丁灯,余兆聪.基于傅里叶级数展开式的有效期权定价方法[J].数学研究及应用,2011,31(1):12~22
基于傅里叶级数展开式的有效期权定价方法
Efficient Option Pricing Methods Based on Fourier Series Expansions
投稿时间:2009-11-11  最后修改时间:2010-01-19
DOI:10.3770/j.issn:1000-341X.2011.01.002
中文关键词:  期权定价  勒维过程  傅里叶变换  傅里叶展开.
英文关键词:option pricing  L\'evy process  Fourier transform  Fourier expansions.
基金项目:澳门大学基金 (Grants Nos.UL020/08-Y3/MAT/JXQ01/FST; RG058/09-10S/DD/FST).
作者单位
丁灯 澳门大学数学系 
余兆聪 澳门大学数学系 
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中文摘要:
      近来Fang和 Oosterlee 提出了一种新颖的基于傅里叶余弦展开式的期权定价方法 ([1], 2008). 受这一方法的启发, 本文分别提出三种基于傅里叶级数, 傅里叶余弦和傅里叶正弦展开式的期权定价方法. 这些方法在计算多个执行价格时更为有效. 本文还通过在若干 exp-L\'evy 模型下的实验对这些新方法与 Fang和 Oosterlee 的方法和别的现有方法进行数值比较.
英文摘要:
      A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L\'evy models are also given to compare these new methods with the Fang and Oosterlee's method and other methods.
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