In this paper, an alternative approach to pricing barrier options is presented that relies on the use of the first hitting time density to the barrier. The lateral Chapman-Kolmogorov relation is used as a major tool in order to determine option prices. It turns out that this approach allows for...

The option to exchange one asset for another is one of the oldest and one of the most popular exotic options. In the present article, we extend the existing literature on options to Parisian exchange options, i.e. the option to exchange one asset for the other contingent on the occurrence of the...