Barrier options are options that are activated or extinguished when the price of the underlying asset reaches the barrier. The underlying asset could be a stock, an exchange rate, an index or something else. For pricing them it is important how often the barrier crossing is checked. For the continuously monitored case there exists a closed formula (Merton 1973). This thesis is focused on the discretely monitored case, when the barrier crossing is checked just in a given time interval (e.g daily). Thereby, as a first step, the financial market model of the lecture "Discrete Time Finance" of Zagst (2010) is extended to be able to work with arbitrary sample spaces. In the second step the approximation for the discretely monitored case of Broadie, Glasserman, and Kou (1997) is introduced. The proof of it is similar to Kou (2003), but in a more general way. At the end this approximation is validated by a Monte-Carlo-Simulation.     «

Barrier options are options that are activated or extinguished when the price of the underlying asset reaches the barrier. The underlying asset could be a stock, an exchange rate, an index or something else. For pricing them it is important how often the barrier crossing is checked. For the continuously monitored case there exists a closed formula (Merton 1973). This thesis is focused on the discretely monitored case, when the barrier crossing is checked just in a given time interval (e.g daily)...     »