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Optimal trade execution: A mean quadratic variation approach

  • Forsyth, P.A.
  • Kennedy, J.S.
  • Tse, S.T.
  • Windcliff, H.
Registered author(s):

    We propose the use of a mean quadratic variation criteria to determine an optimal trading strategy in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) Partial Differential Equation (PDE) for the optimal strategy, assuming the underlying asset follows Geometric Brownian Motion (GBM) or Arithmetic Brownian Motion (ABM). The exact solution of the ABM formulation is in fact identical to the static (price-independent) approximate solution for the mean–variance objective function in Almgren and Chriss (2000). The optimal trading strategy in the GBM case is in general a function of the asset price. The static strategy determined in the ABM formulation turns out to be an excellent approximation for the GBM case, even when volatility is large.

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    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 36 (2012)
    Issue (Month): 12 ()
    Pages: 1971-1991

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    Handle: RePEc:eee:dyncon:v:36:y:2012:i:12:p:1971-1991
    Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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    1. 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.
    2. 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.
    3. Carl Chiarella & Giulia Iori & Josep Perello, 2007. "The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows," Papers 0711.3581, arXiv.org.
    4. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    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. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    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. Wang, J. & Forsyth, P.A., 2010. "Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 207-230, February.
    9. Nikolaus Hautsch & Ruihong Huang, 2009. "The Market Impact of a Limit Order," SFB 649 Discussion Papers SFB649DP2009-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. 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.
    11. Basak, Suleyman & Chabakauri, Georgy, 2009. "Dynamic Mean-Variance Asset Allocation," CEPR Discussion Papers 7256, C.E.P.R. Discussion Papers.
    12. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    13. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
    14. 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.
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