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Optimal execution and block trade pricing: a general framework

  • Olivier Gu\'eant
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    In this article, we develop a general framework to study optimal execution and to price block trades. We prove existence of optimal liquidation strategies and we provide regularity results for optimal strategies under very general hypotheses. We exhibit a Hamiltonian characterization for the optimal strategy that can be used for numerical approximation. We also focus on the important topic of block trade pricing and we propose a methodology to give a price to financial (il)liquidity. In particular, we provide a closed-form formula for the price of a block trade when there is no time constraint to liquidate.

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    File URL: http://arxiv.org/pdf/1210.6372
    File Function: Latest version
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    Paper provided by arXiv.org in its series Papers with number 1210.6372.

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    Date of creation: Oct 2012
    Date of revision: Dec 2014
    Handle: RePEc:arx:papers:1210.6372
    Contact details of provider: Web page: http://arxiv.org/

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    1. Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    2. 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.
    3. Erhan Bayraktar & Michael Ludkovski, 2011. "Liquidation in Limit Order Books with Controlled Intensity," Papers 1105.0247, arXiv.org, revised Jan 2012.
    4. Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
    5. 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.
    6. Peter Kratz & Torsten Sch\"oneborn, 2012. "Portfolio liquidation in dark pools in continuous time," Papers 1201.6130, arXiv.org, revised Aug 2012.
    7. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    8. 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.
    9. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
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