信用风险相关性度量模型的构建及其应用研究
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摘要
信用是市场经济的基石,违约及信用风险倍受金融界关注。现代信用风险通常具有易传染性特征,进入21世纪以来,爆发在实体经济领域和金融市场的信用风险传染事件层出不穷。在此背景下,在信用风险管理过程中需要考虑信用风险之间的相关性,特别是极端风险事件下的相关性。所以,考虑信用风险相关性,并在此基础上实施信贷组合管理成为了信用风险管理的一种发展趋势。目前,学界和业界对信用风险的建模进行了较多的研究,但是对信贷组合管理中的相关性度量还较少进行系统深入的分析。本文以信用相关性为研究对象,沿着机理分析到模型和实证研究,再到应用研究的思路,对信用风险相关性的形成机理、度量模型及其在信贷组合管理中的应用进行系统的探索。
在信用风险相关性的机理研究部分,首先界定信用风险以及信用风险相关性等概念,并分析信用风险的形成原因;接着探寻信用风险相关性产生的机理,认为宏观经济环境、宏观经济变量、政治及政策事件、公共安全事件、技术因素和社会因素等共同因素,产品市场和股权市场上的信用风险传染,以及耦合因素是信用风险产生的重要原因。
在信用风险及其相关性度量模型的构建部分,对信用风险及相关性的度量进行了相应的建模,以1990～2010年中国上市公司的数据进行了实证研究,检验了模型的有效性,并运用相关模型描述了样本期内信用风险变化的特征和规律。首先,考虑信用风险的非线性变化特征,运用信用风险评价模型为基础,建立了行业信用风险指数,并对行业信用风险进行了分层聚类。综合MDA模型、SVM模型以及KMV模型的Hybrid模型较好地融合了财务信息与资本市场相关信息,能有效地对企业信用风险进行评价；在亚超度量空间下,运用最小生成树方法对行业信用风险进行分层聚类,对信贷组合管理实现了降维处理,认为电力、煤气及水的生产和供应业,批发、零售、贸易业,石油、化学、塑胶、塑料以及信息技术业)可以作为强周期性行业、防御型行业、弱周期性行业以及成长型行业的代表行业,Johnasen协整检验表明这4类行业的信用风险存在长期协整关系。然后,基于静态Copula模型,对信用风险相关性的总体特征进行了描述。从总体上看,行业信用风险相关性具有非对称的特征,这表现为信用风险相关性在下尾处对外界环境的变化比较敏感。再后,考虑信用风险相关性的动态变化、跳跃以及状态转换特征,构建了二元稳结构动态Copula模型、跳跃变结构和状态转换变结构Copula模型。K-S检验和A-D检验的结果表明Jump Clayton Copula函数的拟合优度较高,综合考虑各模型所计算出的动态相关系数表明样本行业的信用风险相关程度比较高,并表现出非对称、下尾处敏感、易受系统风险影响等特征。最后,构建了信用风险相关性度量的多元Copula模型。分别基于Canonical藤和D藤结构,建立Pair Copula模型,进行相应的参数估计,得到了能较准确度量多元特征的信用风险相关性度量模型。实证结果表明,Canonical藤分解结构下,多元Copula的拟合效果相对较佳,对比Clayton Pair Copula和Jump Clayton Copula模型所计算出的信用风险相关系数可以发现,Clayton pair copula所计算出的信用风险相关系数相对较小,表明多个信贷资产信用风险联合变动的可能性相对较低。
在信用风险相关性度量模型的应用研究部分,提出基于Copula VaR模型的商业银行信贷组合管理的方法。以Pair Copula模型为基础,设计信贷组合管理的Copula VaR的计算步骤,以样本商业银行为例,对其信贷组合进行分析,提出其信贷组合优化的方向。同时,根据信贷组合管理的现状,提出商业银行信贷组合管理的实施对策,为商业银行信贷组合管理的实施提供可供选择的建议。
Credit is the cornerstone of market economy, and the harm of credit risk has been widely paid attention by financial industry. Modern credit risk is featured of contagion, and the credit risk burst of one financial institution or industrial company may lead to a wide range of credit default, thus the credit risk may spread nonlinearly among the enterprises and financial institutions. Since the21st century, the credit risk contagion events among the real economy and the financial market have emerged enomorously, and under this background, the correlation among credit risks especially extreme risk events should be taken into consideration in the process of credit risk management. Thus, the implementation of credit portfolio management has become a development trend for credit risk management.
A large amount of researches have been conducted to detect the credit risk, but there is still not paid enough attention on the measurement of the correlation in the credit portfolio management. Therefore, this paper chooses the credit relationship as the study object, and a theoretical analysis, modeling analysis and application study are respectively conducted to explore the mechanism of credit risk correlation, evaluate the correlation of credit risk, and apply the correlation in credit portfolio management.
In the section of mechanism study of credit risk correlation, some related concepts including credit risk, credit risk correlation are defined, and then the formation mechanism of credit risk correlation. And the factors influencing the credit risk correlation contain common factors such as macroscopically economy environment, macro economic variables, political and policy events, public safety events, technical factors and social factor, contagion factors from market and equity market, and coupling factors of contagious and common factors.
In the section of credit risk and correlation modeling, credit risk and correlation evaluation models are constructed by using Chinese Listed Company data from1990to2010, and the effectiveness of the models are examined, then the characteristics of credit risk correlation are evaluated through the model analysis. This section is organized as follows. Firstly, industry credit risk indexes are established based on credit risk evaluation models, and a hierarchical cluster analysis is conducted for the industry credit risk. The Hybrid model integrating MDA model, SVM model and KMV model can better synthesize financial information and capital market information and effectively evaluate enterprises' credit risk. In the SU space, the minimum spamming tree is applied to conduct hierarchical cluster on the industry credit risk for the purpose of dimension reduction. The empirical results show that electronically power industry, food industry, petrochemical industry and information technology industry can represent the strong cyclical industry, defensive industry, weak cyclical industry and growing industry. The Johnasen cointegration test shows that there is cointegration relationship among the above industries'credit risk. Secondly, the overall features of credit risk coorelation are described based on the static Copula models. On the whole, industry credit risk correlation has an asymmetric characteristic, and the credit risk correlation is more sensitive to disadvantergous external environment changes. Thirdly, considering the characteristics of dynamic change, jump and regime switching, the bivariate dynamic Copula models, Jump Copula model and Markov Regime Switching Copula models are respectively built. The KS test and AD test shows that the Jump Clayton copula is superior to other Copula models by judging the goodness fit of the models. And the dynamic correlation coefficient indicates that the credit correlation of sample industries is high and is featured with asymmetric, low tail sensibility, and susceptible to systematic risks. Fourthly, a multivariate copula model is constructed to measure the credit risk correlation. Under the pair copula framework, the multivariate copula is decomposed following the Canonical vine and D vine structure. A multivariate copula model that can accurately describe the multivariate credit risk correlation is acquired through the empirical study. Additionally, the multivariate correlation is relatively lower than the bivariate correlation, indicating that multiple credit assets jointly change with a relatively lower possibility.
In the section of application study of the credit risk correlation models, the Copula VaR model is applied in credit portfolio management. On the basis of Pair Copula model, the critical steps of credit portfolio management based on the Copula VaR model is designed. By analyzing the credit portfolio of the sample commercial bank, the optimization directs of the credit portfolio management are pointed out. And finally, based on the theoretical and empirical study, some available suggestions for the implementation of commercial banks'credit portfolio management are proposed.
在信用风险相关性的机理研究部分,首先界定信用风险以及信用风险相关性等概念,并分析信用风险的形成原因;接着探寻信用风险相关性产生的机理,认为宏观经济环境、宏观经济变量、政治及政策事件、公共安全事件、技术因素和社会因素等共同因素,产品市场和股权市场上的信用风险传染,以及耦合因素是信用风险产生的重要原因。
在信用风险及其相关性度量模型的构建部分,对信用风险及相关性的度量进行了相应的建模,以1990～2010年中国上市公司的数据进行了实证研究,检验了模型的有效性,并运用相关模型描述了样本期内信用风险变化的特征和规律。首先,考虑信用风险的非线性变化特征,运用信用风险评价模型为基础,建立了行业信用风险指数,并对行业信用风险进行了分层聚类。综合MDA模型、SVM模型以及KMV模型的Hybrid模型较好地融合了财务信息与资本市场相关信息,能有效地对企业信用风险进行评价；在亚超度量空间下,运用最小生成树方法对行业信用风险进行分层聚类,对信贷组合管理实现了降维处理,认为电力、煤气及水的生产和供应业,批发、零售、贸易业,石油、化学、塑胶、塑料以及信息技术业)可以作为强周期性行业、防御型行业、弱周期性行业以及成长型行业的代表行业,Johnasen协整检验表明这4类行业的信用风险存在长期协整关系。然后,基于静态Copula模型,对信用风险相关性的总体特征进行了描述。从总体上看,行业信用风险相关性具有非对称的特征,这表现为信用风险相关性在下尾处对外界环境的变化比较敏感。再后,考虑信用风险相关性的动态变化、跳跃以及状态转换特征,构建了二元稳结构动态Copula模型、跳跃变结构和状态转换变结构Copula模型。K-S检验和A-D检验的结果表明Jump Clayton Copula函数的拟合优度较高,综合考虑各模型所计算出的动态相关系数表明样本行业的信用风险相关程度比较高,并表现出非对称、下尾处敏感、易受系统风险影响等特征。最后,构建了信用风险相关性度量的多元Copula模型。分别基于Canonical藤和D藤结构,建立Pair Copula模型,进行相应的参数估计,得到了能较准确度量多元特征的信用风险相关性度量模型。实证结果表明,Canonical藤分解结构下,多元Copula的拟合效果相对较佳,对比Clayton Pair Copula和Jump Clayton Copula模型所计算出的信用风险相关系数可以发现,Clayton pair copula所计算出的信用风险相关系数相对较小,表明多个信贷资产信用风险联合变动的可能性相对较低。
在信用风险相关性度量模型的应用研究部分,提出基于Copula VaR模型的商业银行信贷组合管理的方法。以Pair Copula模型为基础,设计信贷组合管理的Copula VaR的计算步骤,以样本商业银行为例,对其信贷组合进行分析,提出其信贷组合优化的方向。同时,根据信贷组合管理的现状,提出商业银行信贷组合管理的实施对策,为商业银行信贷组合管理的实施提供可供选择的建议。
Credit is the cornerstone of market economy, and the harm of credit risk has been widely paid attention by financial industry. Modern credit risk is featured of contagion, and the credit risk burst of one financial institution or industrial company may lead to a wide range of credit default, thus the credit risk may spread nonlinearly among the enterprises and financial institutions. Since the21st century, the credit risk contagion events among the real economy and the financial market have emerged enomorously, and under this background, the correlation among credit risks especially extreme risk events should be taken into consideration in the process of credit risk management. Thus, the implementation of credit portfolio management has become a development trend for credit risk management.
A large amount of researches have been conducted to detect the credit risk, but there is still not paid enough attention on the measurement of the correlation in the credit portfolio management. Therefore, this paper chooses the credit relationship as the study object, and a theoretical analysis, modeling analysis and application study are respectively conducted to explore the mechanism of credit risk correlation, evaluate the correlation of credit risk, and apply the correlation in credit portfolio management.
In the section of mechanism study of credit risk correlation, some related concepts including credit risk, credit risk correlation are defined, and then the formation mechanism of credit risk correlation. And the factors influencing the credit risk correlation contain common factors such as macroscopically economy environment, macro economic variables, political and policy events, public safety events, technical factors and social factor, contagion factors from market and equity market, and coupling factors of contagious and common factors.
In the section of credit risk and correlation modeling, credit risk and correlation evaluation models are constructed by using Chinese Listed Company data from1990to2010, and the effectiveness of the models are examined, then the characteristics of credit risk correlation are evaluated through the model analysis. This section is organized as follows. Firstly, industry credit risk indexes are established based on credit risk evaluation models, and a hierarchical cluster analysis is conducted for the industry credit risk. The Hybrid model integrating MDA model, SVM model and KMV model can better synthesize financial information and capital market information and effectively evaluate enterprises' credit risk. In the SU space, the minimum spamming tree is applied to conduct hierarchical cluster on the industry credit risk for the purpose of dimension reduction. The empirical results show that electronically power industry, food industry, petrochemical industry and information technology industry can represent the strong cyclical industry, defensive industry, weak cyclical industry and growing industry. The Johnasen cointegration test shows that there is cointegration relationship among the above industries'credit risk. Secondly, the overall features of credit risk coorelation are described based on the static Copula models. On the whole, industry credit risk correlation has an asymmetric characteristic, and the credit risk correlation is more sensitive to disadvantergous external environment changes. Thirdly, considering the characteristics of dynamic change, jump and regime switching, the bivariate dynamic Copula models, Jump Copula model and Markov Regime Switching Copula models are respectively built. The KS test and AD test shows that the Jump Clayton copula is superior to other Copula models by judging the goodness fit of the models. And the dynamic correlation coefficient indicates that the credit correlation of sample industries is high and is featured with asymmetric, low tail sensibility, and susceptible to systematic risks. Fourthly, a multivariate copula model is constructed to measure the credit risk correlation. Under the pair copula framework, the multivariate copula is decomposed following the Canonical vine and D vine structure. A multivariate copula model that can accurately describe the multivariate credit risk correlation is acquired through the empirical study. Additionally, the multivariate correlation is relatively lower than the bivariate correlation, indicating that multiple credit assets jointly change with a relatively lower possibility.
In the section of application study of the credit risk correlation models, the Copula VaR model is applied in credit portfolio management. On the basis of Pair Copula model, the critical steps of credit portfolio management based on the Copula VaR model is designed. By analyzing the credit portfolio of the sample commercial bank, the optimization directs of the credit portfolio management are pointed out. And finally, based on the theoretical and empirical study, some available suggestions for the implementation of commercial banks'credit portfolio management are proposed.
引文
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