Abstract
In this thesis we study barrier options. As a background we rst consider European options. To price barrier options we also need to know the distribution of a Brownian motion absorbed at a certain value. Such distributions are found using the reection principle. We then price some standard contracts and nd the implicit volatility of some contracts that are currently traded. Finally we study some general properties of barrier options, in particular the asymptotic behavior of the price as the volatility tends to innity. These results we have not seen elsewhere.