Perpetual American options in incomplete markets: the infinitely divisible case

Vicky Henderson and David Hobson

Quantitative Finance, 2008, vol. 8, issue 5, 461-469

Abstract: We consider the exercise of a number of American options in an incomplete market. In this paper we are interested in the case where the options are infinitely divisible. We make the simplifying assumptions that the options have infinite maturity, and the holder has exponential utility. Our contribution is to solve this problem explicitly and we show that, except at the initial time when it may be advantageous to exercise a positive fraction of his holdings, it is never optimal for the holder to exercise a tranche of options. Instead, the process of option exercises is continuous; however, it is singular with respect to calendar time. Exercise takes place when the stock price reaches a convex boundary which we identify.

Keywords: Perpetual American options; Incomplete markets; Infinitely divisible (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1080/14697680701400986

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