A lattice framework for calculating upper and lower bounds of an american option with transaction costs

摘要

Thie paper proposes a framework for calculating both upper and lower bounds of an American option with proportional transaction costs by using binomial and trinomial lattice process. Both bounds are derived by applying no arbitrage condition. The problem to calculate the upper bound of an american option can be formulated as a convex problem. On the other hand, since the problem to calculate the lower bound could be formulated as a nonconvex problem, two heuristics are proposed to solve the lower bound practically.