Abstract
A selection of Fourier transform methodologies for option pricing is presented. The focus is aimed at the cosine method which is endowed with attractive properties. The methodologies are applied to a particularly selected pricing problem and also are compared against closed-form formulas if these are available. To thoroughly test these methods, we have chosen option data exhibiting a significant volatility smile which could rule out some of the methodologies if these are unable to capture the special properties of ITM or OTM options. It is shown that in some cases the transform approaches outperforms the closed-form formulas also in speed. In particular, the Fourier-cosine expansion is robust, general, very fast and therefore it seems to be an ideal candidate for implementation of option-pricing model even by the practitioners.
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