Pitfalls in static superhedging of barrier options

If the cost of carry is non-zero and only finitely many options are traded, static hedging of barrier options is in general impossible. Alternatively, one can set up a static superhedging strategy. We demonstrate that such a superhedge may perform poorly close to the maturity of the barrier option if the strikes of the options used to superhedge the barrier option are not carefully chosen. Model risk amplifies this effect.