The acceleration of an option pricing technique based on Fourier cosine expansions on the graphics processing unit (GPU) is reported. European options, in particular with multiple strikes, and Bermudan options will be discussed. The influence of the number of terms in the Fourier cosine series expansion, the number of strikes, as well as the number of exercise dates for Bermudan options is explored. We also give details about the different ways of implementing on a GPU. Numerical examples include asset price processes on the basis of a Lévy process of infinite activity and the stochastic volatility Heston model. Furthermore, we discuss the issue of precision on the present GPU systems. Copyright © 2012 John Wiley & Sons, Ltd.