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With the evolution of graphics processing units (GPUs) into powerful and cost-efficient computing architectures, their range of application has expanded tremendously, especially in the area of computational finance. Current research in the area, however, is limited in terms of options priced and complexity of stock price models. This paper presents algorithms, based on the Fourier space time-stepping (FST) method, for pricing single and multi-asset European and American options with Levy underliers on a GPU. Furthermore, the single-asset pricing algorithm is parallelized to attain greater efficiency.