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Static hedging of barrier options in discrete and continuous time

In this project, we discuss some hedging strategies which are widely used in the financial world. We start from the Delta Hedging that is the most basic tool to hedge risks. However, our aim is to hedge more complicated options such as barrier options. Since the delta of a barrier option is extremely large around the barrier region, Delta Hedging does not work in this case. Then we investigate another hedging technique called Static Hedging. We describe how to statically hedge a barrier option both in discrete and in continuous time. In this project, two different static hedging strategies are considered. One is static hedging with maturity varying options; the other one is static hedging with strike varying options. We also show how to implement these hedging techniques in a practical point of view.