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Illiquidity and Derivative Valuation

  • Ulrich Horst
  • Felix Naujokat

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/pdf/0901.0091
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Paper provided by arXiv.org in its series 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. Kumar, Praveen & Seppi, Duane J, 1992. " Futures Manipulation with "Cash Settlement."," Journal of Finance, American Finance Association, vol. 47(4), pages 1485-502, September.
  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.
  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.
  4. Aur\'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
  5. Michael Gallmeyer & Duane Seppi, . "Derivative Security Induced Price Manipulation," GSIA Working Papers 2000-E41, Carnegie Mellon University, Tepper School of Business.
  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.
  7. Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October.
  8. Joel M. Vanden, 2005. "Digital Contracts and Price Manipulation," The Journal of Business, University of Chicago Press, vol. 78(5), pages 1891-1916, September.
  9. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
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