Illiquidity and derivative valuation

Ulrich Horst and Felix Naujokat

No 2010-011, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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.

Keywords: Stochastic differential games; illiquidity; market impact; derivative valuation (search for similar items in EconPapers)
JEL-codes: C73 G12 G13 (search for similar items in EconPapers)
Date: 2010
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Working Paper: Illiquidity and Derivative Valuation (2008)
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