基于极值理论的我国商业银行操作风险度量
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摘要
从“巴林”到“法兴”,这些在经营过程中不断暴露的操作风险案件给国际银行业和监管当局再次敲响了金融风险管理的警钟——重视操作风险的“管理和监管”。而有效管理的前提就是度量,本文正是在这种背景下,通过从公开媒体收集的我国商业银行操作风险损失案件,在对国内外操作风险相关文献成果进行深入研究的基础上,将我国操作风险度量与我国商业银行实际联系起来,探讨操作风险计量和资本金配置问题,为我国商业银行操作风险度量提供参考和借鉴。
本文主要思路是尝试将极值理论用于度量我国商业银行操作风险,针对极值理论应用中阈值选取的难点问题,提出了基于变点理论进行定量式极值分布阈值选取的新方法;并基于该理论度量了我国商业银行的操作风险。同时针对我国商业银行操作风险业务类型和风险事件的相依结构,提出了Copula-EVT模型计算操作风险的总VaR值。
主要内容有:
1、综述了操作风险基本定义、分类和操作风险管理框架以及操作风险度量的一般理论和方法。重点介绍新巴塞尔协议关于操作风险度量模型的建议,并就其推荐的基本指标法、标准法以及高级计量法的模型以及适用范围等进行了进一步介绍。
2、通过对从公开媒体收集的我国操作风险损失案件进行实证分析,分别从案件发生的业务类型、时间、风险类型、产权、层级、地域、损失金额等分布特征入手分析我国商业银行操作风险的基本状况、呈现的主要特征和深层次的发生机理,并对总体操作风险损失事件进行评述。
3、基于变点理论改进了在极值分布中的阈值选取方法,实现定量式阈值选取。极值理论被广泛应用于解决金融、保险等领域的厚尾分布问题,在利用极值理论解决我国商业银行操作风险损失数据呈现“厚尾”问题时,其实际应用的重点和难点就是阈值的选取。本文讨论了变点理论进行阈值选取的基本原理和方法,并利用Burr分布产生的随机样本进行模拟,证明该方法具有较好效果,并在此基础上运用S&P500和Danish火灾保险数据进行了实证分析。
4、基于改进的阈值选取方法,结合从公开媒体收集的我国商业银行操作风险损失案件数据度量了我国商业银行操作风险在不同置信水平下的VaR和ES值,并据此讨论我国商业银行操作风险监管资本配置问题。利用极值理论中的POT模型对操作风险损失数据进行建模,采用变点理论进行定量的选取域值,进而利用bootstrap再抽样方法,估计POT模型参数,给出我国商业银行操作风险在不同置信水平下的VaR和ES值。建模结果表明:基于超过阈值的尾部数据进行建模的POT模型克服了经典VaR技术和ES方法可能对预期损失低估的缺点,能更好的刻画操作风险分布的尾部信息,在操作风险度量中具有较好的应用效果。
5、应用Copula函数分析我国商业银行各类操作风险之间的相依结构,将操作风险度量从一维拓展到多维。采用损失分布法度量操作风险时要首先明确业务类型/事件类型组合,计算每个业务类型/事件类型的VaR值,然后对所有的业务类型/事件类型值简单加总求得操作风险的总资本要求,这就没有考虑业务类型/事件类型之间的相关性,这与实际情况是不符合的。为此本文在分析银行各类操作风险之间的相依性及其对银行整体操作风险的影响基础上,运用Copula函数建立实际操作风险的相依结构并通过计算操作风险总VaR值的Copula-EVT模型,由此计算操作风险的总VaR值,并从公开媒体报道收集的操作风险损失数据进行实证分析,结果表明基于t-Copula度量的在险值比传统简单直接相加的方法至少减少8%以上。
通过极值理论对我国商业银行操作风险的度量,为商业银行管理者和金融机构监管者提供了我国商业银行操作风险的敞口数据。由于极端情况下银行的非预期损失远远超过了其通常情况下所需的资本,所以银行不大可能在事前准备足够的资本来应付这种现象。这样存在着对外部的依赖性,即由外部来承担极端情况下的损失。所以金融机构监管者很有必要加强对银行业的监管,选择客观、科学的方法准确度量我国商业银行操作风险,为我国商业银行操作风险经济资本的分配提供科学依据,以推动商业银行对风险的管理、维护我国金融体系的稳定。
From Barings to Societe Generale,these cases of operational risk's exposing alarm the international banking and the regulatory authorities again about the commercial risk management -- we should value the management and supervise the operational risk. Measuring is just the guarantee of the valid management.In this situation,by collecting the cases of commercial bank operational risk loss through public media,the paper linked the operational risk measurement with the commercial banks and discussed the problem of operational risk and the capital allocation, where our commercial banks can draw lessons from.
The paper tried to use Extreme Value Theory to measure the commercial bank's operational risk.Aiming at the difficulty in selecting threshold,the paper put forward a new method using the Change Point Theory to select quantitative extreme distribution threshold.Based on the changing point, we measured the operational risk of the commercial bank, and aiming at the mutually construction between the operational risk type and the risk affairs, we put forward EVT-Copula model to calculate the sum of VaR value. The main content of the paper contains:
1.We overviewed the definition of the basic operational risk, the frame of division and managing risk,and the theory and methods of measuring risks.In this paper, we focused on the suggestion that Basel II gave to operational risk measuring model, and also introduced the basic index method, standard method,advanced calculating model and the application scopes.
2.Through the demonstration analysis of those cases we collected from the public medium, we analyzed our commercial banks' status, main characteristics and Mechanisms through these cases' type, time, risk type, property right,layer class, region and loss from the case, etc. Then we overviewed these operational risk loss affairs.
3.Based on Change Point Theory, improved the method of selecting threshold in the extreme value distribution and realized quantitative-threshold selection.Extreme Value Theory has been widely used in the solutions of the distribution problems in the field of finance and insurance. When using Extreme Value Theory to solve the problem that commercial banks' operational risk loss data showing thickness distribution problems, selection of threshold, however, has long been treated as the key point and a difficult task to perform in the application. The fundamental and the basic method used in the selection of threshold value using Change Point Theory has been analyzed and numerical simulation has been performed by random sample generated from Burr distribution method, and a good result is obtained. Moreover, the empirical analysis is also carried out by using the $SP500 and Danish fire insurance data.
4. Method of selecting threshold are based on improvements. Considering the operation risk loss cases' data collection, we calculated Chinese commercial banks' VaR and ES value at different confidence levels, and discussed Chinese commercial banks' capital allocation. We also used POT model in Extreme Value Theory on modeling, and selected threshold quantitatively area value through change point theory. Re-sampled with bootstrap, estimated the POT model parameter, and gave our commercial banks' VaR and ES value at different confidence levels. The result indicated that, the POT model which modeled with the bottom data exceeding threshold overcame the possibility of underestimate loss that classical VaR and ES method had, and depicted the bottom distribution information more deeply. Also it can usually lead good implicated result.
5.We applied Copula function to analyze our country commercial bank s' various operational risks dependency set. It would widen the measurement of operational risk from one-dimension to multidimension. The adoption of Loss Distribution Approachesto measure operational risk needs to definite business type or affairs type combination, compute each business type/ the VaR of the affairs type value, then sum all business type/ affairs type the value could simply result in the gross begs the total capital that the operational risk requests.This had no consideration business /type, and did not match the actual circumstance. Therefore, based on the dependencies among various operation risks and the influence of operational risks, the paper used Copula function to establish the risks' dependent frame and used Copula-EVT model to calculate the sum of VaR value so as to do empirical analysis combining operation risk the loss data collected. The result expressed that t- Copula measure method can reduce at least 8% than the traditional direct addition method.
Through measuring Chiese commercial banks' risk using Extreme Value Theory canprovide the entrance to operate our country's commercial banks' risks for Bank managers and financial institutions regulators.Because in extreme circumstance, the bank's non-expecting loss exceeds far ahead its common capital,the bank may not prepare enough fund to cope with this phenomenon beforehand. So external dependence exists,which is used to undertake the extreme loss,and the financing institutions have the necessity to take charge of the banking and choose objective and accurate methods to measure commercial banks' operational risk to provide a scientific basis to promote the commercial banks' risk management for Chinese commercial banks' operational risk capital allocation, and safeguard the stability of China's financial system.
本文主要思路是尝试将极值理论用于度量我国商业银行操作风险,针对极值理论应用中阈值选取的难点问题,提出了基于变点理论进行定量式极值分布阈值选取的新方法;并基于该理论度量了我国商业银行的操作风险。同时针对我国商业银行操作风险业务类型和风险事件的相依结构,提出了Copula-EVT模型计算操作风险的总VaR值。
主要内容有:
1、综述了操作风险基本定义、分类和操作风险管理框架以及操作风险度量的一般理论和方法。重点介绍新巴塞尔协议关于操作风险度量模型的建议,并就其推荐的基本指标法、标准法以及高级计量法的模型以及适用范围等进行了进一步介绍。
2、通过对从公开媒体收集的我国操作风险损失案件进行实证分析,分别从案件发生的业务类型、时间、风险类型、产权、层级、地域、损失金额等分布特征入手分析我国商业银行操作风险的基本状况、呈现的主要特征和深层次的发生机理,并对总体操作风险损失事件进行评述。
3、基于变点理论改进了在极值分布中的阈值选取方法,实现定量式阈值选取。极值理论被广泛应用于解决金融、保险等领域的厚尾分布问题,在利用极值理论解决我国商业银行操作风险损失数据呈现“厚尾”问题时,其实际应用的重点和难点就是阈值的选取。本文讨论了变点理论进行阈值选取的基本原理和方法,并利用Burr分布产生的随机样本进行模拟,证明该方法具有较好效果,并在此基础上运用S&P500和Danish火灾保险数据进行了实证分析。
4、基于改进的阈值选取方法,结合从公开媒体收集的我国商业银行操作风险损失案件数据度量了我国商业银行操作风险在不同置信水平下的VaR和ES值,并据此讨论我国商业银行操作风险监管资本配置问题。利用极值理论中的POT模型对操作风险损失数据进行建模,采用变点理论进行定量的选取域值,进而利用bootstrap再抽样方法,估计POT模型参数,给出我国商业银行操作风险在不同置信水平下的VaR和ES值。建模结果表明:基于超过阈值的尾部数据进行建模的POT模型克服了经典VaR技术和ES方法可能对预期损失低估的缺点,能更好的刻画操作风险分布的尾部信息,在操作风险度量中具有较好的应用效果。
5、应用Copula函数分析我国商业银行各类操作风险之间的相依结构,将操作风险度量从一维拓展到多维。采用损失分布法度量操作风险时要首先明确业务类型/事件类型组合,计算每个业务类型/事件类型的VaR值,然后对所有的业务类型/事件类型值简单加总求得操作风险的总资本要求,这就没有考虑业务类型/事件类型之间的相关性,这与实际情况是不符合的。为此本文在分析银行各类操作风险之间的相依性及其对银行整体操作风险的影响基础上,运用Copula函数建立实际操作风险的相依结构并通过计算操作风险总VaR值的Copula-EVT模型,由此计算操作风险的总VaR值,并从公开媒体报道收集的操作风险损失数据进行实证分析,结果表明基于t-Copula度量的在险值比传统简单直接相加的方法至少减少8%以上。
通过极值理论对我国商业银行操作风险的度量,为商业银行管理者和金融机构监管者提供了我国商业银行操作风险的敞口数据。由于极端情况下银行的非预期损失远远超过了其通常情况下所需的资本,所以银行不大可能在事前准备足够的资本来应付这种现象。这样存在着对外部的依赖性,即由外部来承担极端情况下的损失。所以金融机构监管者很有必要加强对银行业的监管,选择客观、科学的方法准确度量我国商业银行操作风险,为我国商业银行操作风险经济资本的分配提供科学依据,以推动商业银行对风险的管理、维护我国金融体系的稳定。
From Barings to Societe Generale,these cases of operational risk's exposing alarm the international banking and the regulatory authorities again about the commercial risk management -- we should value the management and supervise the operational risk. Measuring is just the guarantee of the valid management.In this situation,by collecting the cases of commercial bank operational risk loss through public media,the paper linked the operational risk measurement with the commercial banks and discussed the problem of operational risk and the capital allocation, where our commercial banks can draw lessons from.
The paper tried to use Extreme Value Theory to measure the commercial bank's operational risk.Aiming at the difficulty in selecting threshold,the paper put forward a new method using the Change Point Theory to select quantitative extreme distribution threshold.Based on the changing point, we measured the operational risk of the commercial bank, and aiming at the mutually construction between the operational risk type and the risk affairs, we put forward EVT-Copula model to calculate the sum of VaR value. The main content of the paper contains:
1.We overviewed the definition of the basic operational risk, the frame of division and managing risk,and the theory and methods of measuring risks.In this paper, we focused on the suggestion that Basel II gave to operational risk measuring model, and also introduced the basic index method, standard method,advanced calculating model and the application scopes.
2.Through the demonstration analysis of those cases we collected from the public medium, we analyzed our commercial banks' status, main characteristics and Mechanisms through these cases' type, time, risk type, property right,layer class, region and loss from the case, etc. Then we overviewed these operational risk loss affairs.
3.Based on Change Point Theory, improved the method of selecting threshold in the extreme value distribution and realized quantitative-threshold selection.Extreme Value Theory has been widely used in the solutions of the distribution problems in the field of finance and insurance. When using Extreme Value Theory to solve the problem that commercial banks' operational risk loss data showing thickness distribution problems, selection of threshold, however, has long been treated as the key point and a difficult task to perform in the application. The fundamental and the basic method used in the selection of threshold value using Change Point Theory has been analyzed and numerical simulation has been performed by random sample generated from Burr distribution method, and a good result is obtained. Moreover, the empirical analysis is also carried out by using the $SP500 and Danish fire insurance data.
4. Method of selecting threshold are based on improvements. Considering the operation risk loss cases' data collection, we calculated Chinese commercial banks' VaR and ES value at different confidence levels, and discussed Chinese commercial banks' capital allocation. We also used POT model in Extreme Value Theory on modeling, and selected threshold quantitatively area value through change point theory. Re-sampled with bootstrap, estimated the POT model parameter, and gave our commercial banks' VaR and ES value at different confidence levels. The result indicated that, the POT model which modeled with the bottom data exceeding threshold overcame the possibility of underestimate loss that classical VaR and ES method had, and depicted the bottom distribution information more deeply. Also it can usually lead good implicated result.
5.We applied Copula function to analyze our country commercial bank s' various operational risks dependency set. It would widen the measurement of operational risk from one-dimension to multidimension. The adoption of Loss Distribution Approachesto measure operational risk needs to definite business type or affairs type combination, compute each business type/ the VaR of the affairs type value, then sum all business type/ affairs type the value could simply result in the gross begs the total capital that the operational risk requests.This had no consideration business /type, and did not match the actual circumstance. Therefore, based on the dependencies among various operation risks and the influence of operational risks, the paper used Copula function to establish the risks' dependent frame and used Copula-EVT model to calculate the sum of VaR value so as to do empirical analysis combining operation risk the loss data collected. The result expressed that t- Copula measure method can reduce at least 8% than the traditional direct addition method.
Through measuring Chiese commercial banks' risk using Extreme Value Theory canprovide the entrance to operate our country's commercial banks' risks for Bank managers and financial institutions regulators.Because in extreme circumstance, the bank's non-expecting loss exceeds far ahead its common capital,the bank may not prepare enough fund to cope with this phenomenon beforehand. So external dependence exists,which is used to undertake the extreme loss,and the financing institutions have the necessity to take charge of the banking and choose objective and accurate methods to measure commercial banks' operational risk to provide a scientific basis to promote the commercial banks' risk management for Chinese commercial banks' operational risk capital allocation, and safeguard the stability of China's financial system.
引文
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[1]Beirlant J,Dierckx G,Goegebeur Y,Matthys G.1999.Tail Index Estimation and an Exponential Regression Model[J].Springer,177-200.
[2]陈学华,杨辉耀,黄向阳.2003.POT模型在商业银行操作风险度量中的应用[J].管理科学,49-52.
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