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Option pricing for large agents

Author

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  • Mattias Jonsson
  • Jussi Keppo

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.

Suggested Citation

  • Mattias Jonsson & Jussi Keppo, 2002. "Option pricing for large agents," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(4), pages 261-272.
    • Handle: RePEc:taf:apmtfi:v:9:y:2002:i:4:p:261-272
    DOI: 10.1080/1350486022000025471
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    References listed on IDEAS

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    1. 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.
    2. Amihud, Yakov & Mendelson, Haim & Lauterbach, Beni, 1997. "Market microstructure and securities values: Evidence from the Tel Aviv Stock Exchange," Journal of Financial Economics, Elsevier, vol. 45(3), pages 365-390, September.
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    4. 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..
    5. 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.
    6. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141.
    7. repec:dau:papers:123456789/5640 is not listed on IDEAS
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    Cited by:

    1. Suhas Nayak & George Papanicolaou, 2008. "Market Influence of Portfolio Optimizers," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(1), pages 21-40.
    2. Jungmin Choi & Mattias Jonsson, 2009. "Partial Hedging in Financial Markets with a Large Agent," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(4), pages 331-346.
    3. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    4. 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.

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