Abstract
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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References
Tucker, A.B.: Computer Science and Engineering Handbook. CRC Press, Boca Raton (1997)
Haugh, M.B., Lo, A.W.: Computational Challenges in Portfolio Management - Tomorrow’s Hardest Problem. Computing in Science and Engineering 3(3), 54–59 (2001)
Kontoghiorghes, E.J., Nagurnec, A., Rustem, B.: Parallel Computing in Economics, Finance and Decision-making. Parallel Computing 26, 207–209 (2000)
Zenios, S.A.: High-Performance Computing in Finance: The Last 10 Years and the Next. Parallel Computing 25, 2149–2075 (1999)
Cox, J.C., Ross, S.A., Rubinstein, M.: Option Pricing: A Simplified Approach. Journal of Financial Economics 7, 229–263 (1979)
Carr, P., Madan, D.B.: Option Valuation using the Fast Fourier Transform. The Journal of Computational Finance 2(4), 61–73 (1999)
Dempster, M.A.H., Hong, S.S.G.: Spread Option Valuation and the Fast Fourier Transform. Technical Report WP 26/2000, Judge Institute of Management Studies, Cambridge, England (2000)
Thulasiram, R.K., Thulasiraman, P.: Performance Evaluation of a Multithreaded Fast Fourier Transform Algorithm for Derivative Pricing. The Journal of Supercomputing 26(1), 43–58 (2003)
Thulasiram, R.K., Thulasiraman, P.: A Parallel FFT Approach for Derivative Pricing. In: Siegel, H.J. (ed.) Proceedings of SPIE: Commercial Applications for High Performance Computing, Denver, CO, August 2001, vol. 4528, pp. 181–192 (2001)
Thulasiram, R.K., Litov, L., Nojumi, H., Downing, C.T., Gao, G.R.: Multithreaded Algorithms for Pricing a Class of Complex Options. In: Proceedings of the International Parallel and Distributed Processing Symposium (IPDPS), San Francisco, CA (April 2001) (CD-ROM)
Cooley, J.W., Lewis, P.A., Welch, P.D.: The Fast Fourier Transform and its Application to Time Series Analysis. In: Statistical Methods for Digital Computers, Wiley, New York (1977)
Grama, A., Gupta, A., Kumar, V., Karypis, G.: Introduction to Parallel Computing, 2nd edn. Pearson Educarion Limited, Edinburgh Gate (2003)
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Barua, S., Thulasiram, R.K., Thulasiraman, P. (2004). Fast Fourier Transform for Option Pricing: Improved Mathematical Modeling and Design of Efficient Parallel Algorithm. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_72
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DOI: https://doi.org/10.1007/978-3-540-24767-8_72
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