexity of market impact function" but also "price recovery effect" (or, in other words, transience of market impact) are essential to make a trader execute the security gradually to mitigate the effect of market impact.

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    File URL: http://arxiv.org/pdf/1107.1787
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    Paper provided by arXiv.org in its series Papers with number 1107.1787.

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    Date of creation: Jul 2011
    Date of revision: Jul 2014
    Handle: RePEc:arx:papers:1107.1787
    Contact details of provider: Web page: http://arxiv.org/

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    This paper has been announced in the following NEP Reports:

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    1. Gur Huberman & Werner Stanzl, 2005. "Optimal Liquidity Trading," Review of Finance, Springer, vol. 9(2), pages 165-200, 06.
    2. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    3. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    4. repec:hal:wpaper:hal-00397652 is not listed on IDEAS
    5. Aur\'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    6. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    7. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    8. Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474.
    9. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
    10. Hua He & Harry Mamaysky, 2001. "Dynamic Trading Policies With Price Impact," Yale School of Management Working Papers ysm244, Yale School of Management, revised 01 Jan 2002.
    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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    Cited by:

    1. Kensuke Ishitani & Takashi Kato, 2015. "Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact," Papers 1506.02789, arXiv.org, revised Aug 2015.
    2. Masashi Ieda, 2015. "A dynamic optimal execution strategy under stochastic price recovery," Papers 1502.04521, arXiv.org.
    3. Takashi Kato, 2014. "VWAP Execution as an Optimal Strategy," Papers 1408.6118, arXiv.org, revised Feb 2015.

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