金融机构操作风险的度量及实证研究
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摘要
面对瞬息变化的外部环境和日益激烈的行业竞争格局,无论是在金融体系中处于主导地位的商业银行还是传统的非银行金融机构(本论文主要包括投资银行和保险公司),都不可避免地面临越来越复杂的挑战。因为操作风险广泛存在于金融机构的经营环节,事关金融机构的内部控制结构,其发生机制和控制方法等均有与其它风险不同的鲜明特点。面临着损失加剧、危害日趋严重的操作风险,金融监管部门和金融机构均愈加重视对操作风险的防范。
目前,国外理论界与实务界都在积极研究操作风险的管控技术与方法,以期达到有效识别、准确度量和严格控制的目的。虽然我国金融机构对操作风险的管控越来越重视,但目前只在操作风险的特征和生成机理上,也就是操作风险识别的研究方面初见成效。对于操作风险度量技术和方法的研究,以及内部管理和监管体制方面的研究,都与国外同行存在较大差距。风险的度量是风险控制和管理的前提。因此,操作风险的度量对于我国的金融业是需要迫切解决的课题。
本论文的研究意义为：
1.对三类金融机构面临操作风险的本质特征加以分析,以实现对其有效地度量
目前国内外对商业银行操作风险度量的研究相对深入,而对其它金融机构(如投资银行和保险公司)的研究则相对较少。那么适用于商业银行的度量技术是否也合适于投资银行和保险公司呢?通过揭示三类金融机构操作风险的本质特征,能够加深对三类金融行业操作风险的认识,避免盲目地量化风险,并找到通用于三类金融机构的操作风险度量技术。
2.操作风险度量的准确性关系到能否对其实施有效的管理
风险的度量是风险管理体系中的重要环节,若跳过风险度量的研究而直奔风险管理的讨论,有本末倒置之嫌。毕竟选择的度量模型和技术方法关系到风险管理的实际成效,度量结果的准确性决定了风险内控制度和管理的有效性。但由于对操作风险研究的起步较晚,与发展相对成熟的信用风险和市场风险的度量相比,国外对操作风险的度量尚未形成统一的认识。我国金融业对操作风险的重视和研究程度远未及国外业界,并且国内目前正处于经济转型的变革时期,除了自身的管理以外,我国金融业还面临外部环境不确定性和政府政策变动对业务的影响。也就是说,操作风险来自内部管理和外部干扰两个方面。因此,改进操作风险度量技术对增加金融机构的竞争力具有重要意义。
3.操作风险度量的准确性关系到经济资本能否发挥应有的作用
经济资本与风险总额在数量上是相等的,是衡量和防御金融机构超额的损失的指标,是对资源配置进行优化、有效提高风险收益的核心工具。因此,若测量出其所要求的经济资本,那么金融机构就能够进行经济资本的配置。从这个角度说,量化的准确性影响着经济资本配置的效果。
本论文的研究内容为：
1.前两章交待了研究背景、各国监管部门针对操作风险出台的相关规定、研究意义、技术路线以及创新点,并对国内外业界和学界度量操作风险的研究现状进行比较,特别重点评述了损失分布法框架下的极值理论法、贝叶斯法以及信度模型的研究情况,以为在这三个方面提出修正性的度量方法奠定基础。
2.如果对操作风险概念、特征、事故类型、损失金额之间内在关系没有深刻地理解就直接对其采用量化模型可能引起量化结果的盲目性和无针对性。因此在第三章中先对三类金融机构的操作风险进行统一界定,并按成因和业务部门这两条线分别对操作风险进行分类,这样就为收集三类金融机构的操作风险历史损失数据提供了统一的标准。然后分析引发三类金融机构操作风险的原因,并通过收集历史损失数据来对比三类金融机构的操作风险暴露特征,从而在这个意义上得到了三类金融机构面临的操作风险在本质上是相同的结论。那么在损失数据量和损失数据数学特征相同的情况下,适合于一类金融机构的操作风险也同样适合于其它类别的金融机构。本章是第四、五和六章的理论铺垫。
3.第四章在损失分布法框架下用POT模型来度量操作风险。巴塞尔委员会提出了三大类操作风险度量方法,其中高级计量法中的损失分布法是基于操作风险历史损失数据之上的,其且所采用的技术是开放式的,因此它是目前国内外学者研究最频繁的方法之一。操作风险服从尖峰厚尾的分布,也就是说分布的尾部更能反映出极端操作风险事件所引发的巨额损失,若能处理好分布的尾部就能更真实地反映出操作风险的特征。而POT模型能够针对性地拟合损失的尾部分布,是公认的能较好地衡量分布尾部及损失极值的方法。但在实际应用中,如何客观、精确地确定POT模型的阈值(临界点)仍是一道关键的障碍。
第四章用变点理论对阈值位置进行精确定位以准确获取阈值。鉴于三类金融机构面临的操作风险从风险成因意义而言在本质上是相同的,且收集到的我国商业银行的操作风险损失事件远远多于其它金融机构的,所以就以监管部门公布以及国内外媒体公开报导的279件商业银行操作风险损失事件为例,来说明提出的基于变点理论的POT模型阈值确定方法度量操作风险的有效性。
4.第五章用贝叶斯法来度量操作风险。操作风险损失数据的严重缺失是阻碍操作风险度量的难题。虽然贝叶斯法在小样本推断下有较好的效果,但在实际求解参数的后验分布中却存在高维积分运算这个异常复杂的数值计算困难。所以,如何解决贝叶斯法的实际应用问题仍值得研究。
第五章选择两参数帕累托分布和负二项分布分别描述操作风险损失事件的发生强度和发生频率,然后借助于WinBUGS软件采用马尔科夫链蒙特卡罗模拟方法来解决贝叶斯的实际应用问题。以监管部门公布以及国内外媒体公开报导的279件商业银行操作风险损失事件为例,来说明提出的基于贝叶斯推断的马尔科夫链蒙特卡罗模拟方法度量操作风险的有效性。计算所得与第四章采用方法的结果接近。
5.第六章采用信度理论中的Buhlmann-Straub模型来度量操作风险。为解决单个金融机构损失数据缺乏而不能度量操作风险的问题,大多数学者是把内(单个金融机构)、外(同行业的其它金融机构)部损失数据简单合并在一起使用的。但简单地混合内外数据来当作单个金融机构的损失数据的做法比较牵强。虽然目前有学者提出将外部损失数据调整后再合并入内部损失数据的思路,但调整权重是收入指标或情景分析数据,这种方法仍然值得商榷,所以有效整合内外损失数据仍是一道关键的障碍。此外,在目前操作风险损失数据匮乏的情况下,单个金融机构很难预测本机构下一年操作风险的发生强度和频率,在数据严重不足的情况下实现上述预测也是一道障碍。
第六章先利用贝叶斯马尔科夫链蒙特卡罗模拟方法在数据不完备的情况下对损失次数逐年进行校正。再根据校正好的损失次数数据,利用以贝叶斯马尔科夫链蒙特卡罗模拟方法为基础构建的Biihlmann-Straub模型,得到每家金融机构下一年信度风险暴露量的最优无偏估计。通过对已发生的279个商业银行操作风险损失事故中筛选出国内4大国有商业银行的操作风险损失事件(共125件)来说明基于马尔科夫链蒙特卡罗模拟的信度模型对操作风险度量的有效性。
本论文的主要观点为：
1.对三类金融机构的操作风险按成因分为内部因素和外部因素。内部因素引发的操作风险分为制度类(由于制度、产品和系统的不完善所致)、技能类(由于员工知识结构不完善或理解错误所致)、失控类(由于员工无恶意主观过失所致)、欺诈类(由于员工出于私利主观故意所致)四种。外部因素引发的操作风险分为宏观政策类、欺诈类和其它类三种。其中,内部欺诈无论是在数量上还是在金额上所占比例均最大。
2.在损失分布法的框架下采用POT模型虽然能够更真实地反映出操作风险的特征,但它只针对超过较大阈值(临界点)的数据建模,因此需要设定合理的高阈值。因为如果阈值取得太高,则可取的损失数据样本点就会很少而不足以建模；而如果阈值取得太低,就会把分布接近中部的样本点也看作尾部分布来处理,不能突出POT模型的优势。目前学者在阈值的选取上一般需要在观察图形的基础上借助于主观经验来进行模糊判断。所以,如何在确定较高阈值和保证较充足样本数据之间找到平衡点仍值得研究。
3.操作风险损失数据的严重缺失是阻碍操作风险度量的难题。虽然贝叶斯法在小样本推断下有较好的效果,但在实际求解参数的后验分布中却存在高维积分运算这个异常复杂的数值计算困难。所以,如何解决贝叶斯法的实际应用问题仍值得研究。
4.鉴于操作风险损失数据的缺乏,目前大多数学者对将内(单个金融机构)、外(同行业的其它金融机构)部损失数据简单合并在一起作为整个行业来使用。但由于不同商业银行(或不同投资银行,或不同保险公司)的资产规模、产品线、业务流程、风险偏好及风控体系是有差别的,即便都是同一行业,单个金融机构的损失数据也是服从不同分布的。因此,简单地把整个行业的损失数据混合在一起会改变原有数据的分布特征,由此得到的度量结果的精确性会存在一定问题。所以,如何有效整合内、外部损失数据,甚至是如何在现有小样本情况下预测出次年单个金融机构操作风险的损失情况均有较大研究价值。
本论文的创新点为：
1.从风险成因意义上揭示操作风险对于三类金融机构在本质上的一致性
对操作风险进行度量的前提是收集和整理损失数据。因此,论文就在巴塞尔委员会定义的基础上对三类金融机构的操作风险进行了统一界定,以理顺概念的名目之争。并结合操作风险的特征对三类金融机构的操作风险按成因和业务部门这两条线分别进行分类。这项工作贡献在于保证操作风险数据收集、整理和度量范围的一致性,为后面通过实证分析说明所修正模型的度量效果提供统一、有效的数据支持。
虽然三类金融机构的业务重点和风控制度有较大差异,但从组织结构、业务流程、信息系统和从业人员这四个风险源分析操作风险的结果来看,它们无一不面临着因制度不完善、技能不熟练、操作不正确和内部欺诈等内部因素的操作风险,以及宏观政策改变和外部欺诈等外部因素的操作风险所导致的损失,可以说操作风险的特点和形成机理并无差别。而且收集了三类金融机构各自的损失数据来对比操作风险的风险暴露特征,发现它们面临的操作风险的成因也主要是“人”所引起的。因而从成因这个意义上来看,三类金融机构操作风险在本质上是一致的。从理论上来说,在损失数据数学特征相同的情况下,适用于一类金融机构的操作风险度量模型也同样适用于其它类的金融机构,这样弥补了其它金融机构缺乏操作风险度量技术的不足。
2.对POT模型中阈值确定问题的修正
在借鉴前人研究的基础上,引入变点理论来修正性地解决定量确定阈值的问题。变点统计分析的目的是对变点的存在、个数和位置进行判断以及检验,以对变点的跃度实施有效的估计。某时间点前后的数据(均值或概率分布或模型参数)发生明显变化,则将该时间点定义为(均值或概率或某模型参数)变点。结合变点理论和POT模型,认为阈值就是Hill图曲线(以临界样本的序号为横轴、以尾部指数的Hill统计量α为纵轴)非稳定区域与稳定区域的分界点,如果与一阶差分最大值相结合找到最接近曲线稳定区域的二阶差分的最大值,其所在区域就是变点所处区间,α进入稳定状态的起始位置就是变点具体所在的位置,从而能够计算得到阈值的精确数值以改善极值理论的尾部估计。这样就修正性地解决POT模型中仅凭肉眼或经验来人为确定阈值的问题。
3.对贝叶斯后验分布高维积分运算问题的修正
在借鉴前人研究的基础上,引入马尔科夫链蒙特卡罗模拟方法,选择Gibbs抽样来求解参数的后验分布,并采用WinBUGS软件进行10万次抽样来估计所构建模型的参数。在得到参数的后验估计后,通过图形诊断法、相关性诊断法和Gelman-Rubin诊断法三种方法来判断马尔科夫链蒙特卡罗模拟的收敛性,以认定参数估计结果的可信性,从而得到操作风险的监管资本。这样就修正性地解决贝叶斯法后验分布高维积分运算问题。
4.用信度模型解决内外数据混合问题及预测单个金融机构次年的损失量
在借鉴保险精算学中厘定保费研究的基础上,引入信度模型来修正性地解决数据混合与预测单个金融机构次年损失量的问题。信度理论的Buhlmann-Straub信度模型是通过合理利用本保单组合近期损失数据和主观选择的类似险种同期损失数据来估计和预测后验保费的。认为单个金融机构次年的操作风险损失金额完全可以根据本机构和行业内其它金融机构的历史损失数据以信度因子为权重来分摊推断。这里,也借助于WinBUGS软件用贝叶斯马尔科夫链蒙特卡罗模拟的方法进行10万次抽样来得到信度风险暴露量、信度因子以及其它参数的后验估计量,并还原出单个金融机构次年操作风险的损失量与发生次数。从信度因子集中于0.7的结果可看到,单个金融机构与行业内其它金融机构的操作风险损失事件具有非同质性,不能简单地混合在一起使用。因此,所采用的方法可以有效解决上述两个问题。
With rapidly changing external environment and increasingly fierce industrial competition, financial institutions meet more and more complicated challenges. Because operational risk exists widely in the daily operation of financial institutions, and its characteristic and controlling method is significantly different from other risks. So facing over-growing operational risk, financial supervision department and financial institutions pay more and more attention on the measures against it.
Nowadays, managing and controlling techniques of operational risk have been researched among the academia and practice circle. Although there was increasing focus on it for domestic financial institutions, preliminary results were only achieved at the following aspects:characteristic and formation mechanism. Large gap still exists in operational risk measurement and methods compared with foreign peers. Control and management of operational risk start from measurement. Therefore, it is urgent issue for discussion to solve how to measure operational risk for domestic financial industry.
This thesis has the following three research significances:
1. Operational risk of financial institutions is same in essence. This conclusion helps to measure operational risk for all types of financial institution.
Nowadays, research of measurement on commercial bank's operational risk has been relatively deep at both home and abroad. But researches on other types of financial institution are rare. Then, whether measurement technique adapted for commercial bank can also be applied for other financial institution? Only by revealing operational risk's essential of three-type financial institutions can deepen knowledge of operational risk, avoid risk quantification blindly and find out common measurement technique of operational risk for all financial institutions.
2. Measurement accuracy of operational risk is related to whether implement of management is effective or not.
Risk measurement is the important point of risk management system. It is incorrect for the financial institutions to ignore risk measurement and discuss risk management directly. After all, the choice of measurement technique and method decide the effectiveness of risk internal control mechanism and risk management. But research on operational risk starts late compared with credit risk and market risk, unified understanding about operational risk measurement has't been formed. Meanwhile, difference between domestic research and foreign research on operational risk is huge. Therefore, improved measurement technique of operational risk has vital significance to enhance competitiveness of financial institutions.
3. Measurement accuracy of operational risk is related to whether economical capital can exert its effect or not.
Economical capital is equal to unexpected loss amount of risk in quantity. It is used to measure and defend the part of loss exceeding expected loss. It is the core tool of optimizing resource allocation and raising risk adjusted return on capital (RAROC). After economical capitale is calculated, conomical capital can be allocated. From this perspective, measurement accuracy of operational risk is important for financial institutions.
The main research content of this thesis is:
1. The first two chapter introduce background, significance, innovation of this thesis. Then aimed at laying theoretical foundation for the following chapters, a comprehensive literature review is made on operational risk measurement method, particularly on three methods:Loss Distribution Approach, Extreme Theory Approach, Bayes Method and Credibility Model.
2. If there is no profound understanding about relationship with concept, characteristic and type of operational risk, quantitative model is useless. So the third chapter firstly gives the unified definition of financial institution. Then classify operational risk according to cause and business department. Finally analyze what triggers operational risk and compare the operational risk's feature of three-type financial institution. Through the above analysis, this thesis has one conclusion:operational risk of financial institution is same in essence. Thereby, operational risk's measurement technique suited to one type's financial institution can also be applied to the other type's financial institution. This chapter establishes the solid foundation for the following chapter.
3. In the fourth chapter, Loss Distribution Approach (LDA) is used to measure operational risk. BCBS proposes three types'operational risk measurement methods. Among the Advanced Measurement Approach (AMA), LDA is the most frequently used method. Because LDA is based on historical loss data, measurement result is relatively objective. Under the framework of LDA, Peaks over Threshold Approach (POT) is used to measure operational risk. The tail behavior of distribution is more important for the extreme huge loss data. Because Extreme Value Theory (EVT) is targeted on fitting tail of distribution, it is publicly accepted method. But how to select threshold precisely is still one key obstacle in the practical application.
In the fourth chapter, to select threshold quantitatively and more accurately, a corrected method using change point theory to locate stable state of Hill curve is proposed. Empirical research with example of commercial bank's operational risk loss data (totaled279pieces reported by domestic and overseas media) is done to test the effectiveness of this corrected method.
4. In the fifth chapter, Bayes Method is used to measure operational risk. Although this method is widely accepted in the case of small sample, it still has one difficulty in the practical application.
In the fifth chapter, Pareto Distribution and Negative Binominal Distribution are used to describe severity and frequency of operational risk respectively. Then difficulty is solved by adopting MCMC simulation method with using WinBUGS software. Because three-type financial institution face the exactly same operational risk, empirical research with example of commercial bank's operational risk loss data (totaled279pieces reported by domestic and overseas media) can test the effectiveness of this corrected model.
5. In the sixth chapter, Credibility Model is used to measure operational risk. To solving the problem of deficient loss data, majority of scholars combine the internal and external loss data directly. But due to the heterogeneity of risk, this data processing method is inappropriate. So how to integrate internal and external loss data, even how predict the operational risk loss of the next year just for one individual financial institution is still the difficult problem in the practical application.
In the sixth chapter, Buhlmann-Straub credibility model is used to get risk exposure of operational risk by using MCMC algorithm with the implement of WinBUGS in the event of insufficient loss data. Empirical research with example of stated-own commercial bank's operational risk loss data (totaled125pieces reported by domestic and overseas media) is done to test the effectiveness of this method.
The main viewpoint of this thesis is:
1. According to cause of formation, operational risk is classified into internal factor and external factor. Internal factor is also divided into four categories: system, skill, out of control as well as fraud. Here, system category refers to the operational risk caused by imperfect system and product. Skill category refers to the operational risk caused by employees'imperfect knowledge and incorrect understanding. Out of control category refers to the operational risk caused by employees' subjective negligence without malice. While fraud category refers to the operational risk caused by employees'subjective negligence motivated by self-interest. External factor can be divided into three categories:Macro-policy, fraud and other. Among the above category, internal fraud risk has the biggest share in quantity and amount.
2. Although POT can describe the characteristic of operational risk better, it has one key obstacle:how to determine threshold. If bigger threshold is selected, fewer samples. can be used. If smaller threshold is selected, more samples that don't belong to tail of distribution will be used. The above two kinds of circumstances will bring biased result. So how to determine threshold more accurately is still worthy of researching.
3. Although Bayes Method is has better prospective, it has one obstacle: high-dimensional value computation of posteriori distribution. This process is far more complicated. So how to put this method into practice is still worthy of researching.
4. Due to insufficient loss data, most scholars solve this problem by mixing internal and external loss data directly. But every financial institution has different product line, operation procedure, risk preference and risk control system. In other words, risk heterogeny exists among financial institution. And the accuracy of measurement result can be doubted with application of this data process. So how to integrate internal and external loss data more efficiently, even how to predict the next year's operational loss for one financial institution is still worthy of researching.
The innovation of this thesis is:
1. Operational risk of financial institution is same in essence.
The premise of operational risk measurement is collecting loss data. Aimed at standardize data collection and build up solid foundation for the latter empirical research, definition of operational risk for financial institution is made. Although product line and risk control system of each financial institution have differences, the characteristic and cause of operational risk is basically same by analyzing sources of risk (organization structure, work flow, information system as well as employee). Meanwhile, through comparing loss data of three-type financial institution, we find that they face common main cause of formation:employee. So operational risk of three-type financial institution is same in essence.
2. Threshold selection of POT model based on change point theory.
Based on the former research, change point theory is introduced to solve the difficulty of selecting threshold quantitively and more accurately for Peak over Threshold Theory. Threshold is located at the stable state of Hill curve. It can be selected combined maximum value of first-order differential and maximum value of second-order differential. Empirical results show that a good evaluation of capital requirement for operational risk can be obtained.
3. Applying Bayes Method based on MCMC simulation.
Based on the former research, MCMC simulation by applying Bayesian approach is introduced to solve the difficulty of insufficient loss data. So this thesis discusses how to conduct a Markov Chain for Negative Binominal distribution and Pareto distribution with Gibbs sampling in order to get posterior distributions of loss severity and frequency dynamically as well as capital requirement for operational risk. Then put WINBUGS software to use to estimate parameters of distributions. Thus, better evaluation of capital requirement for operational risk can be obtained compared with the maximum likelihood estimation method.
4. Mixing internal and external loss data and predicting loss for one financial institution by using credibility model.
Based on the former research, credibility model is introduced to solve the difficulty of mixing internal and external loss data. Due to the deficient data and heterogeneity of risk, it's hard for financial institution to get the unbiased estimated measurement by mixing the internal and external event of loss. Buhlmann-Straub credibility model is conducted to get risk exposure of operational risk by using MCMC algorithm with the implement of WinBUGS in the event of insufficient loss data. Then the amount of loss in the next year can be predicted for the individual financial institution. Empirical results show that measuring operational risk is inappropriate by mixing loss data of financial institution with different risk features. The stochastic simulation method applied by this thesis can improve the precision of estimators.
目前,国外理论界与实务界都在积极研究操作风险的管控技术与方法,以期达到有效识别、准确度量和严格控制的目的。虽然我国金融机构对操作风险的管控越来越重视,但目前只在操作风险的特征和生成机理上,也就是操作风险识别的研究方面初见成效。对于操作风险度量技术和方法的研究,以及内部管理和监管体制方面的研究,都与国外同行存在较大差距。风险的度量是风险控制和管理的前提。因此,操作风险的度量对于我国的金融业是需要迫切解决的课题。
本论文的研究意义为：
1.对三类金融机构面临操作风险的本质特征加以分析,以实现对其有效地度量
目前国内外对商业银行操作风险度量的研究相对深入,而对其它金融机构(如投资银行和保险公司)的研究则相对较少。那么适用于商业银行的度量技术是否也合适于投资银行和保险公司呢?通过揭示三类金融机构操作风险的本质特征,能够加深对三类金融行业操作风险的认识,避免盲目地量化风险,并找到通用于三类金融机构的操作风险度量技术。
2.操作风险度量的准确性关系到能否对其实施有效的管理
风险的度量是风险管理体系中的重要环节,若跳过风险度量的研究而直奔风险管理的讨论,有本末倒置之嫌。毕竟选择的度量模型和技术方法关系到风险管理的实际成效,度量结果的准确性决定了风险内控制度和管理的有效性。但由于对操作风险研究的起步较晚,与发展相对成熟的信用风险和市场风险的度量相比,国外对操作风险的度量尚未形成统一的认识。我国金融业对操作风险的重视和研究程度远未及国外业界,并且国内目前正处于经济转型的变革时期,除了自身的管理以外,我国金融业还面临外部环境不确定性和政府政策变动对业务的影响。也就是说,操作风险来自内部管理和外部干扰两个方面。因此,改进操作风险度量技术对增加金融机构的竞争力具有重要意义。
3.操作风险度量的准确性关系到经济资本能否发挥应有的作用
经济资本与风险总额在数量上是相等的,是衡量和防御金融机构超额的损失的指标,是对资源配置进行优化、有效提高风险收益的核心工具。因此,若测量出其所要求的经济资本,那么金融机构就能够进行经济资本的配置。从这个角度说,量化的准确性影响着经济资本配置的效果。
本论文的研究内容为：
1.前两章交待了研究背景、各国监管部门针对操作风险出台的相关规定、研究意义、技术路线以及创新点,并对国内外业界和学界度量操作风险的研究现状进行比较,特别重点评述了损失分布法框架下的极值理论法、贝叶斯法以及信度模型的研究情况,以为在这三个方面提出修正性的度量方法奠定基础。
2.如果对操作风险概念、特征、事故类型、损失金额之间内在关系没有深刻地理解就直接对其采用量化模型可能引起量化结果的盲目性和无针对性。因此在第三章中先对三类金融机构的操作风险进行统一界定,并按成因和业务部门这两条线分别对操作风险进行分类,这样就为收集三类金融机构的操作风险历史损失数据提供了统一的标准。然后分析引发三类金融机构操作风险的原因,并通过收集历史损失数据来对比三类金融机构的操作风险暴露特征,从而在这个意义上得到了三类金融机构面临的操作风险在本质上是相同的结论。那么在损失数据量和损失数据数学特征相同的情况下,适合于一类金融机构的操作风险也同样适合于其它类别的金融机构。本章是第四、五和六章的理论铺垫。
3.第四章在损失分布法框架下用POT模型来度量操作风险。巴塞尔委员会提出了三大类操作风险度量方法,其中高级计量法中的损失分布法是基于操作风险历史损失数据之上的,其且所采用的技术是开放式的,因此它是目前国内外学者研究最频繁的方法之一。操作风险服从尖峰厚尾的分布,也就是说分布的尾部更能反映出极端操作风险事件所引发的巨额损失,若能处理好分布的尾部就能更真实地反映出操作风险的特征。而POT模型能够针对性地拟合损失的尾部分布,是公认的能较好地衡量分布尾部及损失极值的方法。但在实际应用中,如何客观、精确地确定POT模型的阈值(临界点)仍是一道关键的障碍。
第四章用变点理论对阈值位置进行精确定位以准确获取阈值。鉴于三类金融机构面临的操作风险从风险成因意义而言在本质上是相同的,且收集到的我国商业银行的操作风险损失事件远远多于其它金融机构的,所以就以监管部门公布以及国内外媒体公开报导的279件商业银行操作风险损失事件为例,来说明提出的基于变点理论的POT模型阈值确定方法度量操作风险的有效性。
4.第五章用贝叶斯法来度量操作风险。操作风险损失数据的严重缺失是阻碍操作风险度量的难题。虽然贝叶斯法在小样本推断下有较好的效果,但在实际求解参数的后验分布中却存在高维积分运算这个异常复杂的数值计算困难。所以,如何解决贝叶斯法的实际应用问题仍值得研究。
第五章选择两参数帕累托分布和负二项分布分别描述操作风险损失事件的发生强度和发生频率,然后借助于WinBUGS软件采用马尔科夫链蒙特卡罗模拟方法来解决贝叶斯的实际应用问题。以监管部门公布以及国内外媒体公开报导的279件商业银行操作风险损失事件为例,来说明提出的基于贝叶斯推断的马尔科夫链蒙特卡罗模拟方法度量操作风险的有效性。计算所得与第四章采用方法的结果接近。
5.第六章采用信度理论中的Buhlmann-Straub模型来度量操作风险。为解决单个金融机构损失数据缺乏而不能度量操作风险的问题,大多数学者是把内(单个金融机构)、外(同行业的其它金融机构)部损失数据简单合并在一起使用的。但简单地混合内外数据来当作单个金融机构的损失数据的做法比较牵强。虽然目前有学者提出将外部损失数据调整后再合并入内部损失数据的思路,但调整权重是收入指标或情景分析数据,这种方法仍然值得商榷,所以有效整合内外损失数据仍是一道关键的障碍。此外,在目前操作风险损失数据匮乏的情况下,单个金融机构很难预测本机构下一年操作风险的发生强度和频率,在数据严重不足的情况下实现上述预测也是一道障碍。
第六章先利用贝叶斯马尔科夫链蒙特卡罗模拟方法在数据不完备的情况下对损失次数逐年进行校正。再根据校正好的损失次数数据,利用以贝叶斯马尔科夫链蒙特卡罗模拟方法为基础构建的Biihlmann-Straub模型,得到每家金融机构下一年信度风险暴露量的最优无偏估计。通过对已发生的279个商业银行操作风险损失事故中筛选出国内4大国有商业银行的操作风险损失事件(共125件)来说明基于马尔科夫链蒙特卡罗模拟的信度模型对操作风险度量的有效性。
本论文的主要观点为：
1.对三类金融机构的操作风险按成因分为内部因素和外部因素。内部因素引发的操作风险分为制度类(由于制度、产品和系统的不完善所致)、技能类(由于员工知识结构不完善或理解错误所致)、失控类(由于员工无恶意主观过失所致)、欺诈类(由于员工出于私利主观故意所致)四种。外部因素引发的操作风险分为宏观政策类、欺诈类和其它类三种。其中,内部欺诈无论是在数量上还是在金额上所占比例均最大。
2.在损失分布法的框架下采用POT模型虽然能够更真实地反映出操作风险的特征,但它只针对超过较大阈值(临界点)的数据建模,因此需要设定合理的高阈值。因为如果阈值取得太高,则可取的损失数据样本点就会很少而不足以建模；而如果阈值取得太低,就会把分布接近中部的样本点也看作尾部分布来处理,不能突出POT模型的优势。目前学者在阈值的选取上一般需要在观察图形的基础上借助于主观经验来进行模糊判断。所以,如何在确定较高阈值和保证较充足样本数据之间找到平衡点仍值得研究。
3.操作风险损失数据的严重缺失是阻碍操作风险度量的难题。虽然贝叶斯法在小样本推断下有较好的效果,但在实际求解参数的后验分布中却存在高维积分运算这个异常复杂的数值计算困难。所以,如何解决贝叶斯法的实际应用问题仍值得研究。
4.鉴于操作风险损失数据的缺乏,目前大多数学者对将内(单个金融机构)、外(同行业的其它金融机构)部损失数据简单合并在一起作为整个行业来使用。但由于不同商业银行(或不同投资银行,或不同保险公司)的资产规模、产品线、业务流程、风险偏好及风控体系是有差别的,即便都是同一行业,单个金融机构的损失数据也是服从不同分布的。因此,简单地把整个行业的损失数据混合在一起会改变原有数据的分布特征,由此得到的度量结果的精确性会存在一定问题。所以,如何有效整合内、外部损失数据,甚至是如何在现有小样本情况下预测出次年单个金融机构操作风险的损失情况均有较大研究价值。
本论文的创新点为：
1.从风险成因意义上揭示操作风险对于三类金融机构在本质上的一致性
对操作风险进行度量的前提是收集和整理损失数据。因此,论文就在巴塞尔委员会定义的基础上对三类金融机构的操作风险进行了统一界定,以理顺概念的名目之争。并结合操作风险的特征对三类金融机构的操作风险按成因和业务部门这两条线分别进行分类。这项工作贡献在于保证操作风险数据收集、整理和度量范围的一致性,为后面通过实证分析说明所修正模型的度量效果提供统一、有效的数据支持。
虽然三类金融机构的业务重点和风控制度有较大差异,但从组织结构、业务流程、信息系统和从业人员这四个风险源分析操作风险的结果来看,它们无一不面临着因制度不完善、技能不熟练、操作不正确和内部欺诈等内部因素的操作风险,以及宏观政策改变和外部欺诈等外部因素的操作风险所导致的损失,可以说操作风险的特点和形成机理并无差别。而且收集了三类金融机构各自的损失数据来对比操作风险的风险暴露特征,发现它们面临的操作风险的成因也主要是“人”所引起的。因而从成因这个意义上来看,三类金融机构操作风险在本质上是一致的。从理论上来说,在损失数据数学特征相同的情况下,适用于一类金融机构的操作风险度量模型也同样适用于其它类的金融机构,这样弥补了其它金融机构缺乏操作风险度量技术的不足。
2.对POT模型中阈值确定问题的修正
在借鉴前人研究的基础上,引入变点理论来修正性地解决定量确定阈值的问题。变点统计分析的目的是对变点的存在、个数和位置进行判断以及检验,以对变点的跃度实施有效的估计。某时间点前后的数据(均值或概率分布或模型参数)发生明显变化,则将该时间点定义为(均值或概率或某模型参数)变点。结合变点理论和POT模型,认为阈值就是Hill图曲线(以临界样本的序号为横轴、以尾部指数的Hill统计量α为纵轴)非稳定区域与稳定区域的分界点,如果与一阶差分最大值相结合找到最接近曲线稳定区域的二阶差分的最大值,其所在区域就是变点所处区间,α进入稳定状态的起始位置就是变点具体所在的位置,从而能够计算得到阈值的精确数值以改善极值理论的尾部估计。这样就修正性地解决POT模型中仅凭肉眼或经验来人为确定阈值的问题。
3.对贝叶斯后验分布高维积分运算问题的修正
在借鉴前人研究的基础上,引入马尔科夫链蒙特卡罗模拟方法,选择Gibbs抽样来求解参数的后验分布,并采用WinBUGS软件进行10万次抽样来估计所构建模型的参数。在得到参数的后验估计后,通过图形诊断法、相关性诊断法和Gelman-Rubin诊断法三种方法来判断马尔科夫链蒙特卡罗模拟的收敛性,以认定参数估计结果的可信性,从而得到操作风险的监管资本。这样就修正性地解决贝叶斯法后验分布高维积分运算问题。
4.用信度模型解决内外数据混合问题及预测单个金融机构次年的损失量
在借鉴保险精算学中厘定保费研究的基础上,引入信度模型来修正性地解决数据混合与预测单个金融机构次年损失量的问题。信度理论的Buhlmann-Straub信度模型是通过合理利用本保单组合近期损失数据和主观选择的类似险种同期损失数据来估计和预测后验保费的。认为单个金融机构次年的操作风险损失金额完全可以根据本机构和行业内其它金融机构的历史损失数据以信度因子为权重来分摊推断。这里,也借助于WinBUGS软件用贝叶斯马尔科夫链蒙特卡罗模拟的方法进行10万次抽样来得到信度风险暴露量、信度因子以及其它参数的后验估计量,并还原出单个金融机构次年操作风险的损失量与发生次数。从信度因子集中于0.7的结果可看到,单个金融机构与行业内其它金融机构的操作风险损失事件具有非同质性,不能简单地混合在一起使用。因此,所采用的方法可以有效解决上述两个问题。
With rapidly changing external environment and increasingly fierce industrial competition, financial institutions meet more and more complicated challenges. Because operational risk exists widely in the daily operation of financial institutions, and its characteristic and controlling method is significantly different from other risks. So facing over-growing operational risk, financial supervision department and financial institutions pay more and more attention on the measures against it.
Nowadays, managing and controlling techniques of operational risk have been researched among the academia and practice circle. Although there was increasing focus on it for domestic financial institutions, preliminary results were only achieved at the following aspects:characteristic and formation mechanism. Large gap still exists in operational risk measurement and methods compared with foreign peers. Control and management of operational risk start from measurement. Therefore, it is urgent issue for discussion to solve how to measure operational risk for domestic financial industry.
This thesis has the following three research significances:
1. Operational risk of financial institutions is same in essence. This conclusion helps to measure operational risk for all types of financial institution.
Nowadays, research of measurement on commercial bank's operational risk has been relatively deep at both home and abroad. But researches on other types of financial institution are rare. Then, whether measurement technique adapted for commercial bank can also be applied for other financial institution? Only by revealing operational risk's essential of three-type financial institutions can deepen knowledge of operational risk, avoid risk quantification blindly and find out common measurement technique of operational risk for all financial institutions.
2. Measurement accuracy of operational risk is related to whether implement of management is effective or not.
Risk measurement is the important point of risk management system. It is incorrect for the financial institutions to ignore risk measurement and discuss risk management directly. After all, the choice of measurement technique and method decide the effectiveness of risk internal control mechanism and risk management. But research on operational risk starts late compared with credit risk and market risk, unified understanding about operational risk measurement has't been formed. Meanwhile, difference between domestic research and foreign research on operational risk is huge. Therefore, improved measurement technique of operational risk has vital significance to enhance competitiveness of financial institutions.
3. Measurement accuracy of operational risk is related to whether economical capital can exert its effect or not.
Economical capital is equal to unexpected loss amount of risk in quantity. It is used to measure and defend the part of loss exceeding expected loss. It is the core tool of optimizing resource allocation and raising risk adjusted return on capital (RAROC). After economical capitale is calculated, conomical capital can be allocated. From this perspective, measurement accuracy of operational risk is important for financial institutions.
The main research content of this thesis is:
1. The first two chapter introduce background, significance, innovation of this thesis. Then aimed at laying theoretical foundation for the following chapters, a comprehensive literature review is made on operational risk measurement method, particularly on three methods:Loss Distribution Approach, Extreme Theory Approach, Bayes Method and Credibility Model.
2. If there is no profound understanding about relationship with concept, characteristic and type of operational risk, quantitative model is useless. So the third chapter firstly gives the unified definition of financial institution. Then classify operational risk according to cause and business department. Finally analyze what triggers operational risk and compare the operational risk's feature of three-type financial institution. Through the above analysis, this thesis has one conclusion:operational risk of financial institution is same in essence. Thereby, operational risk's measurement technique suited to one type's financial institution can also be applied to the other type's financial institution. This chapter establishes the solid foundation for the following chapter.
3. In the fourth chapter, Loss Distribution Approach (LDA) is used to measure operational risk. BCBS proposes three types'operational risk measurement methods. Among the Advanced Measurement Approach (AMA), LDA is the most frequently used method. Because LDA is based on historical loss data, measurement result is relatively objective. Under the framework of LDA, Peaks over Threshold Approach (POT) is used to measure operational risk. The tail behavior of distribution is more important for the extreme huge loss data. Because Extreme Value Theory (EVT) is targeted on fitting tail of distribution, it is publicly accepted method. But how to select threshold precisely is still one key obstacle in the practical application.
In the fourth chapter, to select threshold quantitatively and more accurately, a corrected method using change point theory to locate stable state of Hill curve is proposed. Empirical research with example of commercial bank's operational risk loss data (totaled279pieces reported by domestic and overseas media) is done to test the effectiveness of this corrected method.
4. In the fifth chapter, Bayes Method is used to measure operational risk. Although this method is widely accepted in the case of small sample, it still has one difficulty in the practical application.
In the fifth chapter, Pareto Distribution and Negative Binominal Distribution are used to describe severity and frequency of operational risk respectively. Then difficulty is solved by adopting MCMC simulation method with using WinBUGS software. Because three-type financial institution face the exactly same operational risk, empirical research with example of commercial bank's operational risk loss data (totaled279pieces reported by domestic and overseas media) can test the effectiveness of this corrected model.
5. In the sixth chapter, Credibility Model is used to measure operational risk. To solving the problem of deficient loss data, majority of scholars combine the internal and external loss data directly. But due to the heterogeneity of risk, this data processing method is inappropriate. So how to integrate internal and external loss data, even how predict the operational risk loss of the next year just for one individual financial institution is still the difficult problem in the practical application.
In the sixth chapter, Buhlmann-Straub credibility model is used to get risk exposure of operational risk by using MCMC algorithm with the implement of WinBUGS in the event of insufficient loss data. Empirical research with example of stated-own commercial bank's operational risk loss data (totaled125pieces reported by domestic and overseas media) is done to test the effectiveness of this method.
The main viewpoint of this thesis is:
1. According to cause of formation, operational risk is classified into internal factor and external factor. Internal factor is also divided into four categories: system, skill, out of control as well as fraud. Here, system category refers to the operational risk caused by imperfect system and product. Skill category refers to the operational risk caused by employees'imperfect knowledge and incorrect understanding. Out of control category refers to the operational risk caused by employees' subjective negligence without malice. While fraud category refers to the operational risk caused by employees'subjective negligence motivated by self-interest. External factor can be divided into three categories:Macro-policy, fraud and other. Among the above category, internal fraud risk has the biggest share in quantity and amount.
2. Although POT can describe the characteristic of operational risk better, it has one key obstacle:how to determine threshold. If bigger threshold is selected, fewer samples. can be used. If smaller threshold is selected, more samples that don't belong to tail of distribution will be used. The above two kinds of circumstances will bring biased result. So how to determine threshold more accurately is still worthy of researching.
3. Although Bayes Method is has better prospective, it has one obstacle: high-dimensional value computation of posteriori distribution. This process is far more complicated. So how to put this method into practice is still worthy of researching.
4. Due to insufficient loss data, most scholars solve this problem by mixing internal and external loss data directly. But every financial institution has different product line, operation procedure, risk preference and risk control system. In other words, risk heterogeny exists among financial institution. And the accuracy of measurement result can be doubted with application of this data process. So how to integrate internal and external loss data more efficiently, even how to predict the next year's operational loss for one financial institution is still worthy of researching.
The innovation of this thesis is:
1. Operational risk of financial institution is same in essence.
The premise of operational risk measurement is collecting loss data. Aimed at standardize data collection and build up solid foundation for the latter empirical research, definition of operational risk for financial institution is made. Although product line and risk control system of each financial institution have differences, the characteristic and cause of operational risk is basically same by analyzing sources of risk (organization structure, work flow, information system as well as employee). Meanwhile, through comparing loss data of three-type financial institution, we find that they face common main cause of formation:employee. So operational risk of three-type financial institution is same in essence.
2. Threshold selection of POT model based on change point theory.
Based on the former research, change point theory is introduced to solve the difficulty of selecting threshold quantitively and more accurately for Peak over Threshold Theory. Threshold is located at the stable state of Hill curve. It can be selected combined maximum value of first-order differential and maximum value of second-order differential. Empirical results show that a good evaluation of capital requirement for operational risk can be obtained.
3. Applying Bayes Method based on MCMC simulation.
Based on the former research, MCMC simulation by applying Bayesian approach is introduced to solve the difficulty of insufficient loss data. So this thesis discusses how to conduct a Markov Chain for Negative Binominal distribution and Pareto distribution with Gibbs sampling in order to get posterior distributions of loss severity and frequency dynamically as well as capital requirement for operational risk. Then put WINBUGS software to use to estimate parameters of distributions. Thus, better evaluation of capital requirement for operational risk can be obtained compared with the maximum likelihood estimation method.
4. Mixing internal and external loss data and predicting loss for one financial institution by using credibility model.
Based on the former research, credibility model is introduced to solve the difficulty of mixing internal and external loss data. Due to the deficient data and heterogeneity of risk, it's hard for financial institution to get the unbiased estimated measurement by mixing the internal and external event of loss. Buhlmann-Straub credibility model is conducted to get risk exposure of operational risk by using MCMC algorithm with the implement of WinBUGS in the event of insufficient loss data. Then the amount of loss in the next year can be predicted for the individual financial institution. Empirical results show that measuring operational risk is inappropriate by mixing loss data of financial institution with different risk features. The stochastic simulation method applied by this thesis can improve the precision of estimators.
引文
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