In this article, we develop new upper and lower bounds on American option prices which
improve the bounds by Broadie and Detemple. The main idea is the consideration of
doubly capped call options which have two cap prices. We present a new option price
approximation based on the two upper bounds. On average, our upper bound
extrapolation (named UBE) has an average accuracy better than a 1,000 time-step
binomial tree with a computation speed comparable to a 100 time-step binomial tree. We
also provide a new method of approximating the optimal exercise boundaries of
American options.
Key Words: American option, Optimal exercise boundary, Approximation, Bound, Cap

