Journal of Optimization Theory and Applications

, Volume 180, Issue 2, pp 608–633 | Cite as

The Valuation of American Passport Options: A Viscosity Solution Approach

  • Yang WangEmail author
  • Baojun Bian
  • Zijiang Yang
  • Jizhou Zhang


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.


American passport option Viscosity solution Uniqueness Convexity-preserving property Optimal exercise boundary 

Mathematics Subject Classification

91B02 35B05 49L25 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shanghai Normal UniversityShanghaiChina
  2. 2.Tongji UniversityShanghaiChina
  3. 3.York UniversityTorontoCanada

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