American option valuation using first-passage densities

�scar Guti�rrez

Quantitative Finance, 2013, vol. 13, issue 11, 1831-1843

Abstract: 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.

Date: 2013
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DOI: 10.1080/14697688.2013.794387

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