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Perfect option hedging for a large trader

  • RØdiger Frey

    ()

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

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    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.

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    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 2 (1998)
    Issue (Month): 2 ()
    Pages: 115-141

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    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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    1. Sanford J. Grossman, 1987. "An Analysis of the Implications for Stock and Futures Price Volatility of Program Trading and Dynamic Hedging Strategies," NBER Working Papers 2357, National Bureau of Economic Research, Inc.
    2. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374.
    3. E. Platen & M. Schweizer, 1997. "On Feedback Effects from Hedging Derivatives," SFB 373 Discussion Papers 1997,83, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, . "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.
    5. 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.
    6. Grossman, Sanford J & Zhou, Zhongquan, 1996. " Equilibrium Analysis of Portfolio Insurance," Journal of Finance, American Finance Association, vol. 51(4), pages 1379-1403, September.
    7. Gerard Gennotte and Hayne Leland., 1989. "Market Liquidity, Hedging and Crashes," Research Program in Finance Working Papers RPF-184, University of California at Berkeley.
    8. Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23.
    9. Jarrow, Robert A., 1992. "Market Manipulation, Bubbles, Corners, and Short Squeezes," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(03), pages 311-336, September.
    10. Holthausen, Robert W. & Leftwich, Richard W. & Mayers, David, 1987. "The effect of large block transactions on security prices: A cross-sectional analysis," Journal of Financial Economics, Elsevier, vol. 19(2), pages 237-267, December.
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