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Optimal trade execution under price-sensitive risk preferences

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  • Stefan Ankirchner
  • Thomas Kruse

Abstract

We consider the problem of how to close a large asset position in an illiquid market in such a way that very high liquidation costs are unlikely. To this end we introduce a discrete-time model that provides a simple device for designing and controlling the distribution of the revenues/costs from unwinding the position. By appealing to dynamic programming we derive semi-explicit formulas for the optimal execution strategies. We then present a numerical algorithm for approximating optimal execution rates as functions of the price. We provide error bounds and prove convergence. Finally, examples for the liquidation of forward positions in illiquid energy markets illustrate the efficiency of the algorithm.

Suggested Citation

  • Stefan Ankirchner & Thomas Kruse, 2013. "Optimal trade execution under price-sensitive risk preferences," Quantitative Finance, Taylor & Francis Journals, vol. 13(9), pages 1395-1409, September.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:9:p:1395-1409
    DOI: 10.1080/14697688.2012.762613
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    References listed on IDEAS

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    1. Sebastian Ebert & Daniel Wiesen, 2011. "Testing for Prudence and Skewness Seeking," Management Science, INFORMS, vol. 57(7), pages 1334-1349, July.
    2. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
    3. Christoph Weber & Oliver Woll, 2007. "Portfolio Optimization In Electricity Trading With Limited Liquidity," EWL Working Papers 0702, University of Duisburg-Essen, Chair for Management Science and Energy Economics, revised Jul 2007.
    4. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
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    Citations

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    Cited by:

    1. Ash Booth & Enrico Gerding & Frank McGroarty, 2015. "Performance-weighted ensembles of random forests for predicting price impact," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1823-1835, November.
    2. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," Papers 1503.07007, arXiv.org, revised Sep 2015.
    3. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CARF F-Series CARF-F-360, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2015.
    4. Masaaki Fujii, 2015. "Optimal Position Management for a Market Maker with Stochastic Price Impacts," CIRJE F-Series CIRJE-F-963, CIRJE, Faculty of Economics, University of Tokyo.
    5. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.

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