收益率服从奇异分布的金融资产的相关问题研究

发布时间：2018-03-16 08:53

本文选题：极端风险　切入点：奇异分布　出处：《哈尔滨工业大学》2014年硕士论文　论文类型：学位论文

【摘要】：在金融投资活动中，既需要描绘出资产的收益状况，又需要准确度量资产的风险状况。金融资产的收益分布的研究是金融风险测量的基础，对收益率分布形式的研究不仅有利于解决投资者的现实需求，而且有助于金融市场的管理。本文尝试将金融资产的极端收益率与正常分布的收益率合在一起研究，所以首先分析了该研究的可行性。通过对正常收益的波动因素，以及极端收益波动因素的分析，结合理论与实际两方面，界定了极端风险的内涵；同时搜集了281家上市股票在2004年到2013年的市场收益数据样本，从实际的金融股票市场中找出样本数据中极端风险发生的实例，共统计了48次极端收益率，在此基础上提出了将金融资产的极端收益率与正常收益率合在一起研究的研究思路。本文针对一般风险和极端风险分别构造了两个密度函数，正常分布密度函数反映了一般风险，尾部分布密度函数反映极端风险，联合得到一个新的分布，，称之为奇异分布。根据均值——方差法，推导了该模型的数学期望与标准差，以及由极端风险引起的均值、方差以及高阶矩变化的公式。并用样本数据分析极端风险对均值方差的影响，结果表明金融资产的实际收益率低于正常分布的收益率，而真实风险要高于正常分布的风险。最后，本文运用VaR方法评估奇异分布的风险水平，推导出相关的公式；分析了极端风险发生的概率这一参数对奇异分布曲线的影响；并用样本数据计算出在不同置信度下，正常分布与奇异分布的VaR。结果显示，在收益的尾部，相同的置信水平上，奇异分布的VaR明显要低于正常分布的VaR，也就是投资者面临着更大的真实风险。
[Abstract]:In the financial investment activities, it is necessary not only to depict the income situation of the assets, but also to measure the risk of the assets accurately. The study of the distribution of the income of the financial assets is the basis of the financial risk measurement. The study of yield distribution is not only helpful to solve the real demand of investors, but also helpful to the management of financial market. This paper tries to combine the extreme return rate of financial assets with the return rate of normal distribution, so the feasibility of the study is analyzed. Combined with theory and practice, this paper defines the connotation of extreme risk, collects the data samples of 281 listed stocks from 2004 to 2013, and finds out the examples of extreme risk in the sample data from the actual financial stock market. On the basis of the statistics of 48 times of extreme rate of return, this paper puts forward the research idea of combining the extreme rate of return of financial assets with the normal rate of return. In this paper, two density functions are constructed for general risk and extreme risk respectively. The normal distribution density function reflects the general risk, the tail distribution density function reflects the extreme risk, and a new distribution is obtained. Called singular distribution, the mathematical expectation and standard deviation of the model and the mean value caused by extreme risk are derived according to the mean-variance method. The influence of extreme risk on mean variance is analyzed with sample data. The results show that the real return rate of financial assets is lower than that of normal distribution, but the real risk is higher than that of normal distribution. Finally, this paper uses VaR method to evaluate the risk level of singular distribution, deduces the relevant formula, analyzes the influence of the probability of extreme risk occurrence on the singular distribution curve, and calculates the different confidence degree with the sample data. The results show that the VaR of singular distribution is obviously lower than that of normal distribution at the same confidence level at the end of the return, that is, investors are facing a greater real risk.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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