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Option Pricing For Incomplete Markets Via Stochastic Optimization: Transaction Costs, Adaptive Control And Forecast

Author

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  • SERGEI FEDOTOV

    (Mathematics Department, UMIST, Manchester M60 1QD, UK)

  • SERGEI MIKHAILOV

    (University of Wuppertal, D-42097 Wuppertal, Germany)

Abstract

The problem of determining the European-style option price in incomplete markets is examined within the framework of stochastic optimization. An analytic method based on the stochastic optimization is developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal feedback control) that reduces the total risk inherent in writing the option. The cases involving transaction costs, the stochastic volatility with uncertainty, stochastic adaptive process, and forecasting process are considered. A software package for the option pricing for incomplete markets is developed and the results of numerical simulations are presented.

Suggested Citation

  • Sergei Fedotov & Sergei Mikhailov, 2001. "Option Pricing For Incomplete Markets Via Stochastic Optimization: Transaction Costs, Adaptive Control And Forecast," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 179-195.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:01:n:s0219024901000912
    DOI: 10.1142/S0219024901000912
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    References listed on IDEAS

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    Cited by:

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    3. Valeriy Ryabchenko & Sergey Sarykalin & Stan Uryasev, 2004. "Pricing European Options by Numerical Replication: Quadratic Programming with Constraints," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 301-333, September.
    4. Gerasimos G. Rigatos, 2016. "Boundary Control Of The Black–Scholes Pde For Option Dynamics Stabilization," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-29, June.
    5. Yuji Yamada & James Primbs, 2004. "Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 335-365, September.
    6. Coleman, Thomas F. & Levchenkov, Dmitriy & Li, Yuying, 2007. "Discrete hedging of American-type options using local risk minimization," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3398-3419, November.

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