Hedging Barrier Options: Current Methods and Alternatives

Abstract: This paper applies to the static hedge of barrier options a technique, mean-square hedging, designed to minimize the size of the hedging error when perfect replication is not possible. It introduces an extension of this technique which preserves the computational efficiency of mean-square hedging while being consistent with any prior pricing model or with any linear constraint on the hedging residual. This improves on current static hedging methods, which aim at exactly replicating barrier options and rely on strong assumptions on the availability of traded options with certain strikes or maturities, or on the distribution of the underlying asset.