Rational Bounds on the Prices of Exotic Options

Abstract

The paper explores the bounds which can be placed on the price of exotic options while making minimal assumptions about the price process. In particular, we identify the bounds on the price of a general barrier option given the price of a set of European call options. We show the hedging strategies which enforce those bounds. The hedging strategies are robust in that, after inception, trading occurs only when the barrier is breached. The hedge strategies put a floor on the maximum loss. The distribution of hedge errors under the strategy is compared with that under alternative strategies.