OPTION PRICING WITH FEEDBACK EFFECTS

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

International Journal of Theoretical and Applied Finance (IJTAF), 2004, vol. 07, issue 06, 757-768

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".

Keywords: Option pricing; Black–Scholes formula; feedbacks effects; volatility smile; stochastic volatility; liquidity (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1142/S0219024904002633

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