Dynamic and Static Hedging of Barrier options

Abstract: In this paper the performance of a static hedging strategy of European barrier options are evaluated, first introduced by Carr, Ellis and Gupta in 1998. Two dynamic hedging strategies are used as benchmarks; the delta hedging and delta-gamma hedging strategy, respectively. To increase realism to the system only discrete rebalancing of the replicating portfolios are possible. In addition, transaction costs are assumed and included. The analysis is limited to the down-and-out and up-and-out call European options. Hedging of European put barrier options could easily be constructed from the put-call-parity and European in-barrier options from the fact that a European option is equal to the sum of the in- and out-barrier option with the same barrier. The static hedge outperforms the two dynamic hedging strategies in particular when transaction costs are included. The static hedge is more successful in reducing the risk and delivers a higher average return.