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Perpetual American options in incomplete markets: the infinitely divisible case

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  • Vicky Henderson
  • David Hobson

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.

Suggested Citation

  • Vicky Henderson & David Hobson, 2008. "Perpetual American options in incomplete markets: the infinitely divisible case," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 461-469.
    • Handle: RePEc:taf:quantf:v:8:y:2008:i:5:p:461-469
    DOI: 10.1080/14697680701400986
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    References listed on IDEAS

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    1. Optimal 10b5-1 Monetization
      by quantivity in Quantivity on 2011-09-27 12:02:52

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