基于copula函数的信用风险组合一致性风险量度研究
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摘要
信用风险的组合管理研究中，违约相关结构的准确建模一直是研究的热点领域。本文充分利用copula函数在建模相关结构中的便利性和灵活性，对基于copula函数的信用风险组合相关结构的建模问题以及由此而造成的对组合损失分布和一致性风险量度的影响程度进行了系统的讨论和分析。
首先，本文在现有的信用风险组合模型之一——特征变量模型的基础上，针对其在相关结构建模中存在的问题，提出了基于copula函数的、以行业收益指数为系统风险因素的信用风险组合模型框架，讨论了在新模型框架下组合各种违约状态的联合概率的计算，阐述了模型中参数的确定方法以及copula函数的选择问题。分析表明：在利用copula函数为信用风险组合建模时，t-copula函数将可作为现有模型中Gaussian copula函数的一个比较恰当的替代选择。
其次，基于我国目前信用债券市场不够成熟、没有可靠的信用数据可获得的现实，本文利用资本市场这一个公开的、比较有效的信息源提供的数据信息来构造行业收益指数时间序列，估计行业收益指数的边际分布和相关结构参数。在运用偏t-GARCH(1,1)对行业收益指数的边际分布建模时，考虑到现有的偏t分布函数在描述偏度时缺乏灵活性，本文在现有偏t分布变量构造的基础上，提出了一种新的构造方法。通过模拟比较，发现新构造的偏t分布在表现分布的有偏性方面优于现有方法。同时利用数据分别对Gaussian copula函数和t-copula函数的行业收益指数相关结构模型进行了参数估计和拟合优度检验。检验结果表明，由于t-copula函数考虑到了行业收益指数间的尾部相关性，因而比Gaussian copula函数有更好的拟合度。
最后，在估计的相关结构模型基础上，本文通过一个假想组合详细讨论了信用风险组合模型中相关结构的变化对组合损失分布和一致性风险量度所产生的影响程度。为了提高预期短缺ES估计的精度，本文利用重要性抽样方法计算了相关结构分别为Gaussian copula函数和t-copula函数时的组合损失分布和风险量度。结果表明：相关结构的变化对组合损失分布产生显著的影响，尤其是在损失分布的尾部，导致两种相关结构模型产生的风险量度间的差异随着置信水平的提高而增加；另一方面，VaR和ES间的差异随着置信水平的提高而减小。
The modelling of defaults dependence has been a key field for risk managementof credit portfolio. Using the facility and flexibility of copula function in the modelingof dependence structure, the paper studys the modeling of credit portfolio basedcopula funtion, and analyses the effect of the change of dependence structure ofdefaults on the portfolio loss distribution and coherent risk measure.
Firstly, based on the latent variable model, one of the existing models of creditportfolio, and aimed at its drawbacks in dependence structure, the paper proposes amodel framework of credit portfolio, which is based on copula functions and wherethe indexes of industry return are considered as a systematic risk factors, discusses thecalculation of joint probability for various default states of credit portfolio in theframework, illustrates the approach of determining the parameter in the model and thechoose of copula functions. The analysis shows t-copula function is a preferablesubstitute for Gaussian copula of the existing models when using copula functions tomodel dependence structure of defaults.
Secondly, due to the fact that,in Chinese, the market of credit bonds aredeveloping, and that the reliable credit datas are not available, using the datainformation provided by the capital market,which is open and effective, the paperconstructs the time series of index of industry return, and estimates the parameters ofthe marginal distribution and dependence structure. When using skew t-GARCH(1,1)to model the marginal distribution of index of industry return, the paper develops anew construction of skew student t distribution based on the existing skew studentt distribution which is lack of flexibility in describing the skewness of distribution.In terms of simulation, It is found that the new skew student t distribution is betterthan the existing in describing the skewness of distribution. Also, the parameters ofdependence structure of index of industry return for Gaussian copula and t-copulafunctions are estimated, respectively. The test results of the good-of-fitness show thatt-copula function has better good-of-fitness than Gaussian copula function, due tot-copula function considering the tail dependence of index of industry return.
Lastly, based on the above estimated model of dependence structure, the degree of effect of the change of dependence structure in credit portfolio on the portfolio lossdistribution and coherent risk measure is discussed by a constructed creidit portfolio.In order to improve the estimation accuracy of ES, the paper calculates the portfolioloss distributions and risk measures for the dependence strcture of Gaussian copulafunction and t-copula function by using Important Sampling approach. The resultsshow that the change of dependence strctures has a significant effect on the portfolioloss distribution, especially on the tail of portfolio loss distribution, and this effectmakes the difference between the risk measure caused by the two dependence strcturemodel increase with the confidence level, on the other hand, the difference betweenVaR and ES decreases with the confidence level.
首先，本文在现有的信用风险组合模型之一——特征变量模型的基础上，针对其在相关结构建模中存在的问题，提出了基于copula函数的、以行业收益指数为系统风险因素的信用风险组合模型框架，讨论了在新模型框架下组合各种违约状态的联合概率的计算，阐述了模型中参数的确定方法以及copula函数的选择问题。分析表明：在利用copula函数为信用风险组合建模时，t-copula函数将可作为现有模型中Gaussian copula函数的一个比较恰当的替代选择。
其次，基于我国目前信用债券市场不够成熟、没有可靠的信用数据可获得的现实，本文利用资本市场这一个公开的、比较有效的信息源提供的数据信息来构造行业收益指数时间序列，估计行业收益指数的边际分布和相关结构参数。在运用偏t-GARCH(1,1)对行业收益指数的边际分布建模时，考虑到现有的偏t分布函数在描述偏度时缺乏灵活性，本文在现有偏t分布变量构造的基础上，提出了一种新的构造方法。通过模拟比较，发现新构造的偏t分布在表现分布的有偏性方面优于现有方法。同时利用数据分别对Gaussian copula函数和t-copula函数的行业收益指数相关结构模型进行了参数估计和拟合优度检验。检验结果表明，由于t-copula函数考虑到了行业收益指数间的尾部相关性，因而比Gaussian copula函数有更好的拟合度。
最后，在估计的相关结构模型基础上，本文通过一个假想组合详细讨论了信用风险组合模型中相关结构的变化对组合损失分布和一致性风险量度所产生的影响程度。为了提高预期短缺ES估计的精度，本文利用重要性抽样方法计算了相关结构分别为Gaussian copula函数和t-copula函数时的组合损失分布和风险量度。结果表明：相关结构的变化对组合损失分布产生显著的影响，尤其是在损失分布的尾部，导致两种相关结构模型产生的风险量度间的差异随着置信水平的提高而增加；另一方面，VaR和ES间的差异随着置信水平的提高而减小。
The modelling of defaults dependence has been a key field for risk managementof credit portfolio. Using the facility and flexibility of copula function in the modelingof dependence structure, the paper studys the modeling of credit portfolio basedcopula funtion, and analyses the effect of the change of dependence structure ofdefaults on the portfolio loss distribution and coherent risk measure.
Firstly, based on the latent variable model, one of the existing models of creditportfolio, and aimed at its drawbacks in dependence structure, the paper proposes amodel framework of credit portfolio, which is based on copula functions and wherethe indexes of industry return are considered as a systematic risk factors, discusses thecalculation of joint probability for various default states of credit portfolio in theframework, illustrates the approach of determining the parameter in the model and thechoose of copula functions. The analysis shows t-copula function is a preferablesubstitute for Gaussian copula of the existing models when using copula functions tomodel dependence structure of defaults.
Secondly, due to the fact that,in Chinese, the market of credit bonds aredeveloping, and that the reliable credit datas are not available, using the datainformation provided by the capital market,which is open and effective, the paperconstructs the time series of index of industry return, and estimates the parameters ofthe marginal distribution and dependence structure. When using skew t-GARCH(1,1)to model the marginal distribution of index of industry return, the paper develops anew construction of skew student t distribution based on the existing skew studentt distribution which is lack of flexibility in describing the skewness of distribution.In terms of simulation, It is found that the new skew student t distribution is betterthan the existing in describing the skewness of distribution. Also, the parameters ofdependence structure of index of industry return for Gaussian copula and t-copulafunctions are estimated, respectively. The test results of the good-of-fitness show thatt-copula function has better good-of-fitness than Gaussian copula function, due tot-copula function considering the tail dependence of index of industry return.
Lastly, based on the above estimated model of dependence structure, the degree of effect of the change of dependence structure in credit portfolio on the portfolio lossdistribution and coherent risk measure is discussed by a constructed creidit portfolio.In order to improve the estimation accuracy of ES, the paper calculates the portfolioloss distributions and risk measures for the dependence strcture of Gaussian copulafunction and t-copula function by using Important Sampling approach. The resultsshow that the change of dependence strctures has a significant effect on the portfolioloss distribution, especially on the tail of portfolio loss distribution, and this effectmakes the difference between the risk measure caused by the two dependence strcturemodel increase with the confidence level, on the other hand, the difference betweenVaR and ES decreases with the confidence level.
引文
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