基于Copula函数的谱风险度量的研究及应用
发布时间：2018-11-17 15:07
【摘要】：随着金融市场的迅猛发展,金融衍生工具频频出新,市场的多元化对风险度量提出了更高的要求,对风险的定量分析显得尤为重要。 本文在介绍谱风险度量理论及风险厌恶度量理论的基础上,给出了双曲型风险谱函数等三种风险谱函数的形式,得到了谱风险度量的估计量,从而构造出投资组合的优化模型。采用样本外数据对模型的有效性进行Kupiec检验。实证部分计算了单个资产及多个资产投资组合的谱风险度量值。实证结果表明,风险厌恶因子和置信水平的选取均对单一资产的双曲型谱风险度量值产生影响,风险厌恶因子可以作为谱风险度量的数值表征；对给定的置信水平和风险厌恶因子,随着期望收益率的增加,高收益的股票所占权重逐渐增大。 将Copula函数运用到投资组合的谱风险度量模型中是本文的一个重要创新点。通过Copula函数研究资产之间的相依结构,可以提高SRM估计的准确性。核密度估计对样本的拟合度高,本文选用其确定边缘分布,选择Copula函数描述尾部相依性。用极大似然估计和非参数方法估计Copula函数的参数,结合经验Copula函数,运用平方欧氏距离对参数的估计进行评价。最后,通过Monte Carlo模拟方法得到一种新的Copula-SRM算法。实证部分得到了五种Copula函数的参数估计值及Kendall秩相关系数和Spearman秩相关系数。实证结果表明上证指数和深证指数的日对数收益率存在较强的正相关,t-Copula模型能更好地拟合原始数据,且Copula-SRM算法比传统的SRM算法得到的结果更准确。
[Abstract]:With the rapid development of the financial market, the financial derivatives frequently come out new, the diversification of the market put forward higher requirements for risk measurement, the quantitative analysis of risk is particularly important. On the basis of introducing the theory of spectral risk measurement and the theory of risk aversion, this paper gives the form of three kinds of risk spectrum functions such as hyperbolic risk spectrum function, obtains the estimator of spectral risk measurement, and constructs the optimal model of investment portfolio. The validity of the model is tested by Kupiec with the data outside the sample. The empirical part calculates the spectral risk measures of individual assets and multiple asset portfolios. The empirical results show that the selection of risk aversion factor and confidence level have an effect on the hyperbolic spectral risk measure of a single asset, and risk aversion factor can be used as a numerical representation of spectral risk measurement. For a given confidence level and risk aversion factor, with the increase of expected rate of return, the weight of high yield stock increases gradually. It is an important innovation of this paper to apply the Copula function to the portfolio spectral risk measurement model. The accuracy of SRM estimation can be improved by studying the dependent structure of assets by Copula function. The kernel density estimation has a high fitting degree to the sample. In this paper, the edge distribution is determined and the Copula function is chosen to describe the tail dependence. The parameters of Copula function are estimated by maximum likelihood estimation and nonparametric method, and the estimation of parameters is evaluated by square Euclidean distance combined with empirical Copula function. Finally, a new Copula-SRM algorithm is obtained by Monte Carlo simulation. In the empirical part, the parameter estimates of five kinds of Copula functions and the Kendall rank correlation coefficients and Spearman rank correlation coefficients are obtained. The empirical results show that there is a strong positive correlation between the daily logarithmic returns of Shanghai Stock Exchange Index and Shenzhen Stock Exchange Index, and the t-Copula model can better fit the original data, and the Copula-SRM algorithm is more accurate than the traditional SRM algorithm.
【学位授予单位】：北京化工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
[Abstract]:With the rapid development of the financial market, the financial derivatives frequently come out new, the diversification of the market put forward higher requirements for risk measurement, the quantitative analysis of risk is particularly important. On the basis of introducing the theory of spectral risk measurement and the theory of risk aversion, this paper gives the form of three kinds of risk spectrum functions such as hyperbolic risk spectrum function, obtains the estimator of spectral risk measurement, and constructs the optimal model of investment portfolio. The validity of the model is tested by Kupiec with the data outside the sample. The empirical part calculates the spectral risk measures of individual assets and multiple asset portfolios. The empirical results show that the selection of risk aversion factor and confidence level have an effect on the hyperbolic spectral risk measure of a single asset, and risk aversion factor can be used as a numerical representation of spectral risk measurement. For a given confidence level and risk aversion factor, with the increase of expected rate of return, the weight of high yield stock increases gradually. It is an important innovation of this paper to apply the Copula function to the portfolio spectral risk measurement model. The accuracy of SRM estimation can be improved by studying the dependent structure of assets by Copula function. The kernel density estimation has a high fitting degree to the sample. In this paper, the edge distribution is determined and the Copula function is chosen to describe the tail dependence. The parameters of Copula function are estimated by maximum likelihood estimation and nonparametric method, and the estimation of parameters is evaluated by square Euclidean distance combined with empirical Copula function. Finally, a new Copula-SRM algorithm is obtained by Monte Carlo simulation. In the empirical part, the parameter estimates of five kinds of Copula functions and the Kendall rank correlation coefficients and Spearman rank correlation coefficients are obtained. The empirical results show that there is a strong positive correlation between the daily logarithmic returns of Shanghai Stock Exchange Index and Shenzhen Stock Exchange Index, and the t-Copula model can better fit the original data, and the Copula-SRM algorithm is more accurate than the traditional SRM algorithm.
【学位授予单位】：北京化工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
【参考文献】
相关期刊论文 前10条
1 石媛昌,韩立岩;金融风险度量方法的新进展[J];首都经济贸易大学学报;2005年04期
2 史道济;李t，
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