IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v180y2019i2d10.1007_s10957-018-1411-5.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1411-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-018-1411-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Josef Teichmann & Hanna Wutte, 2023. "Machine Learning-powered Pricing of the Multidimensional Passport Option," Papers 2307.14887, arXiv.org.
    3. Peter Buchen & Hamish Malloch, 2014. "CLA's, PLA's and a new method for pricing general passport options," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1201-1209, July.
    4. Anselm Hudde & Ludger Rüschendorf, 2023. "European and Asian Greeks for Exponential Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.
    5. Shih-Hsien Tseng & Tien Son Nguyen & Ruei-Ci Wang, 2021. "The Lie Algebraic Approach for Determining Pricing for Trade Account Options," Mathematics, MDPI, vol. 9(3), pages 1-9, January.
    6. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
    7. Hyungsok Ahn & Antony Penaud & Paul Wilmott, 1999. "Various passport options and their valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(4), pages 275-292.
    8. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
    9. Serguei Pergamenchtchikov & Alena Shishkova, 2020. "Hedging problems for Asian options with transactions costs," Papers 2001.01443, arXiv.org.
    10. J. N. Dewynne & N. El-Hassan, 2017. "The Valuation Of Self-Funding Instalment Warrants," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-48, June.
    11. Zakaria Marah, 2023. "American Passport options in an exponential L\'evy model," Papers 2307.16649, arXiv.org.
    12. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    13. Mahayni, Antje & Schoenmakers, John G.M., 2011. "Minimum return guarantees with fund switching rights—An optimal stopping problem," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1880-1897.
    14. Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
    15. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1411-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.