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American barrier options of the knock-in type involve non-Markouian optimal stopping problems for early exercise. They therefore cannot be priced via standard methods such as binomial or trinomial trees and finite-difference schemes for free-boundary partial differential equations. This article provides a modified tree method to price these options. It also develops fast and accurate analytic approximations for the price and hedge parameters.doi:10.3905/jod.2004.391034 fatcat:3fqbtkjcgzee5ki4zpop5pzohu