Cost-optimal static super-replication of barrier options: an optimization approach

ABSTRACT Exact static hedging results for barrier options are usually based on unrealistic assumptions such as the availability of an infinite number of standard options or zero cost of carry. If these assumptions are dropped, static hedges may lead to large losses close to maturity of the barrier option. To avoid this, we analyze the well-known concept of super-replication in the context of static hedging both theoretically and numerically and apply it to the case of hedging barrier options in a stochastic volatility context. Numerical results show that our approach leads to very attractive static hedging strategies which super-replicate the barrier option’s payoff, match the delta and vega of the target option and only consist of a handful of liquidly traded standard options. Surprisingly, the identified cost-optimal static super-replication portfolios are only marginally more expensive than the barrier option itself.