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Perfect option hedging for a large trader

Author

Listed:
  • RØdiger Frey

    (Department of Mathematics, ETH ZØrich, ETH-Zentrum, CH-8092 ZØrich, Switzerland)

Abstract

Standard derivative pricing theory is based on the assumption of agents acting as price takers on the market for the underlying asset. We relax this hypothesis and study if and how a large agent whose trades move prices can replicate the payoff of a derivative security. Our analysis extends prior work of Jarrow to economies with continuous security trading. We characterize the solution to the hedge problem in terms of a nonlinear partial differential equation and provide results on existence and uniqueness of this equation. Simulations are used to compare the hedging strategies in our model to standard Black-Scholes strategies.

Suggested Citation

  • RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    • Handle: RePEc:spr:finsto:v:2:y:1998:i:2:p:115-141
    Note: received: April 1996; final version received: April 1997
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    References listed on IDEAS

    as
    1. Grossman, Sanford J, 1988. "An Analysis of the Implications for Stock and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies," The Journal of Business, University of Chicago Press, vol. 61(3), pages 275-298, July.
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    3. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84, January.
    4. 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..
    5. Gennotte, Gerard & Leland, Hayne, 1990. "Market Liquidity, Hedging, and Crashes," American Economic Review, American Economic Association, vol. 80(5), pages 999-1021, December.
    6. 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..
    7. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    8. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374, October.
    9. Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23, January.
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    11. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, "undated". "Theory of Rational Option Pricing: II (Revised: 1-96)," Rodney L. White Center for Financial Research Working Papers 11-95, Wharton School Rodney L. White Center for Financial Research.
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    More about this item

    Keywords

    Option pricing; Black-Scholes model; hedging; large trader; feedback effects;
    All these keywords.

    JEL classification:

    • 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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