呂育道臺灣大學：資訊工程學研究所蘇正雄Shu, Cheng HsiungCheng HsiungShu2007-11-262018-07-052007-11-262018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/54007This thesis investigates the fast Fourier transform-based pricing algorithm for discrete Asian options by Benhamou [1]. We compare it with other methods and combine it with extrapolation to increase numerical accuracy. We also apply it to the continuous case by using extrapolation. Running the algorithm with different numbers of grid points, we observe the convergence of option values both in the continuous case and in the discrete case. The disadvantages of the algorithm are also discussed.1.Introduction 1 2.Background 5 3.The Fourier Convolution Method 8 3.1 Steward and Hodges factorization ﹒﹒ 9 3.2 Re-centering the densities﹒﹒﹒﹒﹒﹒ 11 3.3 The interpolation formula﹒﹒﹒﹒﹒﹒﹒ 12 3.4 The pricing algorithm﹒﹒﹒﹒﹒﹒﹒﹒﹒ 14 3.5 The choice of parameters﹒﹒﹒﹒﹒﹒﹒ 14 4.Numerical Results 16 4.1 Discrete case﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒ 16 4.2 Continuous case﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒﹒ 17 5.Conclusions 20en-US離散型亞式選擇權連續型亞式選擇權傅立葉轉換旋積機率密度函數外插法Discrete Asian OptionContinuous Asian OptionFourier TransformConvolutionProbability Density FunctionExtrapolationthesis