Bounds and robust hedging of the American option

Abstract

The value of an American option depends on the information that the holder will acquire over the option’s life. Much of the literature makes restrictive assumptions about information revelation – for example that the underlying price process is Markov. With a richer information structure, the American feature becomes more valuable. This paper identifies the least upper bound on the price of an American option, placing no assumptions on the information structure. It shows that the American premium in standard models is a small fraction of its upper bound, and shows what features make the American feature most valuable. The bounds can be tightened by excluding implausible processes, and these bounds are enforced by a hedging strategy that is robust to model error