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The Valuation of American Passport Options: A Viscosity Solution Approach

Author

Listed:
  • Yang Wang

    (Shanghai Normal University)

  • Baojun Bian

    (Tongji University)

  • Zijiang Yang

    (York University)

  • Jizhou Zhang

    (Shanghai Normal University)

Abstract

The passport option, introduced and marketed by Bankers Trust, is a call option on the balance of a trading account. This paper concerns the American passport option. We rigorously establish the mathematical foundation for pricing the American passport option. We derive the pricing equation, using the dynamic programming principle, and prove that the option value is a viscosity solution of variational inequality, which is a fully nonlinear equation. We also establish the comparison principle, which yields uniqueness of the viscosity solution. Moreover, we prove convexity-preserving property for the viscosity solution. In addition, we obtain further properties of the optimal exercise boundary. Finally, we give several numerical examples and financial analysis.

Suggested Citation

  • Yang Wang & Baojun Bian & Zijiang Yang & Jizhou Zhang, 2019. "The Valuation of American Passport Options: A Viscosity Solution Approach," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 608-633, February.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1411-5
    DOI: 10.1007/s10957-018-1411-5
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    References listed on IDEAS

    as
    1. Vicky Henderson & David Hobson & Glenn Kentwell, 2002. "A New Class Of Commodity Hedging Strategies: A Passport Options Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 255-278.
    2. Steven E. Shreve & Jan Vecer, 2000. "Options on a traded account: Vacation calls, vacation puts and passport options," Finance and Stochastics, Springer, vol. 4(3), pages 255-274.
    3. H. Ahn & Jeff Dewynne & P. Hua & Antony Penaud & Paul Wilmott, 2002. "The End-Of-The-Year Bonus: How To Optimally Reward A Trader?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 279-306.
    4. Yang Wang & Baojun Bian & Jizhou Zhang, 2014. "Viscosity Solutions of Integro-Differential Equations and Passport Options in a Jump-Diffusion Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 122-144, April.
    5. Vicky Henderson & David Hobson, 2001. "Passport options with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(2), pages 97-118.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Zakaria Marah, 2023. "American Passport options in an exponential L\'evy model," Papers 2307.16649, arXiv.org.

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