The Annals of Applied Probability

The valuation of American call options on the minimum of two dividend-paying assets

Jerome Detemple, Shui Feng, and Weidong Tian

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Abstract

This paper examines the valuation of call options on the minimum of two dividend-paying assets. We show that the optimal exercise boundary consists of three components, two continuous curves and one component along the diagonal with empty interior. The option price is shown to satisfy the early exercise premium representation in which the gains from exercise involve the local time of the minimum of the two underlying asset prices. A system of recursive integral equations for the exercise boundary components is derived. Using a class of simple stopping times we also construct lower and upper bounds for the American call min-option price: these are easy to compute and can be employed to design efficient approximations of the contract value.

Article information

Source
Ann. Appl. Probab., Volume 13, Number 3 (2003), 953-983.

Dates
First available in Project Euclid: 6 August 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1060202832

Digital Object Identifier
doi:10.1214/aoap/1060202832

Mathematical Reviews number (MathSciNet)
MR1994042

Zentralblatt MATH identifier
1091.91034

Subjects
Primary: 91B28
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62L15: Optimal stopping [See also 60G40, 91A60]

Keywords
Option valuation calls American-style minimum of two assets dividends exercise premium local time lower and upper bounds numerical computation

Citation

Detemple, Jerome; Feng, Shui; Tian, Weidong. The valuation of American call options on the minimum of two dividend-paying assets. Ann. Appl. Probab. 13 (2003), no. 3, 953--983. doi:10.1214/aoap/1060202832. https://projecteuclid.org/euclid.aoap/1060202832


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