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The Valuation of American Passport Options: A Viscosity Solution Approach

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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.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation for Young Scientists of China (No: 11701377) and MOE (Ministry of Education in China) Project of Humanities and Social Sciences (No: 17YJCZH044). The authors would like to thank the reviewers for their very helpful comments and suggestions.

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Authors and Affiliations

  1. Shanghai Normal University, Shanghai, China

    Yang Wang & Jizhou Zhang

  2. Tongji University, Shanghai, China

    Baojun Bian

  3. York University, Toronto, Canada

    Zijiang Yang

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  1. Yang Wang
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  2. Baojun Bian
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  3. Zijiang Yang
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  4. Jizhou Zhang
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Correspondence to Yang Wang.

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Communicated by Nizar Touzi.

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Wang, Y., Bian, B., Yang, Z. et al. The Valuation of American Passport Options: A Viscosity Solution Approach. J Optim Theory Appl 180, 608–633 (2019). https://doi.org/10.1007/s10957-018-1411-5

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