IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v35y2011i11p1898-1915.html
   My bibliography  Save this article

Large traders and illiquid options: Hedging vs. manipulation

Author

Listed:
  • Kraft, Holger
  • Kühn, Christoph

Abstract

In this article, we study the effects on derivative pricing arising from price impacts by large traders. When a large trader issues a derivative and (partially) hedges his risk by trading in the underlying, he influences both his hedge portfolio and the derivative's payoff. In a Black–Scholes model with a price impact on the drift, we analyze the resulting trade-off by explicitly solving the utility maximization problem of a large investor endowed with an illiquid contingent claim. We find several interesting phenomena which cannot occur in frictionless markets. First, the indifference price is a convex function of the contingent claim – and not concave as in frictionless markets – implying that for any claim the buyer's indifference price is larger than the seller's indifference price. Second, the seller's indifference prices of large positions in derivatives are smaller than the Black–Scholes replication costs. Therefore, a large trader might have an incentive to issue options if they are traded at Black–Scholes prices. Furthermore, he hedges option positions only partly if he has a negative price impact and thus exploits his ability to manipulate the option's payoff. For a positive price impact he overhedges the option position leading to an extra profit from the stock position exceeding a perfect hedge. Finally, we also study a model where the large shareholder has a price impact on both drift and volatility.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:35:y:2011:i:11:p:1898-1915
    DOI: 10.1016/j.jedc.2011.06.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188911001060
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Umut Çetin & L. C. G. Rogers, 2007. "Modeling Liquidity Effects In Discrete Time," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 15-29.
    2. Ting, Christopher & Warachka, Mitch & Zhao, Yonggan, 2007. "Optimal liquidation strategies and their implications," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1431-1450, April.
    3. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18.
    4. Clifford G. Holderness, 2003. "A survey of blockholders and corporate control," Economic Policy Review, Federal Reserve Bank of New York, issue Apr, pages 51-64.
    5. Peter M. DeMarzo & Branko Uro, 2006. "Ownership Dynamics and Asset Pricing with a Large Shareholder," Journal of Political Economy, University of Chicago Press, vol. 114(4), pages 774-815, August.
    6. Suleyman Basak, 1997. "Consumption choice and asset pricing with a non-price-taking agent," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 437-462.
    7. Robert A. Jarrow, 2008. "Market Manipulation, Bubbles, Corners, and Short Squeezes," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 6, pages 105-130 World Scientific Publishing Co. Pte. Ltd..
    8. Henrik Cronqvist & Rüdiger Fahlenbrach, 2009. "Large Shareholders and Corporate Policies," Review of Financial Studies, Society for Financial Studies, vol. 22(10), pages 3941-3976, October.
    9. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183 World Scientific Publishing Co. Pte. Ltd..
    10. Isaenko, Sergei, 2010. "Portfolio choice under transitory price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2375-2389, November.
    11. Cuoco, Domenico & Cvitanic, Jaksa, 1998. "Optimal consumption choices for a 'large' investor," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 401-436, March.
    12. 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..
    13. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373.
    14. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    15. He, Hua & Mamaysky, Harry, 2005. "Dynamic trading policies with price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 891-930, May.
    16. Ulrich Horst & Felix Naujokat, 2008. "Illiquidity and Derivative Valuation," Papers 0901.0091, arXiv.org.
    17. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Suhan Altay & Katia Colaneri & Zehra Eksi, 2017. "Portfolio optimization for a large investor controlling market sentiment under partial information," Papers 1706.03567, arXiv.org.
    2. repec:spr:mathme:v:86:y:2017:i:3:d:10.1007_s00186-017-0589-x is not listed on IDEAS

    More about this item

    Keywords

    Price impact; Illiquidity; Option pricing; Portfolio choice; Manipulation;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:35:y:2011:i:11:p:1898-1915. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jedc .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.