Improvements on Fast Fourier Transform Option Pricing

• Main Authors: Chen, Yu-Ting, 陳郁婷
• Other Authors: Dai, Tian-Shyr
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/10332076657999300822

碩士 === 國立交通大學 === 財務金融研究所 === 99 === This thesis analyzes and improves FFT-based pricing algorithms that can be applied to price a wide class of derivatives under Levy processes. Convolutions and interpolations are widely used in these algorithms. Our paper constructs faster error convergence rate algorithms by improving error convergence rate of these convolutions and interpolations. Both backward and forward induction methods can be applied in our algorithms. Our paper derives the fundamental properties of FFT-based algorithms with backward induction method and the related applications, like the pricing algorithms for Bermudan options, barrier options and lookback options. We also price Asian options with FFT and forward induction method. Our paper also derives a control variates methods on (probability) distribution that can significantly improve the convergence rate for pricing Asian options.