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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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

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

First available in Project Euclid: 6 August 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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