商业银行操作风险与系统性风险度量研究
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摘要
本文从商业银行风险管理的实际需求出发,从精细化风险管理的角度着手,采用风险度量的技术对风险进行建模、估计和分析。研究的风险度量主体不是传统商业银行的信用风险和市场风险,而是新资本协议要求必须分配资本金的操作风险和第三版巴塞尔资本协议关注的银行系统性风险。
本文研究的主要内容和创新点包括以下几个方面：
首先,本文对风险度量的理论和方法进行了抽象、归纳和总结,给出了风险度量的流程和思路。其包括了基础、关键、实现和优化四个环节,并将风险建模细分为八个步骤,该风险度量思路的提出是对以往项目经历和论文写作经验的总结和凝练,为风险度量提供理论基础和指导方法。
其次,对商业银行操作风险的度量及其资本金分配进行了研究。对影响操作风险度量结果的损失厚尾性、计算精度问题、模型稳定性问题、数据有偏性问题、数据陈旧性问题、操作风险的相关性问题进行了研究：
(1)针对操作风险损失厚尾性的特点和一阶近似算法准确性较差的问题,提出采用二阶近似的算法计算操作风险及其资本金。根据次指数分布的特点推导出基于二阶近似的操作风险解析解,针对厚尾性的问题采用广义帕累托分布拟合极值损失,并在此基础上得到操作风险。并将结果与一阶近似模型、均值修正模型和模拟结果进行了对比分析,发现二阶近似模型提高了结果的计算精度。
(2)针对操作风险参数方法结果的不稳定性问题,提出了操作风险度量的组合估计模型。组合估计模型把贝叶斯的思想引进到操作风险的估计模型中,将风险估计分为两个层次：单个模型的估计和估计的信念。组合估计方法中估计结果是模型结果的线性函数,该方法集成不同厚尾性分布的特点、同时增强模型结果的稳定性和鲁棒性。
(3)针对数据有偏性与陈旧性问题、操作风险的相关性问题,提出了基于条件分布—广义线性模型—copula函数的多维集成模型来度量操作风险。该模型在损失分布的框架下,采用条件分布对有偏的左截尾数据进行建模解决数据有偏性问题；通过建立操作风险与宏观经济和银行自身变量的稳定关系来预测未来操作风险的发生情况,来解决数据陈旧的问题；通过copula函数来对操作风险之间的相关性进行建模,解决操作风险的相关性问题；并综合这些方法建立了基于该集成方法的模拟程序。
再次,对银行系统性风险度量进行了研究。在分析银行系统性风险机理和特征的基础上,对系统性风险度量中考虑银行关联性问题、风险相关性问题、风险的亲周期问题、流动性风险的内生性问题：
(1)基于银行之间关联性的视角,采用银行间市场的网络分析方法度量了银行系统性风险。研究内容包括了：银行业系统性风险的机理分析,其包括了银行间市场和外部市场两个方面,为度量研究工作奠定了基础；银行间市场和风险传染的模型实例研究,通过实例说明银行市场是系统性风险的重要来源,论证了采用该方法的可行性；银行间市场的网络结构的矩阵表达和传染过程分析的数学表达；基于最大熵方法的银行间资产负债矩阵的求解；银行间市场模式对系统性风险的影响,发现银行间市场结构对银行系统性风险的影响较大；然后,设计三种特定银行间市场模式下的矩阵求解算法,使得求解结果更加符合实际银行市场间结构；最后,采用中国银行业的数据进行了实证分析,发现在次贷危机转变为全球金融危机的过程中中国银行业系统性风险也出现了增大的趋势。
(2)提出了基于自上而下的系统性风险的度量方法。基于银行系统性风险是银行面临的整体风险的视角,在研究风险之间相关性表达基础上,采用自上而下方法度量银行系统性风险。在考虑信用风险、市场风险和操作风险相关性的基础上,分别采用方差／协方差方法和copula函数方法利用相关性矩阵和相依函数刻画相关性的基础上来集成多种风险,最后得到银行系统性风险。自上而下方法基于实际的各种风险的分布或者风险值,比较符合目前中国商业管理各种风险分开度量和管理的实际,容易在银行业进行运用和推广
(3)提出了自下而上的系统性风险的度量方法。根据银行系统性风险的机理,考虑银行间市场与外部市场两种市场,综合了本次金融危机暴露的系统性风险的时间维度上亲周期性、空间维度上的传染性和流动性风险的重要性特征,研究基于情景分析的至下而上方法度量银行系统性风险。该模型考虑了信用风险、市场风险、传染风险和流动性风险。对于信用风险的亲周期性的特征通过建立违约概率与宏观经济变量和金融变量的关系来对信用风险违约率进行建模,在设定情景的基础上得到不同情境下的信用风险违约率。然后结合信用风险的违约损失率和风险暴露因子,采用CreditRisk+模型得到信用风险损失。对于市场风险,在与信用风险同样的情景下,分析不同情景下市场风险因子对表内外风险暴露价值的影响。对于传染风险主要是将网络分析方法应运到综合模型中。信用风险、市场风险、传染风险是清算风险,银行不存在清算风险并不代表银行具有稳定性,流动性风险是银行面临的又一重要的风险,因此在模型中将银行融资风险纳入到整体框架中来,而且融资流动性是银行信用风险的内生风险。
According to the actual requirements of the commercial bank risk management, this thesis is devoted to the investigation of risk quantification, including risk modeling, estimation and analysis from the perspective of the refinement of risk management. Risk models are beyond those techniques used for measuring the standard risk types market risk and credit risk, therefore, we consider the quantification of operational risk and systemic risk. Operational risk is a risk that bank must allocate capital in Basel Ⅱ, and Basel Ⅲ highlights the importance of reducing systemic risk to achieve the goal of overall financial stability.
Firstly, the procedure and the general framework of the risk quantification are given by abstracting and summarizing previous project experience and paper writing experience. This general framework has four linked loops:foundation, key point, realization and optimization, and it can be divided into eight steps. The law and the general framework can provide a theoretical basis and guidance for risk measurement.
Secondly, operational risk measurement and capital allocated are researched considering fat tail, calculation accuracy, result instability, data bias, old data, and dependence of operational risk.
(1) For operational risk loss fat tail (which in practice they are) and poor accuracy of first-order closed-form approximation algorithm, a second-order closed-form approximation algorithm is proposed to calculate the operational risk and operational risk capital. The second-order closed-form approximation for operational risk Value-at-Risk can be obtained when sub-exponential distribution is used, and in this paper the generalized Pareto distribution (one of sub-exponential distribution) is used. We find that the second-order closed-form approximation is the most accuracy among first-order closed-form approximation, refinement first-order closed-form approximation by mean correction, and second-order closed-form approximation by comparing these results with enough large simulation results.
(2) We propose a combination model to estimate operational risk in order to integrate characteristics of different heavy-tailed distributions and to reduce uncertainty of operational risk model. Operational risk estimation is divided into two levels: operational risk estimation by single model and belief of operational risk estimation by single model, which is similar to Bayesian estimation model. Measured variable has the linear relationship with model variables, empirical analysis shows the combinational model performs better than any single model and can even outperform the best single model. So the combination model can integrate characteristics of different heavy-tailed distributions and reduce uncertainty of operational risk.
(3) We propose a risk integrated method to resolve problems of data bias, old data, and dependence among operational risk units in operational quantification. We measure operational risk and operational risk capital using a multivariate model under the loss distribution approach framework. Firstly, conditional distribution is used to model left-truncated data. Secondly, general linear model is employed to forecast the frequency of next year's operational risk. Thirdly, copula functions are employed to model the dependence between the operational risk units. We use the integrated approach to measure operational risk and operational risk capital of Chinese commercial banks by our designed simulation procedures. Empirical analysis shows that the approach allows the allocation of capital in a more efficient way than the standard approach.
Thirdly, bank systemic risk measurement is researched considering bank association, risk dependence, risk pro-cyclical and endogeneity of risk based on the mechanism and characteristics of the analysis of bank systemic risk.
(1) Network analysis method is empoyed to measure bank systemic risk by using inter-bank market data from the perspective of bank association. This study includes: the mechanism and characteristics analysis of systemic risk, which are foundation of bank systemic risk measurement;"Domino Model" and "Beyond the Domino Model" both demonstrate that inter-bank market is the important channel of systemic risk and network analysis is feasibe method; the asset-debt matrix expression of the network structure of inter-bank market and the mathematical expression of contagion process are researched; the asset-debt matrix is sloved by the maximum entropy method; the influence of inter-bank market structure to systemic risk is researched, and we find inter-bank market structure can severely change systemic risk, and then three specific inter-bank market structure are elaborated, asset-debt matrix solution algorithms are also given in line with the actual banking market structure; finally, we analyse Chinese banking systemic risk using the network analysis approach, and find systemic risk increased when subprime mortgage crisis extended into the global financial crisis.
(2) Top-down model is proposed to measure bank systemic risk. From the perspective of risk integration and risk dependence, top-down method is proposed to measure bank systemic risk considering risk denpendence among different risk types and separate risk measurement and management practice in banking. Variance/ covariance method and copula method are respectively used to integrate credit risk, market risk and operational risk to get systemic risk, and risk dependence is expressed by risk correlation matrix and copula function. Top-down method integrates different types risk in high level (for example, risk distribution or risk value), but top-down method does not consider the reason of risk dependence. It can be easily used in banking because it is in line with risk measurement and management practice of dividing bank risk into different type risks, and separately measuring and managing these risks.
(3) Bottom-up model is also proposed to measure systemic risk. According to the mechanism of bank systemic risk (inter-bank market and external market), bottom-up method based on scenario analysis is used to measure bank systemic risk considering bank association, risk dependence, risk pro-cyclical, endogeneity and importance of liquidity risk in this crisis. The scenario analysis based bottom-up model takes into account credit risk, market risk, contagion risk and liquidity risk. We distinguish debt that is held between banks from debt held with parties outside of the banking system. While the value of interbank debt is determined in the network analysis, the potential losses from non-interbank debt are captured by a credit risk model. For risk pro-cyclical characteristics, a model translates macroeconomic risk factor changes to default probabilities for different industry sectors. The CreditRisk+model uses default probabilities, loss given default and exposure at default to estimate credit risk in this paper. With respect to market, we construct a mapping from market risk factors to portfolio positions in line with the same credit risk scenarios. We also consider liquidity risk in the model besides credit risk, market risk and contagion risk, and we introduce endogenous funding liquidity into the bottom-up systemic risk assessment framework.
本文研究的主要内容和创新点包括以下几个方面：
首先,本文对风险度量的理论和方法进行了抽象、归纳和总结,给出了风险度量的流程和思路。其包括了基础、关键、实现和优化四个环节,并将风险建模细分为八个步骤,该风险度量思路的提出是对以往项目经历和论文写作经验的总结和凝练,为风险度量提供理论基础和指导方法。
其次,对商业银行操作风险的度量及其资本金分配进行了研究。对影响操作风险度量结果的损失厚尾性、计算精度问题、模型稳定性问题、数据有偏性问题、数据陈旧性问题、操作风险的相关性问题进行了研究：
(1)针对操作风险损失厚尾性的特点和一阶近似算法准确性较差的问题,提出采用二阶近似的算法计算操作风险及其资本金。根据次指数分布的特点推导出基于二阶近似的操作风险解析解,针对厚尾性的问题采用广义帕累托分布拟合极值损失,并在此基础上得到操作风险。并将结果与一阶近似模型、均值修正模型和模拟结果进行了对比分析,发现二阶近似模型提高了结果的计算精度。
(2)针对操作风险参数方法结果的不稳定性问题,提出了操作风险度量的组合估计模型。组合估计模型把贝叶斯的思想引进到操作风险的估计模型中,将风险估计分为两个层次：单个模型的估计和估计的信念。组合估计方法中估计结果是模型结果的线性函数,该方法集成不同厚尾性分布的特点、同时增强模型结果的稳定性和鲁棒性。
(3)针对数据有偏性与陈旧性问题、操作风险的相关性问题,提出了基于条件分布—广义线性模型—copula函数的多维集成模型来度量操作风险。该模型在损失分布的框架下,采用条件分布对有偏的左截尾数据进行建模解决数据有偏性问题；通过建立操作风险与宏观经济和银行自身变量的稳定关系来预测未来操作风险的发生情况,来解决数据陈旧的问题；通过copula函数来对操作风险之间的相关性进行建模,解决操作风险的相关性问题；并综合这些方法建立了基于该集成方法的模拟程序。
再次,对银行系统性风险度量进行了研究。在分析银行系统性风险机理和特征的基础上,对系统性风险度量中考虑银行关联性问题、风险相关性问题、风险的亲周期问题、流动性风险的内生性问题：
(1)基于银行之间关联性的视角,采用银行间市场的网络分析方法度量了银行系统性风险。研究内容包括了：银行业系统性风险的机理分析,其包括了银行间市场和外部市场两个方面,为度量研究工作奠定了基础；银行间市场和风险传染的模型实例研究,通过实例说明银行市场是系统性风险的重要来源,论证了采用该方法的可行性；银行间市场的网络结构的矩阵表达和传染过程分析的数学表达；基于最大熵方法的银行间资产负债矩阵的求解；银行间市场模式对系统性风险的影响,发现银行间市场结构对银行系统性风险的影响较大；然后,设计三种特定银行间市场模式下的矩阵求解算法,使得求解结果更加符合实际银行市场间结构；最后,采用中国银行业的数据进行了实证分析,发现在次贷危机转变为全球金融危机的过程中中国银行业系统性风险也出现了增大的趋势。
(2)提出了基于自上而下的系统性风险的度量方法。基于银行系统性风险是银行面临的整体风险的视角,在研究风险之间相关性表达基础上,采用自上而下方法度量银行系统性风险。在考虑信用风险、市场风险和操作风险相关性的基础上,分别采用方差／协方差方法和copula函数方法利用相关性矩阵和相依函数刻画相关性的基础上来集成多种风险,最后得到银行系统性风险。自上而下方法基于实际的各种风险的分布或者风险值,比较符合目前中国商业管理各种风险分开度量和管理的实际,容易在银行业进行运用和推广
(3)提出了自下而上的系统性风险的度量方法。根据银行系统性风险的机理,考虑银行间市场与外部市场两种市场,综合了本次金融危机暴露的系统性风险的时间维度上亲周期性、空间维度上的传染性和流动性风险的重要性特征,研究基于情景分析的至下而上方法度量银行系统性风险。该模型考虑了信用风险、市场风险、传染风险和流动性风险。对于信用风险的亲周期性的特征通过建立违约概率与宏观经济变量和金融变量的关系来对信用风险违约率进行建模,在设定情景的基础上得到不同情境下的信用风险违约率。然后结合信用风险的违约损失率和风险暴露因子,采用CreditRisk+模型得到信用风险损失。对于市场风险,在与信用风险同样的情景下,分析不同情景下市场风险因子对表内外风险暴露价值的影响。对于传染风险主要是将网络分析方法应运到综合模型中。信用风险、市场风险、传染风险是清算风险,银行不存在清算风险并不代表银行具有稳定性,流动性风险是银行面临的又一重要的风险,因此在模型中将银行融资风险纳入到整体框架中来,而且融资流动性是银行信用风险的内生风险。
According to the actual requirements of the commercial bank risk management, this thesis is devoted to the investigation of risk quantification, including risk modeling, estimation and analysis from the perspective of the refinement of risk management. Risk models are beyond those techniques used for measuring the standard risk types market risk and credit risk, therefore, we consider the quantification of operational risk and systemic risk. Operational risk is a risk that bank must allocate capital in Basel Ⅱ, and Basel Ⅲ highlights the importance of reducing systemic risk to achieve the goal of overall financial stability.
Firstly, the procedure and the general framework of the risk quantification are given by abstracting and summarizing previous project experience and paper writing experience. This general framework has four linked loops:foundation, key point, realization and optimization, and it can be divided into eight steps. The law and the general framework can provide a theoretical basis and guidance for risk measurement.
Secondly, operational risk measurement and capital allocated are researched considering fat tail, calculation accuracy, result instability, data bias, old data, and dependence of operational risk.
(1) For operational risk loss fat tail (which in practice they are) and poor accuracy of first-order closed-form approximation algorithm, a second-order closed-form approximation algorithm is proposed to calculate the operational risk and operational risk capital. The second-order closed-form approximation for operational risk Value-at-Risk can be obtained when sub-exponential distribution is used, and in this paper the generalized Pareto distribution (one of sub-exponential distribution) is used. We find that the second-order closed-form approximation is the most accuracy among first-order closed-form approximation, refinement first-order closed-form approximation by mean correction, and second-order closed-form approximation by comparing these results with enough large simulation results.
(2) We propose a combination model to estimate operational risk in order to integrate characteristics of different heavy-tailed distributions and to reduce uncertainty of operational risk model. Operational risk estimation is divided into two levels: operational risk estimation by single model and belief of operational risk estimation by single model, which is similar to Bayesian estimation model. Measured variable has the linear relationship with model variables, empirical analysis shows the combinational model performs better than any single model and can even outperform the best single model. So the combination model can integrate characteristics of different heavy-tailed distributions and reduce uncertainty of operational risk.
(3) We propose a risk integrated method to resolve problems of data bias, old data, and dependence among operational risk units in operational quantification. We measure operational risk and operational risk capital using a multivariate model under the loss distribution approach framework. Firstly, conditional distribution is used to model left-truncated data. Secondly, general linear model is employed to forecast the frequency of next year's operational risk. Thirdly, copula functions are employed to model the dependence between the operational risk units. We use the integrated approach to measure operational risk and operational risk capital of Chinese commercial banks by our designed simulation procedures. Empirical analysis shows that the approach allows the allocation of capital in a more efficient way than the standard approach.
Thirdly, bank systemic risk measurement is researched considering bank association, risk dependence, risk pro-cyclical and endogeneity of risk based on the mechanism and characteristics of the analysis of bank systemic risk.
(1) Network analysis method is empoyed to measure bank systemic risk by using inter-bank market data from the perspective of bank association. This study includes: the mechanism and characteristics analysis of systemic risk, which are foundation of bank systemic risk measurement;"Domino Model" and "Beyond the Domino Model" both demonstrate that inter-bank market is the important channel of systemic risk and network analysis is feasibe method; the asset-debt matrix expression of the network structure of inter-bank market and the mathematical expression of contagion process are researched; the asset-debt matrix is sloved by the maximum entropy method; the influence of inter-bank market structure to systemic risk is researched, and we find inter-bank market structure can severely change systemic risk, and then three specific inter-bank market structure are elaborated, asset-debt matrix solution algorithms are also given in line with the actual banking market structure; finally, we analyse Chinese banking systemic risk using the network analysis approach, and find systemic risk increased when subprime mortgage crisis extended into the global financial crisis.
(2) Top-down model is proposed to measure bank systemic risk. From the perspective of risk integration and risk dependence, top-down method is proposed to measure bank systemic risk considering risk denpendence among different risk types and separate risk measurement and management practice in banking. Variance/ covariance method and copula method are respectively used to integrate credit risk, market risk and operational risk to get systemic risk, and risk dependence is expressed by risk correlation matrix and copula function. Top-down method integrates different types risk in high level (for example, risk distribution or risk value), but top-down method does not consider the reason of risk dependence. It can be easily used in banking because it is in line with risk measurement and management practice of dividing bank risk into different type risks, and separately measuring and managing these risks.
(3) Bottom-up model is also proposed to measure systemic risk. According to the mechanism of bank systemic risk (inter-bank market and external market), bottom-up method based on scenario analysis is used to measure bank systemic risk considering bank association, risk dependence, risk pro-cyclical, endogeneity and importance of liquidity risk in this crisis. The scenario analysis based bottom-up model takes into account credit risk, market risk, contagion risk and liquidity risk. We distinguish debt that is held between banks from debt held with parties outside of the banking system. While the value of interbank debt is determined in the network analysis, the potential losses from non-interbank debt are captured by a credit risk model. For risk pro-cyclical characteristics, a model translates macroeconomic risk factor changes to default probabilities for different industry sectors. The CreditRisk+model uses default probabilities, loss given default and exposure at default to estimate credit risk in this paper. With respect to market, we construct a mapping from market risk factors to portfolio positions in line with the same credit risk scenarios. We also consider liquidity risk in the model besides credit risk, market risk and contagion risk, and we introduce endogenous funding liquidity into the bottom-up systemic risk assessment framework.
引文
Abramowitz, M., & Stegun, R. A.. Handbook of Mathematical Functions. New York:Dover Pub., 1968.
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