American option valuation using first-passage densities

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7 Citations (Scopus)


This paper explores the advantages of pricing American options using the first-passage density of a Brownian motion to a curved barrier. First, we demonstrate that, under this approach, the exact computation of the optimal boundary becomes secondary. Consequently, a simple approximation to the optimal boundary suffices to obtain accurate prices. Moreover, the first-passage approach tends to give more accurate prices than the early-exercise-premium integral representation. We present two ways of implementing the approach. The first is based on an exact representation of the first-passage density. The second exploits the method of images, which gives us a family of barriers with first-passage densities given in closed form. Both methods are very easy to implement and give accurate prices. In particular, the images-based method is extremely accurate. © 2013 Taylor & Francis.
Original languageEnglish
Pages (from-to)1831-1843
JournalQuantitative Finance
Issue number11
Publication statusPublished - 2 Aug 2013


  • American options pricing
  • Early exercise premium
  • Probability theory
  • Real options


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