Static hedging of chained-type barrier options

• The hedging problem for chained barrier options is studied.
• Static strike-spread hedge portfolios are proposed in the Black–Scholes model.
• The simulation results with adjusted payoffs show the accuracy of hedging strategies.
• Static hedging in this paper is seen as an improvement over delta hedging.

This paper concerns barrier options which are chained together. When the underlying asset price hits a certain barrier level, another barrier option is given to a primary option holder. Then, if the asset price hits another barrier, a third barrier option is given, and so on. The paper studies the hedging problem for these chained-type barrier options. We use the (double) reflection principle and propose a static replication portfolio of vanilla options for hedging of these options in the Black–Scholes model. The Monte Carlo simulation results for vanilla options with adjusted payoffs are provided to demonstrate the accuracy of the hedging strategies. A comparison between static hedging and delta hedging for a chained barrier option shows static hedge performs better than delta hedge.