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Illiquidity and Derivative Valuation

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Author Info
Ulrich Horst
Felix Naujokat
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 Almgren & Chriss (2001) model. 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 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 & Chriss (2001), we obtain (semi) closed form solutions for risk neutral or CARA investors. Finally, we indicate how spread crossing costs discourage market manipulation.

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File URL: http://arxiv.org/abs/0901.0091
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0901.0091.

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Date of creation: Dec 2008
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Handle: RePEc:arx:papers:0901.0091

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  1. Aur\'elien Alfonsi & Alexander Schied & Antje Schulz, 2007. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance Papers 0708.1756, arXiv.org, revised Sep 2007. [Downloadable!]
  2. Schoeneborn, Torsten & Schied, Alexander, 2007. "Liquidation in the Face of Adversity: Stealth Vs. Sunshine Trading, Predatory Trading Vs. Liquidity Provision," MPRA Paper 5548, University Library of Munich, Germany. [Downloadable!]
  3. Schied, Alexander & Schoeneborn, Torsten, 2008. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," MPRA Paper 7105, University Library of Munich, Germany. [Downloadable!]
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  4. Joel M. Vanden, 2005. "Digital Contracts and Price Manipulation," Journal of Business, University of Chicago Press, vol. 78(5), pages 1891-1916, September. [Downloadable!]
  5. Kumar, Praveen & Seppi, Duane J, 1992. " Futures Manipulation with "Cash Settlement."," Journal of Finance, American Finance Association, vol. 47(4), pages 1485-502, September. [Downloadable!] (restricted)
  6. Jarrow, Robert A., 1994. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 241-261, June. [Downloadable!]
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