| 基于正态逆高斯分布的金融建模及其应用 |
| Alternative Title | Financial Modeling and Applications Based on Normal Inverse Gaussian Distribution
|
| 方蔚棠 |
| Thesis Advisor | 焦桂梅
|
| 2004-06-02
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| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 硕士
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| Keyword | 正态逆高斯分布
逆高斯分布
L\'evy过程
|
| Abstract | 最近几年里越来越多的研究中用L\'evy过程代替Brown运动来建立金融市场中价格运动随机模型，其中正态逆高斯L\'evy过程与市场观测数据有很好的拟合。我们回顾了正态逆高斯(NIG)分布的一些重要性质，对正态逆高斯L\'evy过程给出了L\'evy分解和 L\'evy测度。作为对论文以后讨论的准备，回顾了正态逆高斯分布与广义双曲分布簇和广义逆高斯分布的联系。然后讨论了基于正态逆高斯过程的模型，对模型做了简化改进，使之更易于数据处理。然后对德国证券价格进行了数据分析并给出了NIG分布的参数估计。进而，根据无套利定价原则，给出了NIG模型的普通欧式期权的定价并利用调和分析理论计算了欧式看涨期权定价的渐进解析表达式。然后给出了影响期权定价的隐含波动率的估计方法。基于正态逆高斯分布对金融市场数据的拟合程度比正态分布要好，还能解释一些正态分布无法解释的现象，研究采用正态逆高斯模型的证券价格运动和金融衍生产品定价问题，具有很好的现实意义。 |
| Other Abstract | "In recent years more realistic stochastic models for price movements in financial markets have been developed by replacing the classical Brownian motion by l\'evy processes . Normal Inverse Gaussian l\'evy Process turned out to provide an excellent fit to observed market data. We review the most important facts of Normal inverse Gaussian Distribution and give a decomposition of Normal inverse Gaussian l\'evy Process. As a preparation for developments in latter part of the paper; brief review the connection of NIG distribution to the classes of GH an GIG distribution . Then we discuss and study the modelling method based on NIG distribution and NIG l\'evy process and analysis financial statistical data from the German stock prices , give a estimates of parameters of NIG model. Furthermore, we use equilibrant martingale measure to price the vanilla European calls of the NIG model and give a analytical asymptotic approximation of the complex integral containing Bessel functions, then we give out a estimate method of implied volatility which effects the pricing of options. As the better fitness to financial market data of NIG distribution than Normal distribution and explanation to some financial phenomenons that Normal distribution can not ,studying stock prices movements and pricing problems of
derivatives with NIG model have good realistic sense!" |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/225081
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
方蔚棠. 基于正态逆高斯分布的金融建模及其应用[D]. 兰州. 兰州大学,2004.
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