基于损失分布法的重尾性操作风险的度量精度与管理研究
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摘要
现有文献研究表明存在一类操作风险，其操作损失强度为重尾性分布。极值模型法是度量重尾性风险的最佳方法。目前在业界损失分布法是操作风险的主要度量方法。由此，本文将极值模型法和损失分布法结合起来，研究重尾性操作风险的度量精度与管理问题。首先，分析了重尾性操作风险度量偏差的影响因素；然后，以相关实证研究为基础，分别在两类极值模型(BMM类模型和GPD类模型)中选择典型的重尾分布，即Weibull分布和Pareto分布作为操作损失强度分布假设，从理论上探讨了高置信度下重尾性操作风险的度量精度和关键管理参数，并进行了示例分析；最后，提出了一种操作损失强度分布模型的选择方法。通过以上研究，得到如下创新性结论。
(1)本文系统探讨了度量偏差的影响因素，发现该偏差的存在具有客观性。影响因素主要有两个方面：一是样本异质性。在内外部损失样本共享数据库中，不仅存在损失门槛差异，而且存在机构内外部环境等差异而导致的样本异质性，从而导致度量偏差。二是度量中存在分布模型外推问题。操作损失样本量稀少，导致在高置信度下度量操作风险时，存在分布模型外推问题。这使度量结果产生不确定性。以上两方面因素使度量偏差不可忽视。
(2)鉴于重尾性操作风险的度量结果在客观上存在偏差，第三章进一步探讨了度量精度。在损失分布法下，操作风险价值的置信区间长度表征操作风险的度量精度。通过对该度量精度的系统研究，得出如下结论：
1)重尾性操作风险度量精度灵敏度的变动仅与形状参数和频数参数有关。以弹性分析方法，通过对不确定性传递系数灵敏度及其变动的理论研究发现，引起不确定性传递系数灵敏度变动的参数仅为形状参数和频数参数，与尺度参数无关，这表明在其他条件不变的情况下，重尾性操作风险度量精度的变动仅与形状参数和频数参数有关。
2)以本章建立的理论模型，可判别度量精度的关键影响参数。随特征参数变动，不仅度量精度会变动，而且其关键影响参数也将变化。示例分析验证了该理论模型的有效性。
(3)从度量的角度判别出对操作风险影响程度最大的特征参数，作为关键管理参数，将度量模型与管理模型联系在一起，使两模型的整合成为可能，而且可据此建立操作风险动态管理系统。
(4)综合第三章和第四章研究结论可知，随特征参数变化，操作风险价值及其度量精度都同时变化，据此，提出监管资本提取方式的改进建议为：在监管资本置信区间的下限提取监管资本，从置信下限到置信上限，配置以无风险资产。由此使被监管机构在资本配置上具有一定灵活性。
(5)在第五章提出了损失强度分布选择的一种方法，即以操作风险管理系统灵敏度最大为标准进行选择。
Previous literatures have shown that there is a class of operational risk which lossseverity is the heavy-tailed Distribution.The Extreme Value Distribution Model isoptimal approach to measure the operational risk.Currently,the Loss DistributionApproach is a main approach to measure the operational risk in the industry.Thus,thispaper combines the Extreme Value Distribution Model with the Loss DistributionApproach to discuss the measurement precision and management of heavy-tailedoperational risk.Firstly,the paper analyses the factors which affect the measurementdeviation of heavy-tailed operational risk.Additionally,basing on some certaindemonstration researches and choosing typical heavy-tailed distribution that regards theWeibull distribution and Pareto distribution as loss severity distribution from twoclasses of Extreme Value Distribution Models(BMM and GPD),the paper discusses themeasurement precision and key management parameters of heavy-tailed operational riskat high confidence level,and gives the demonstrations.And an analysis of modelapplication is illustrated with a numerical example.Furthermore,the paper bringsforward a choosing method of the loss severity distribution.Based on theafore-mentioned studies,this paper gets main innovative conclusions as follow.
(1) The paper discusses the factors that influence the measurement deviation,andfinds out that the existence of this deviation has objectives.There are two influencefactors:One is sample heterogeneity.In inside and outside pool loss datum,there is notonly the difference threshold,but also the distinctions of internal and externalenvironment lead to the sample heterogeneity,which brings about the measurementdeviation.Secondly,there are distribution model extrapolate problems in themeasurement.The loss datum of heavy-tailed operational risk are rare,as a consequence,there are extrapolate problems when we measure operational risk at high confidencelevel,which lead to uncertainty in measurement results.Because of the above factors,the measurement deviation cannot be ignored.
(2) Basing on the deviation of the measurement results of heavy-tailedoperational risk,in Chapter 3,this paper further discusses the measurement precision.Under the Loss Distribution Approach,the confidence intervals' length of Operational VaR represents the measurement precision.After a systematic study of measurementprecision,we have the conclusions as follow.
1) The changes of measurement precision' sensitvity of heavy-tailed operationalVaR just relate with the shape parameter and the frequency parameter.Using theelasticity analysis method,and basing on the theory researches of uncertain propagationcoefficients' sensitvity and its changes,we have the conclusions that the changes ofuncertain propagation coefficients' sensitvity just relate with the shape parameter andthe frequency parameter,but do not relate to the scale parameter.As a result,thechanges of measurement precision' sensitvity of operational VaR just relate with theshape parameter and the frequency parameter if we keep other conditions unchanged.
2) Using the theory model established in this chapter,the key influencingparameters of measurement precision can be distinguished.With changes of thecharacter parameter,there will be changes in measurement precision and changes in keyinfluencing parameters.The numerical example analysis validates the validity of thistheory model.
(3) From the angle of measurement,the character parameters which impact theoperational risk most can be distinguished.As a key management parameter,it leads tothe possibility of the combination of measurement model and management model.Andwe can build the dynamic management system of operational risk and improvemeasurement efficiency.
(4) Integrating of the conclusion in chapter 3 and 4,we can conclude that thereare changes of operational VaR and measurement precision with the changes ofcharacter parameters.Therefore,the extraction method of regulatory capital can bemended.And the regulatory capital equal to the lower confidence limit.From the lowerto upper confidence limit regulatory capital is allocated by a risk-free asset,which givesthe financial institutions flexibility to allocate the capital.
(5) In Chapter Five,this paper propose a selection method of loss severitydistribution that regards the maximum of the sensitivity of supervised systems ofoperational risk as a choosing standard.
(1)本文系统探讨了度量偏差的影响因素，发现该偏差的存在具有客观性。影响因素主要有两个方面：一是样本异质性。在内外部损失样本共享数据库中，不仅存在损失门槛差异，而且存在机构内外部环境等差异而导致的样本异质性，从而导致度量偏差。二是度量中存在分布模型外推问题。操作损失样本量稀少，导致在高置信度下度量操作风险时，存在分布模型外推问题。这使度量结果产生不确定性。以上两方面因素使度量偏差不可忽视。
(2)鉴于重尾性操作风险的度量结果在客观上存在偏差，第三章进一步探讨了度量精度。在损失分布法下，操作风险价值的置信区间长度表征操作风险的度量精度。通过对该度量精度的系统研究，得出如下结论：
1)重尾性操作风险度量精度灵敏度的变动仅与形状参数和频数参数有关。以弹性分析方法，通过对不确定性传递系数灵敏度及其变动的理论研究发现，引起不确定性传递系数灵敏度变动的参数仅为形状参数和频数参数，与尺度参数无关，这表明在其他条件不变的情况下，重尾性操作风险度量精度的变动仅与形状参数和频数参数有关。
2)以本章建立的理论模型，可判别度量精度的关键影响参数。随特征参数变动，不仅度量精度会变动，而且其关键影响参数也将变化。示例分析验证了该理论模型的有效性。
(3)从度量的角度判别出对操作风险影响程度最大的特征参数，作为关键管理参数，将度量模型与管理模型联系在一起，使两模型的整合成为可能，而且可据此建立操作风险动态管理系统。
(4)综合第三章和第四章研究结论可知，随特征参数变化，操作风险价值及其度量精度都同时变化，据此，提出监管资本提取方式的改进建议为：在监管资本置信区间的下限提取监管资本，从置信下限到置信上限，配置以无风险资产。由此使被监管机构在资本配置上具有一定灵活性。
(5)在第五章提出了损失强度分布选择的一种方法，即以操作风险管理系统灵敏度最大为标准进行选择。
Previous literatures have shown that there is a class of operational risk which lossseverity is the heavy-tailed Distribution.The Extreme Value Distribution Model isoptimal approach to measure the operational risk.Currently,the Loss DistributionApproach is a main approach to measure the operational risk in the industry.Thus,thispaper combines the Extreme Value Distribution Model with the Loss DistributionApproach to discuss the measurement precision and management of heavy-tailedoperational risk.Firstly,the paper analyses the factors which affect the measurementdeviation of heavy-tailed operational risk.Additionally,basing on some certaindemonstration researches and choosing typical heavy-tailed distribution that regards theWeibull distribution and Pareto distribution as loss severity distribution from twoclasses of Extreme Value Distribution Models(BMM and GPD),the paper discusses themeasurement precision and key management parameters of heavy-tailed operational riskat high confidence level,and gives the demonstrations.And an analysis of modelapplication is illustrated with a numerical example.Furthermore,the paper bringsforward a choosing method of the loss severity distribution.Based on theafore-mentioned studies,this paper gets main innovative conclusions as follow.
(1) The paper discusses the factors that influence the measurement deviation,andfinds out that the existence of this deviation has objectives.There are two influencefactors:One is sample heterogeneity.In inside and outside pool loss datum,there is notonly the difference threshold,but also the distinctions of internal and externalenvironment lead to the sample heterogeneity,which brings about the measurementdeviation.Secondly,there are distribution model extrapolate problems in themeasurement.The loss datum of heavy-tailed operational risk are rare,as a consequence,there are extrapolate problems when we measure operational risk at high confidencelevel,which lead to uncertainty in measurement results.Because of the above factors,the measurement deviation cannot be ignored.
(2) Basing on the deviation of the measurement results of heavy-tailedoperational risk,in Chapter 3,this paper further discusses the measurement precision.Under the Loss Distribution Approach,the confidence intervals' length of Operational VaR represents the measurement precision.After a systematic study of measurementprecision,we have the conclusions as follow.
1) The changes of measurement precision' sensitvity of heavy-tailed operationalVaR just relate with the shape parameter and the frequency parameter.Using theelasticity analysis method,and basing on the theory researches of uncertain propagationcoefficients' sensitvity and its changes,we have the conclusions that the changes ofuncertain propagation coefficients' sensitvity just relate with the shape parameter andthe frequency parameter,but do not relate to the scale parameter.As a result,thechanges of measurement precision' sensitvity of operational VaR just relate with theshape parameter and the frequency parameter if we keep other conditions unchanged.
2) Using the theory model established in this chapter,the key influencingparameters of measurement precision can be distinguished.With changes of thecharacter parameter,there will be changes in measurement precision and changes in keyinfluencing parameters.The numerical example analysis validates the validity of thistheory model.
(3) From the angle of measurement,the character parameters which impact theoperational risk most can be distinguished.As a key management parameter,it leads tothe possibility of the combination of measurement model and management model.Andwe can build the dynamic management system of operational risk and improvemeasurement efficiency.
(4) Integrating of the conclusion in chapter 3 and 4,we can conclude that thereare changes of operational VaR and measurement precision with the changes ofcharacter parameters.Therefore,the extraction method of regulatory capital can bemended.And the regulatory capital equal to the lower confidence limit.From the lowerto upper confidence limit regulatory capital is allocated by a risk-free asset,which givesthe financial institutions flexibility to allocate the capital.
(5) In Chapter Five,this paper propose a selection method of loss severitydistribution that regards the maximum of the sensitivity of supervised systems ofoperational risk as a choosing standard.
引文
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