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On derivatives with illiquid underlying and market manipulation


  • Ulrich Horst
  • Felix Naujokat


In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework to construct optimal trading strategies under market impact in a multi-player framework by introducing strategic interactions into the model of Almgren [Appl. Math. Finance, 2003, 10(1), 1-18]. Specifically, we consider a financial market model with several strategically interacting players who hold European contingent claims and whose trading decisions have an impact on the price evolution of the underlying. We establish the existence and uniqueness of equilibrium results for risk-neutral and CARA investors and show that the equilibrium dynamics can be characterized in terms of a coupled system of possibly nonlinear PDEs. For the linear cost function used by Almgren, we obtain a (semi) closed-form solution. Analysing this solution, we show how market manipulation can be reduced.

Suggested Citation

  • Ulrich Horst & Felix Naujokat, 2011. "On derivatives with illiquid underlying and market manipulation," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1051-1066.
  • Handle: RePEc:taf:quantf:v:11:y:2011:i:7:p:1051-1066
    DOI: 10.1080/14697688.2011.552517

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    References listed on IDEAS

    1. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
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    Cited by:

    1. A. Sadoghi & J. Vecer, 2015. "Optimum Liquidation Problem Associated with the Poisson Cluster Process," Papers 1507.06514,, revised Dec 2015.


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