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

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.

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.