Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/39338
Authors: 
Horst, Ulrich
Naujokat, Felix
Year of Publication: 
2010
Series/Report no.: 
SFB 649 discussion paper 2010,011
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.
Subjects: 
Stochastic differential games
illiquidity
market impact
derivative valuation
JEL: 
C73
G12
G13
Document Type: 
Working Paper

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