基于非对称Laplace分布的VaR在投资组合中的应用研究

发布时间：2018-01-17 12:42

本文关键词：基于非对称Laplace分布的VaR在投资组合中的应用研究　出处：《武汉科技大学》2013年硕士论文　论文类型：学位论文

更多相关文章： 投资组合 VaR 非对称Laplace分布

【摘要】：马柯维茨提出的均值方差投资组合理论，奠定了投资定量化的研究基础。在风险度量方面，VaR被广泛应用在目前的研究之中，可以通过简洁地估算出市场风险带给金融机构的风险水平，从而，及时地做出进一步的预警措施。本文首先考虑到资产的收益率具有尖峰性、厚尾性以及有偏性等特征，通过对国内外VaR模型现状的分析和研究，对比了正态分布、混合的正态分布，t分布以及对称的Laplace分布在VaR应用中的优缺点，根据计算数据的统计量，证实大多数资产的收益率分布都具有尖峰、厚尾等特征，Laplace分布可以更好的拟合具有尖峰性的资产收益率分布。其次，根据Laplace分布的位置参数作参照，并且代入示性函数到对称的Laplace分布之中，得到了非对称Laplace分布，接着分析并研究了非对称Laplace分布的性质，，利用大量的历史数据和迭代法对非对称Laplace的参数进行极大似然估计，经过数次后，得出参数值，可以得到非对称Laplace的密度函数，并且同时根据参数，计算出单个资产的VaR，将单个资产的VaR计算，转化为多个资产的VaR度量的同时，利用本文提出的非对称Laplace分布的均值-VaR投资模型得到相应的投资组合比例。最后，对基于非对称Laplace分布的均值-VaR模型进行验证，证实非对称Laplace分布的均值-VaR在投资组合方面尤其是资产收益率符合尖峰、有偏性特征时，有着较好的应用具有一定的实用价值。
[Abstract]:The mean-variance portfolio theory put forward by Markowitz has laid the foundation for the research of investment quantification, and VaR has been widely used in the research of risk measurement. We can estimate the risk level of the market risk to the financial institutions by succinctly, so as to make further early warning measures in time. Firstly, this paper considers that the return rate of assets has peak. By analyzing and studying the current situation of VaR model at home and abroad, the normal distribution and mixed normal distribution are compared. T distribution and symmetrical Laplace distribution in the application of VaR advantages and disadvantages, according to the statistics of the calculation data, it is confirmed that most of the asset yield distribution has the characteristics of peak, thick tail and so on. Laplace distribution can better fit the peak asset return distribution. Secondly, according to the location parameters of Laplace distribution as reference. The asymmetric Laplace distribution is obtained by inserting the representation function into the symmetric Laplace distribution, and then the properties of the asymmetric Laplace distribution are analyzed and studied. The parameters of asymmetric Laplace are estimated by using a large amount of historical data and iterative method. After several times, the density function of asymmetric Laplace can be obtained. At the same time, according to the parameters, the VaR of a single asset is calculated, and the VaR calculation of a single asset is transformed into the VaR measurement of multiple assets at the same time. Using the mean-VaR investment model of asymmetric Laplace distribution proposed in this paper, the corresponding portfolio ratio is obtained. Finally. To verify the mean-VaR model based on asymmetric Laplace distribution, it is proved that the mean value -VaR distribution of asymmetric Laplace distribution is in line with the peak in portfolio, especially the return on assets. When it has the characteristic of bias, it has some practical value for its better application.
【学位授予单位】：武汉科技大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.59;F224

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