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Optimal Trading Strategies in a Limit Order Market with Imperfect Liquidity

  • Kovaleva, P.
  • Iori, G.

We study the optimal execution strategy of selling a security. In a continuous time diffusion framework, a risk-averse trader faces the choice of selling the security promptly or placing a limit order and hence delaying the transaction in order to sell at a more favorable price. We introduce a random delay parameter, which defers limit order execution and characterizes market liquidity. The distribution of expected time-to-fill of limit orders conforms to the empirically observed exponential distribution of trading times, and its variance decreases with liquidity. We obtain a closed-form solution and demonstrate that the presence of the lag factor linearizes the impact of other market parameters on the optimal limit price. Finally, two more stylized facts are rationalized in our model: the equilibrium bid-ask spread decreases with liquidity, but increases with agents risk aversion.

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Paper provided by Department of Economics, City University London in its series Working Papers with number 12/05.

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Date of creation: 2012
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Handle: RePEc:cty:dpaper:12/05
Contact details of provider: Postal: Department of Economics, Social Sciences Building, City University London, Whiskin Street, London, EC1R 0JD, United Kingdom,
Phone: +44 (0)20 7040 8500
Web page: http://www.city.ac.uk

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  1. Thierry Foucault & Ohad Kadan & Eugene Kandel, 2005. "Limit Order Book as a Market for Liquidity," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1171-1217.
  2. Hedvall, Kaj & Niemeyer, Jonas & Rosenqvist, Gunnar, 1997. "Do buyers and sellers behave similarly in a limit order book? A high-frequency data examination of the Finnish stock exchange," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 279-293, June.
  3. Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4601-4641, November.
  4. Seppi, Duane J, 1997. "Liquidity Provision with Limit Orders and a Strategic Specialist," Review of Financial Studies, Society for Financial Studies, vol. 10(1), pages 103-50.
  5. 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.
  6. Foucault, Thierry, 1999. "Order flow composition and trading costs in a dynamic limit order market1," Journal of Financial Markets, Elsevier, vol. 2(2), pages 99-134, May.
  7. Ranaldo, Angelo, 2004. "Order aggressiveness in limit order book markets," Journal of Financial Markets, Elsevier, vol. 7(1), pages 53-74, January.
  8. Burton Hollifield & Robert A. Miller & patrik Sandas, . "An Empirical Analysis of Limit Order Markets," Rodney L. White Center for Financial Research Working Papers 29-99, Wharton School Rodney L. White Center for Financial Research.
  9. 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.
  10. Alex Langnau & Yanko Punchev, 2011. "Stochastic Price Dynamics Implied By the Limit Order Book," Papers 1105.4789, arXiv.org.
  11. Ronald L. Goettler & Christine A. Parlour & Uday Rajan, 2005. "Equilibrium in a Dynamic Limit Order Market," Journal of Finance, American Finance Association, vol. 60(5), pages 2149-2192, October.
  12. Glosten, Lawrence R, 1994. " Is the Electronic Open Limit Order Book Inevitable?," Journal of Finance, American Finance Association, vol. 49(4), pages 1127-61, September.
  13. Paul Milgrom & Nancy L.Stokey, 1979. "Information, Trade, and Common Knowledge," Discussion Papers 377R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Sugato Chakravarty & Craig Holden, 2002. "An Integrated Model of Market and Limit Orders," Finance 0201004, EconWPA.
  15. Szabolcs Mike & J. Doyne Farmer, 2007. "An empirical behavioral model of liquidity and volatility," Papers 0709.0159, arXiv.org.
  16. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
  17. Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
  18. 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.
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