Replication Methods in the Pricing and Hedging of Barrier Options

This paper considers various options replication methods. Firstly, a specific type of barrier option, an up-and-out call, is considered. Other barrier options are briefly also described, and various types of barriers are considered. Secondly, a general definition of replication methods is provided. Two methods are thus examined in detail: The first one, based on ever-changing positions in replicating portfolio, is referred to as a dynamic replication method. The second one is denoted as a static replication method ? its aim is to create a static basket of simple assets that will replicate the option payoff. However, in the real world it is difficult to attain perfect replication; therefore, the expected replication error of both methods is studied via simulation technique.