Fast Fourier Transform with Applications to Pricing Discrete European Barrier Options under Binomial and Trinomial Models

A derivative is a financial instrument which is constructed from other more basic underlying assets, such as bonds or stocks. With the dramatic growth of the derivatives markets, more and more derivatives have been designed and issued by financial institutions. This thesis presents a method that can be used to speed up the pricing of discrete European barrier options under binomial and trinomial tree models. Binomial tree and trinomial tree are two common and efficient models for pricing options. However, in practice, almost all barrier options are discretely monitored and the reXection principle no longer works. It seems that the only way to price discrete barrier options is to traverse the whole tree, which takes quadratic time. This thesis gives