JEL Classication G G C Key words Barrier Options Static Hedging Mean

This paper applies to the static hedge of barrier options a technique meansquare 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 eciency 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 Derivatives markets have become an essential part of the global economic and nancial system in the past decade Growth in trading activity has been particulary fast in overthecounter OTC markets which have become the dominant force in the industry One factor in the success of OTC markets has been their ability to oer new exotic derivatives customized to customers needs Among the most successful OTC option products are barrier options The payo of a barrier option depends on whether th