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Illiquidity and Derivative Valuation

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  • 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 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.

Suggested Citation

  • Ulrich Horst & Felix Naujokat, 2010. "Illiquidity and Derivative Valuation," SFB 649 Discussion Papers SFB649DP2010-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2010-011
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    References listed on IDEAS

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    1. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    2. Michael Gallmeyer & Duane Seppi, "undated". "Derivative Security Induced Price Manipulation," GSIA Working Papers 2000-E41, Carnegie Mellon University, Tepper School of Business.
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    5. Robert A. Jarrow, 2008. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 7, pages 131-151 World Scientific Publishing Co. Pte. Ltd..
    6. 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.
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    Cited by:

    1. Nicole Wiebach & Lutz Hildebrandt, 2010. "Context Effects as Customer Reaction on Delisting of Brands," SFB 649 Discussion Papers SFB649DP2010-056, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Ulrich Horst & Santiago Moreno-Bromberg, 2010. "Efficiency and Equilibria in Games of Optimal Derivative Design," SFB 649 Discussion Papers SFB649DP2010-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    5. Enno Mammen & Christoph Rothe & Melanie Schienle, 2010. "Nonparametric Regression with Nonparametrically Generated Covariates," SFB 649 Discussion Papers SFB649DP2010-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, pages 89-121.
    7. Ralf Sabiwalsky, 2010. "Executive Compensation Regulation and the Dynamics of the Pay-Performance Sensitivity," SFB 649 Discussion Papers SFB649DP2010-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Wolfgang Karl Härdle & Rouslan Moro & Linda Hoffmann, 2010. "Learning Machines Supporting Bankruptcy Prediction," SFB 649 Discussion Papers SFB649DP2010-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, pages 749-754.
    10. Carolin Hecht & Katja Hanewald, 2010. "Sociodemographic, Economic, and Psychological Drivers of the Demand for Life Insurance: Evidence from the German Retirement Income Act," SFB 649 Discussion Papers SFB649DP2010-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Franziska Schulze, 2010. "Spatial Dependencies in German Matching Functions," SFB 649 Discussion Papers SFB649DP2010-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Alexander L. Baranovski, 2010. "Dynamical systems forced by shot noise as a new paradigm in the interest rate modeling," SFB 649 Discussion Papers SFB649DP2010-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Vladimir Panov, 2010. "Estimation of the signal subspace without estimation of the inverse covariance matrix," SFB 649 Discussion Papers SFB649DP2010-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Kraft, Holger & Kühn, Christoph, 2011. "Large traders and illiquid options: Hedging vs. manipulation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1898-1915.
    15. Maria Grith & Volker Krätschmer, 2010. "Parametric estimation of risk neutral density functions," SFB 649 Discussion Papers SFB649DP2010-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Stochastic differential games; illiquidity; market impact; derivative valuation;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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