Illiquidity and derivative valuation

Arbeitspapier

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.

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• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2010,011

Classification and Topics

• Classification: Wirtschaft ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games ; Asset Pricing; Trading Volume; Bond Interest Rates ; Contingent Pricing; Futures Pricing; option pricing
• Subject: Stochastic differential games ; illiquidity ; market impact ; derivative valuation ; Optionspreistheorie ; Marktliquidität ; Wertpapierhandel ; Strategie ; Spieltheorie ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Horst, Ulrich ; Naujokat, Felix
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2010

Further information

• Handle: http://hdl.handle.net/10419/39338