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Option pricing for large agents

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  • Mattias Jonsson
  • Jussi Keppo
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    Abstract

    This paper considers arbitrage-free option pricing in the presence of large agents. These large agents have a significant market power, and their trading strategies influence the dynamics of the financial asset prices. First, a simple asset pricing model in the presence of large agents is presented. Then a nonlinear partial differential equation is found for the prices of European options in the model. The unit option price depends on the large agent's asset holdings. Finally, a game model is introduced for the interaction between different market players. In this game, the outstanding number of options, as well as the option price, is found as a Nash equilibrium.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 9 (2002)
    Issue (Month): 4 ()
    Pages: 261-272

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    Handle: RePEc:taf:apmtfi:v:9:y:2002:i:4:p:261-272

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    1. Jouini, Elyès & Kallal, Hedi, 1993. "General equilibrium with producers and brokers existence and regularity," Economics Papers from University Paris Dauphine 123456789/5640, Paris Dauphine University.
    2. 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.
    3. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    4. Jouini, Elyes & Kallal, Hedi, 1993. "General equilibrium with producers and brokers : Existence and regularity," Economics Letters, Elsevier, vol. 41(3), pages 257-263.
    5. Platen, Eckhard & Martin Schweizer, 1994. "On Smile and Skewness," Discussion Paper Serie B 302, University of Bonn, Germany.
    6. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
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    Cited by:
    1. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    2. Suhas Nayak, 2007. "An Equilibrium-Based Model Of Stock-Pinning," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(03), pages 535-555.
    3. Suhas Nayak & George Papanicolaou, 2008. "Market Influence of Portfolio Optimizers," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(1), pages 21-40.

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