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Pricing Of Rainbow Options: Game Theoretic Approach

Author

Listed:
  • Z. HUCKI

    (Department of Coputing and Mathematics, Nottingham Trent University, Nottingham NG1 4BU, United Kingdom)

  • V. N. KOLOKOLTSOV

    (Department of Statistics, University of Warwick, CV4 7AL, UK;
    The Moscow Institute of Economics, Russia)

Abstract

The general approach for the pricing of rainbow (or colored) options with fixed transaction costs is developed from the game theoretic point of view. The evolution of the underlying common stocks is considered in discrete time. The main result consists in the explicit calculation of the hedge price for a variety of the rainbow options including option delivering the best ofJrisky assets and cash, calls on the maximum ofJrisky assets and the multiple-strike options. The results obtained can be also used in the framework of real options.

Suggested Citation

  • Z. Hucki & V. N. Kolokoltsov, 2007. "Pricing Of Rainbow Options: Game Theoretic Approach," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 215-242.
    • Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:02:n:s0219198907001370
    DOI: 10.1142/S0219198907001370
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    References listed on IDEAS

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    1. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Sergey Smirnov, 2019. "A Guaranteed Deterministic Approach to Superhedging—The Case of Convex Payoff Functions on Options," Mathematics, MDPI, vol. 7(12), pages 1-19, December.
    2. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    3. Wang, Lu & Zhang, Rong & Yang, Lin & Su, Yang & Ma, Feng, 2018. "Pricing geometric Asian rainbow options under fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 8-16.
    4. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.

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    More about this item

    Keywords

    Coloured (or rainbow) options; explicit formulas for hedge; transaction costs; interval model; submodular functions;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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