Robust hedging of barrier options

This article considers the pricing and hedging of barrier options in a mark et in which call options are liquidly traded and can be used as hedging ins truments. This use of call options means that market preferences and belief s about the future behavior of the underlying assets are in some sense inco rporated into the hedge and do not need to be specified exogenously. Thus w e are able to find prices for exotic derivatives which are independent of a ny model for the underlying asset. For example we do not need to assume tha t the underlying assets follow an exponential Brownian motion. We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outs ide these limits then we give simple strategies for generating profits at z ero risk. Examples illustrate that the bounds we give can be fairly tight.