Pricing of the American option in discrete time under proportional transaction costs

In this paper pricing of the American option in a discrete time financial market with proportional transaction costs is studied. Lower bound for the price of the American contingent claim is obtained. Under sufficiently small transaction costs the formula for the cost of a strategy that replicates an option is given and equivalence of replication and option prices is shown. Pricing for a special class of the American options in the Cox–Ross–Rubinstein model is also considered.