[1]柳向东,杨飞.基于期权价格的Lévy过程参数估计研究[J].深圳大学学报理工版,2014,31(3):325-330.[doi:10.3724/SP.J.1249.2014.03325]
　Liu Xiangdong and Yang Fei.The research of parameter estimation under the Lévy process based on option pricing[J].Journal of Shenzhen University Science and Engineering,2014,31(3):325-330.[doi:10.3724/SP.J.1249.2014.03325]
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基于期权价格的Lévy过程参数估计研究()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第31卷
期数:
2014年第3期
页码:
325-330
栏目:
数学与应用数学
出版日期:
2014-05-20

文章信息/Info

Title:
The research of parameter estimation under the Lévy process based on option pricing
文章编号:
201403017
作者:
柳向东; 杨飞
暨南大学经济学院，广州 510632
Author(s):
Liu Xiangdong and Yang Fei
College of Economics，Jinan University，Guangzhou 510632，P.R.China
关键词:
应用统计数学; Lévy过程; 期权定价; 极大似然参数估计; 特征函数; 快速傅里叶变换
Keywords:
application of statistical mathematics;  Lévy process;  option pricing;  maximum likelihood parameter estimation;  characteristic function;  fast Fourier transform
分类号:
O 211.9；F 830
DOI:
10.3724/SP.J.1249.2014.03325
文献标志码:
A
摘要:
Lévy过程可准确描述某些复杂的分布特征，如: 尖峰、厚尾及有偏等，也可将标的资产运动过程中所展现的非连续性体现出来，因此在金融过程中得到了广泛而有效的运用. 本研究基于期权的定价公式，运用极大似然法以及快速傅里叶变换对方差伽马（Variance-Gamma, VG）模型、Carr-Geman-Madan-Yor（CGMY）模型及VGSA模型(VG和Cox-Ingersoll-Ross模型的复合指数模型) 等几种典型Lévy过程的参数进行有效估计，并且通过香港恒生指数期权数据对该方法进行验证.
Abstract:
The Lévy process can accurately describe the complex features of distribution, such as spikes, fat tails, and the discontinuity of the underlying asset reflected in the movement. Thus, the application of the Lévy processes in financial engineering becomes extensive and effective. However, estimation of the Lévy process parameters is difficult. Based on the option pricing formula, we used the maximum likelihood method and the fast Fourier transforms to make valid estimation on several typical Lévy process parameters, including the Variance-Gamma (VG) model, Carr-Geman-Madan-Yor (CGMY) model and VGSA (the exponential form for combining VG with Cox-Ingersoll-Ross) model. The method is tested by the Hong Kong Hang Sheng Index Options data, which is important to promote the achievements of previous results which focus on the Lévy parameter estimation.

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备注/Memo

备注/Memo:
Received：2013-12-13；Accepted：2014-04-17
Foundation：Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (35813003)
Corresponding author：Associate professor Liu Xiangdong. E-mail: tliuxd@jnu.edu.cn
Citation：Liu Xiangdong，Yang Fei. The research of parameter estimation under the Lévy process based on option pricing［J］. Journal of Shenzhen University Science and Engineering, 2014, 31(3): 325-330.（in Chinese）
基金项目：教育部留学回国人员科研启动基金资助项目（35813003）
作者简介：柳向东（1973—），男（汉族），湖南省浏阳市人，暨南大学副教授、博士. E-mail: tliuxd@jnu.edu.cn
引文：柳向东，杨飞. 基于期权价格的Lévy过程参数估计研究［J］. 深圳大学学报理工版，2014，31（3）：325-330.
更新日期/Last Update: 2014-05-01