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On the optimal exercise boundary for an American put option. (English) Zbl 0976.91029

Summary: An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the free boundary close to expiry. Working directly with the underlying partial differential equation, by using asymptotic expansions, we are able to deduce this behavior of the boundary in this limit.

MSC:

91B28 Finance etc. (MSC2000)
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