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Optimal execution and block trade pricing: a general framework

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  • Olivier Gu\'eant
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    Abstract

    In this article, we develop a general CARA framework to study optimal execution and to price block trades. We prove existence and regularity results for optimal liquidation strategies under very general hypotheses, and we provide a hamiltonian characterization for the optimal strategy. We then 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. Numerical methods are eventually discussed.

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    File URL: http://arxiv.org/pdf/1210.6372
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    Bibliographic Info

    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: Jul 2013
    Handle: RePEc:arx:papers:1210.6372

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    Web page: http://arxiv.org/

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