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The Pricing and Hedging of Options in Finitely Elastic Markets

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  • Frey, Rüdiger
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    Abstract

    Standard derivative pricing theory is based on the assumption of the market for the underlying asset being infinitely elastic. We relax this hypothesis and study if and how a large agent whose trades move prices can replicate the payoff of a derivative contract. Our analysis extends a prior work of Jarrow who has analyzed this question in a binomial setting 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 hedge ratio in our model to standard Black-Scholes strategies. Moreover, we discuss how standard option pricing theory can be extended to finitely elastic markets.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb372.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 372.

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    Length: pages
    Date of creation: Jun 1996
    Date of revision:
    Handle: RePEc:bon:bonsfb:372

    Contact details of provider:
    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: market microstructure; feedback effects;

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    References

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    1. Sanford J. Grossman, 1989. "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. Platen, Eckhard & Martin Schweizer, 1994. "On Smile and Skewness," Discussion Paper Serie B 302, University of Bonn, Germany.
    3. Hart, Oliver D, 1977. "On the Profitability of Speculation," The Quarterly Journal of Economics, MIT Press, vol. 91(4), pages 579-97, November.
    4. Gerard Gennotte and Hayne Leland., 1989. "Market Liquidity, Hedging and Crashes," Research Program in Finance Working Papers RPF-192, University of California at Berkeley.
    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. 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.
    7. 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.
    8. Basak, Suleyman, 1995. "A General Equilibrium Model of Portfolio Insurance," Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1059-90.
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    Cited by:
    1. K. Ronnie Sircar & George Papanicolaou, 1998. "General Black-Scholes models accounting for increased market volatility from hedging strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 45-82.

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