Pricing Barrier Options in Discrete Time

This bachelor thesis deals with pricing options and specifically barrier options in discrete time. A special form of barrier options called ‘Parisian options’ will be treated in detail. A binomial tree is used to model possible developments of the price of the underlying. By using so-called risk-neutral probabilities it is possible to view the option price as an expectation. The binomial coefficient is used to calculate the amount of different paths ending in the same node. In the case of barrier options this becomes more complicated but a relatively easy formula that replaces the binomial coefficient can be found. For Parisian options it is not possible to find a direct formula and instead we must use a recursive algorithm.