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Price manipulation in a market impact model with dark pool

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  • Florian Kl\"ock
  • Alexander Schied
  • Yuemeng Sun
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    Abstract

    For a market impact model, price manipulation and related notions play a role that is similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic investigation into such regularity issues when orders can be executed both at a traditional exchange and in a dark pool. To this end, we focus on a class of dark-pool models whose market impact at the exchange is described by an Almgren--Chriss model. Conditions for the absence of price manipulation for all Almgren--Chriss models include the absence of temporary cross-venue impact, the presence of full permanent cross-venue impact, and the additional penalization of orders executed in the dark pool. When a particular Almgren--Chriss model has been fixed, we show by a number of examples that the regularity of the dark-pool model hinges in a subtle way on the interplay of all model parameters and on the liquidation time constraint. The paper can also be seen as a case study for the regularity of market impact models in general.

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    File URL: http://arxiv.org/pdf/1205.4008
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1205.4008.

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    Date of creation: May 2012
    Date of revision: May 2014
    Handle: RePEc:arx:papers:1205.4008

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    Web page: http://arxiv.org/

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    1. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    2. 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.
    3. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    4. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    5. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    6. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
    7. 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.
    8. 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.
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    Cited by:
    1. Paulwin Graewe & Ulrich Horst & Eric S\'er\'e, 2013. "Smooth solutions to portfolio liquidation problems under price-sensitive market impact," Papers 1309.0474, arXiv.org, revised Dec 2013.

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