The Valuation of American Passport Options: A Viscosity Solution Approach

Yang Wang (), Baojun Bian (), Zijiang Yang () and Jizhou Zhang ()
Additional contact information
Yang Wang: Shanghai Normal University
Baojun Bian: Tongji University
Zijiang Yang: York University
Jizhou Zhang: Shanghai Normal University

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 2, No 13, 608-633

Abstract: 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.

Keywords: American passport option; Viscosity solution; Uniqueness; Convexity-preserving property; Optimal exercise boundary; 91B02; 35B05; 49L25 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1411-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:180:y:2019:i:2:d:10.1007_s10957-018-1411-5

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-1411-5

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().