A Survey of the Integral Representation of American Option Prices

This paper surveys some of the literature on American option pricing, in particular the representations of McKean (1965), Kim (1990) and Carr, Jarrow and Myneni (1992). It is proposed that the approach regarding the problem as a free boundary value problem, and solving this via incomplete Fourier transforms, is the most robust for further developments involving more complex payo structures, and higher dimensional problems such as multi-asset American options. Some comparison of dierent numerical solution methods is also provided.