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Illiquidity and derivative valuation

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  • Horst, Ulrich
  • Naujokat, Felix

Abstract

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 within which to value derivatives under market impact in a multi-player framework by introducing strategic interactions into the model of Almgren and Chriss (2001). Specifically, we consider a financial market model with several strategically interacting players that hold European contingent claims and whose trading decisions have an impact on the price evolution of the underlying. We establish 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 non-linear PDEs. For the linear cost function used in Almgren and Chriss (2001), we obtain a (semi) closed form solution. Analyzing this solution, we show how market manipulation can be reduced.

Suggested Citation

  • Horst, Ulrich & Naujokat, Felix, 2010. "Illiquidity and derivative valuation," SFB 649 Discussion Papers 2010-011, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2010-011
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    More about this item

    Keywords

    Stochastic differential games; illiquidity; market impact; derivative valuation;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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