Fast Fourier Transform for Option Pricing: Improved Mathematical Modeling and Design of Efficient Parallel Algorithm

Fast Fourier Transform (FFT) has been used in many scientific and engineering applications. In the current study, we have tried to improve a recently proposed model of FFT for pricing financial derivatives so as to help designing an efficient parallel algorithm. We have then developed a new parallel algorithm to compute the FFT using a swapping technique that exploits data locality, and hence showed higher efficiency of this algorithm. We have tested our algorithm on 20 node SunFire 6800 high performance computing system and compared the new algorithm with the traditional Cooley-Tukey algorithm. As an example, we have also plotted the calculated option values for various strike prices with a proper selection of log strike-price spacing to ensure fine-grid integration for FFT computation as well as to maximize the number of strikes lying in the desired region of the asset price.

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