High Performance Computing for a Financial Application Using Fast Fourier Transform

Fast Fourier Transform (FFT) has been used in many scientific and engineering applications. In the current study, we have applied the FFT for a novel application in finance. We have improved a mathematical model of Fourier transform technique for pricing financial derivatives to help design an effective parallel algorithm. We have then developed a new parallel algorithm for FFT using a swapping technique that exploits data locality. We have analyzed our algorithm theoretically and have reported the significance of the new algorithm. We have implemented our algorithm on 20 node SunFire 6800 high performance computing system and compared the new algorithm with the traditional Cooley-Tukey algorithm both as stand alone comparison of the performance and in relation to our theoretical analysis and showed higher efficiency of our algorithm. We have presented the computed option values for various strike prices with a proper selection of 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.