On the Optimal Super- and Sub-Hedging Strategies (Revised in August 2013; forthcoming in “International Journal of Theoretical and Applied Finance”)

Abstract

This paper proposes the optimal super- and sub-hedging strategies for a derivative on two underlying assets without any specification of underlying processes. Moreover, the strategies are free from any model in terms of the dependency between the underlying asset prices. We derive the optimal pricing bounds through finding a joint distribution under which the derivative price is equal to the hedging portfolio’s value; the portfolio consists of liquid derivatives on each underlying asset.As examples, we obtain new super- and sub-hedging strategies for several exotic options such as quanto options, exchange options, basket options, forward starting options and knock-out options.