Topic: Contributed on Financial modelling Title: Fourier transform in option pricing models Authors:  Marek Kolman - University of Economics Prague (Czech Republic) [presenting]
Abstract: Various option pricing models are compared in within the scope of Fourier transform. It is first shown that there exists a general approach to obtain a characteristic function using a deterministic term called `Jensen correction' $\omega$, which makes Fourier transform methods very attractive. This Jensen correction term is a powerful tool that allows to obtain characteristic functions quickly and with almost no costs. Subsequently, we compare the Madan-Carr approach with a recent transform approach relying on Fourier-Cosine expansion where we also define a more applicable technique for bounds selection. The conclusion is that the Fourier-Cosine is very fast and easy-to-implement method which can easily outperform the standard Madan-Carr approach. With the introduced bounds selection also stable and accurate transform method for option pricing.