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Option Pricing With Feedback Effects

Author

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  • ALEXANDER LYUKOV

    (Computational and Applied Mathematics, University of Texas at Austin, 1 Texas Longhorns, #C0200, Austin, TX 78712, USA)

Abstract

The paper provides a continuous time model for order-driven stock market. The model allows to derive a nonlinear PDE as a modification of Black–Scholes equation for option pricing with a local volatility as a function of the stock price. The solution can be expanded in series in the parameter, which relates to the size of option market. The first-order correction for the option price increases the price of a European call. The second-order correction for volatility allows to describe the "volatility smile".

Suggested Citation

  • Alexander Lyukov, 2004. "Option Pricing With Feedback Effects," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(06), pages 757-768.
    • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:06:n:s0219024904002633
    DOI: 10.1142/S0219024904002633
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    References listed on IDEAS

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    1. Eckhard Platen & Martin Schweizer, 1998. "On Feedback Effects from Hedging Derivatives," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 67-84, January.
    2. William J. Breen & Laurie Simon Hodrick & Robert A. Korajczyk, 2002. "Predicting Equity Liquidity," Management Science, INFORMS, vol. 48(4), pages 470-483, April.
    3. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
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    Cited by:

    1. Kristoffer Glover & Peter W Duck & David P Newton, 2010. "On nonlinear models of markets with finite liquidity: Some cautionary notes," Published Paper Series 2010-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.

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