An Optimal Execution Problem with a Geometric Ornstein-Uhlenbeck Price Process
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.
References listed on IDEAS
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- 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.
- Alexander Schied & Torsten Schöneborn, 2009.
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- Schied, Alexander & Schoeneborn, Torsten, 2008. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," MPRA Paper 7105, University Library of Munich, Germany.
- Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
- Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
- 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.
- Ajay Subramanian & Robert A. Jarrow, 2001. "The Liquidity Discount," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 447-474.
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- Gur Huberman & Werner Stanzl, 2000. "Optimal Liquidity Trading," Yale School of Management Working Papers ysm165, Yale School of Management, revised 01 Aug 2001.
- He, Hua & Mamaysky, Harry, 2005. "Dynamic trading policies with price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 891-930, May.
- 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.
- repec:hal:wpaper:hal-00397652 is not listed on IDEAS
- Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
- Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
- Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759. Full references (including those not matched with items on IDEAS)
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