This paper proposes a unique framework for the determination of the exercise boundary of American put option utilizing the mean value theorem for integration. We have isolated the path‐dependent feature of the problem through a small term, and formulated an iteration procedure that avoids an explicit integration over the exercise boundary in the integral representation of the pricing. Our method outperforms other methods in the literature in terms of accuracy and efficiency for the pricing of American put options with maturity in the region of most practical uses. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:793–815, 2016