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The valuation of American call options on the minimum of two dividend-paying assets. (English) Zbl 1091.91034

Summary: 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.

MSC:

91B28 Finance etc. (MSC2000)
60G40 Stopping times; optimal stopping problems; gambling theory
62L15 Optimal stopping in statistics
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