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General Intensity Shapes in Optimal Liquidation

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  • Olivier Gu\'eant
  • 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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File URL: http://arxiv.org/pdf/1204.0148
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1204.0148.

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Date of creation: Mar 2012
Date of revision: Jun 2013
Handle: RePEc:arx:papers:1204.0148

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Web page: http://arxiv.org/

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References

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  1. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
  2. Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
  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. Guéant, Olivier & Lehalle, Charles-Albert & Tapia, Joaquin Fernandez, 2011. "Optimal Portfolio Liquidation with Limit Orders," Economics Papers from University Paris Dauphine 123456789/7391, Paris Dauphine University.
  5. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
  6. 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.
  7. 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.
  8. 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.
  9. Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag\`es, 2009. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Papers 0910.1166, arXiv.org, revised May 2010.
  10. 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.
  11. 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.
  12. Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
  13. Schied, Alexander & Schöneborn, Torsten, 2007. "Optimal Portfolio Liquidation for CARA Investors," MPRA Paper 5075, University Library of Munich, Germany.
  14. Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag\`es, 2011. "Optimal posting price of limit orders: learning by trading," Papers 1112.2397, arXiv.org, revised Sep 2012.
  15. Gur Huberman & Werner Stanzl, 2000. "Optimal Liquidity Trading," Yale School of Management Working Papers ysm165, Yale School of Management, revised 01 Aug 2001.
  16. Fabien Guilbaud & Mohamed Mnif & Huy\^en Pham, 2010. "Numerical methods for an optimal order execution problem," Papers 1006.0768, arXiv.org.
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Cited by:
  1. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Papers 1210.1625, arXiv.org, revised Jul 2013.
  2. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Working Papers hal-00737491, HAL.

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