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Option Pricing Via Maximization Over Uncertainty And Correction Of Volatility Smile

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  • NIKOLAI DOKUCHAEV

    ()
    (Department of Mathematics & Statistics, Curtin University, GPO Box U1987, Perth, 6845, Western Australia, Australia)

Abstract

The paper presents a pricing rule for market models with stochastic volatility and with an uncertainty in its evolution law. It is shown that the most common stochastic volatility models allow a possibility that the option price calculated for random volatility with an error in volatility forecasts is lower than the price for the market with zero error of volatility forecast. To eliminate this possibility, we suggest a pricing rule based on maximization of the price via a class of possible equivalent risk-neutral measures. It shown that, in a Markovian setting, this pricing rule requires to solve a parabolic Bellman equation. Some existence results and a priory estimates are obtained for this equation.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 14 (2011)
Issue (Month): 04 ()
Pages: 507-524

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Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:04:p:507-524

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Related research

Keywords: Diffusion market model; volatility smile; stochastic volatility; uncertain volatility; Hamilton–Jacobi–Bellman equation;

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Cited by:
  1. Nikolai Dokuchaev, 2011. "On martingale measures and pricing for continuous bond-stock market with stochastic bond," Papers 1108.0719, arXiv.org, revised Apr 2014.

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