商业银行违约损失率估计模型构建研究
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摘要
违约损失率(LGD)是计算监管资本的重要参数,也是按新巴塞尔资本协议实施内部评级法(IRB)高级法的银行必须自行估计的参数。随着国内银行业推进巴塞尔新资本协议实施进程的加快,LGD模型的构建成为国内各家银行攻坚的重点。然而,受贷款违约损失率的影响因素复杂、合格数据缺乏、建模技术要求高等方面因素的影响,目前国内无论在学术界、监管部门还是银行内部,都缺乏成熟的方法和技术。
本文通过借鉴国内外违约损失率计量的研究成果,结合新资本协议有关要求和我国银行业的实际情况,基于中国银行江苏省分行2002年至2010年7月间的违约贷款债项信息数据,尝试对国内银行LGD估计模型的构建方法进行研究。
围绕LGD模型的开发,本文在对LGD的相关理论、文献,现有LGD建模方法以及国内开发LGD模型的难点和约束条件等进行研究分析的基础上,提出了以统计计量模型为核心,辅之以专家调整的LGD混合模型体系的模型构建思路。
为构建LGD统计模型,本文重点对两个关键环节进行突破：一是历史债项LGD的计算及其转换；二是模型自变量的确定。
围绕第一个环节,本文首先从违约和损失的概念界定、清收结束时间的确定、清收中回收部分的计算、清收中成本部分的计算、LGD计算中贴现率的设定和EAD的计算等六个方面入手,突破LGD计算过程中存在的技术难题,完成历史违约债项LGD的计算；在此基础上,通过对样本LGD分布的观察分析,发现该分布与Beta分布较为相似,基于此,对样本LGD分布进行了Beta拟合,并通过Beta分布与正态分布之间转换,将LGD数据序列转换成服从正态分布、可用于统计模型建模的Y序列,而Y值与LGD值之间可以相互转换,从而解决了LGD统计模型的因变量问题。
围绕第二个环节,本文首先梳理出可能影响LGD的潜在因素,其次,对梳理出的潜在影响因素逐个进行单因素分析,鉴于潜在影响因素均为类型变量,采用设定虚拟变量的方式对类型变量进行处理,在单因素分析的过程中,以统计显著性、经济含义等为约束条件,对部分不符合条件的变量做放弃处理,从而筛选出LGD统计模型的备选变量；第三,采用逐步回归的方法进行模型优化和变量选择,最终确定LGD统计模型；第四,从模型的拟合效果、可靠性和准确性三个纬度进行模型检验。通过上述步骤,本文建立了一个包括地区、行业、企业性质、企业规模、贷款占比、贷款溯源、风险缓释类型7个LGD影响因素,共11个虚拟自变量的LGD统计模型。
考虑到在LGD统计模型之外还存在着一些因素可能会对LGD产生较大影响,以及统计模型本身的局限性、数据基础的缺陷性等方面因素,本文在LGD统计模型的基础上引入专家调整法,提出了可用于实践的LGD“混合模型”方案。该方案包括两个层面,第一个层面是：通过专家调整的方式对LGD统计模型中没有考虑到的宏观经济周期因素、借款人的还款顺序、借款人的资产负债率、债项的抵押情况、债项的质押情况、债项的担保情况六个因素进行考虑,形成LGD调整方案,从而使得LGD的预测值能够尽可能多地包含影响LGD因素的信息；第二个层面是,对于由LGD统计模型加上专家调整方案共同组成的LGD混合模型确定的LGD预测值,与传统专家模型下的LGD范围边界值进行比照,一旦突破边界,则启动专家整体复议方案,从而避免模型预测结果出现较大偏差的情况。通过在统计计量模型的基础上引入专家判断调整和人工复议,弥补了单纯LGD统计模型的局限,保证了LGD模型预测结果的准确度和合理性,为LGD模型由理论走向具体实践提供了一个现实可行的方案。
本文可能的创新之处在于：
第一,受LGD影响因素复杂、合格数据缺乏、建模技术要求高等方面因素的影响,国内LGD估计模型的研究还处于起步阶段。本文不仅提出了一个较为完整的LGD估计模型,对模型构建过程中的关键技术也有创新突破,构建的以统计计量模型为核心、辅之以专家调整的LGD混合模型体系,在国内尚属首次。
第二,根据对中国银行江苏省分行历史LGD数据分布的观察,采用Beta拟合技术和Beta分布与正态分布的转换技术,实现了LGD实际数据向LGD统计模型应用数据的转换,解决了LGD模型构建过程中的一个技术难题。此外,针对LGD计算上的难点,基于国内银行实际情况给出了相关概念的界定和具体的LGD计算方案,具有较强的可操作性,为LGD模型的建立奠定了基础。
第三,根据LGD统计模型的潜在自变量多为类型变量、且类型较多的特点,采取了根据不同类型下的平均LGD情况进行重新分类,并在此基础上设定虚拟变量的处理方法,这是本文在探索LGD建模方法中的一个创新,有效解决了LGD影响因素的定性信息向LGD统计模型可用的定量信息的转化难题。
本文的不足之处在于：
第一,本文建模所使用的数据是中国银行江苏省分行2002年至2010年7月间的对公贷款违约债项信息,其间,由于股改上市因素,对一部分不良资产进行了剥离,导致该部分数据的缺失,这可能会对模型的结果产生一定的影响。
第二,在构建LGD混合模型时,本文在LGD统计模型的基础上引入了专家调整法。由于该方法需要基于实践进行探索。因此,本文仅仅是提出了一个专家调整的方案,具体如何在现实中落地未能进行系统的研究。
Loss given default (LGD) is an important parameter for the calculation of regulatory capital, also the parameter must be estimated by banks of their own according the implementation of Basel II internal ratings-based (IRB) Advanced law. With the domestic banking sector to promote the implementation of Basel II to speed up the process, the development of LGD model becomes the focus of tackling domestic banks. However, due to complex factors of LGD, lack of qualified data and modeling requirements of advanced factors, either domestic academia, regulatory authorities or the bank's internal, both lack of proven methods and techniques.
By LGD home and abroad measured research, combining with the relevant requirements of the new Capital Accord and the actual situation of China's banking industry, this paper try to construct the quantitative modeling method for domestic banks'LGD, based on the Bank of China Jiangsu Branch from2002to July2010of default loans debt information.
Around the development of LGD quantitative models, on the base of system analysis of the relevant article in the LGD theory, literature, the existing modeling methods and the domestic development of LGD models such as the difficulties and constraints of research and analysis, this paper propose a construction method of LGD mixed-model system, with the establishment of quantitative models as the core, supplemented by experts.
In order to construction the LGD quantitative models, this paper focus on two key aspects of a breakthrough:The first is to complete calculation and conversion of history debt LGD; and the second is to determine the model variables.
Around the first link, from the six aspects, including the concept of default and loss from the definition of the end of the clear closing time determination, clear recovery of part of the calculation of income, the cost of clearing some of the calculation of income, LGD setting the discount rate calculation and the calculation of EAD, this paper break the technical problems exist to complete the historical default LGD calculation of the debt for LGD calculation; On this basis, by observing and analyzing the distribution of LGD samples, it found that the distribution was similar with the Beta distribution, based on this, through the distribution of LGD Beta fitting, and by switching between Beta distribution and normal distribution, the data sequence into a subject LGD Normal distribution, then it can be used for statistical modeling of the Y sequence, also the Y value and the LGD value can be interchangeable, thus the problem of the dependent variable for LGD statistical model was solved.
Around the second aspect, firstly, this paper teases out the underlying factors that may affect the LGD; Secondly, the potential fators was caome out one by one by single factor analysis. Given the potential influence factors are type variables, this paper set the dummy variable approach to the type variable handling, in the course of a single factor analysis to statistical significance, economic implications such as the constraints on the part of the variables do.not meet the conditions to give up processing to filter out options for variable statistical model LGD:Third, through the use of stepwise regression approach to model optimization and variable selection, the final LGD quantitative models was identified; Fourth, checking the quantitative model from the three dimensions of the fitting results, the reliability and accuracy. Through the above steps, this paper builds the LGD virtual statistical model including11independent variables, such as egion, industry, ownership, firm size, loan accounting, loan source, type of risk mitigation factors.
Base on the LGD statistical model, this paper propose a "hybrid model" program on the base of adjusted by experts. The program includes two aspects, the first, taking into accounting the important factors that do not considered by expert adjustment, including six fators such as macroeconomic cycle factors, the borrower's repayment order, the borrower's debt ratio, mortgage debt situation, pledge debt situation, debt guarantees. By this way. the predictive value of LGD can contain as much as possible factors affect LGD information. The second, comparing the predictive value of LGD mixed model with the traditional expert model of LGD, once breaking the boundary, then starting the whole review experts Program, thus avoiding the predicted results to the case of larger deviations. Statistical measurement model through the introduction of expert judgments on the basis of adjustment and manual review to make up the limitations of purely statistical models LGD, ensuring the accuracy and reasonableness of the LGD model, thus, providing a realistic feasible method of theory to pratice.
The main contribution of this paper is:
1. On the base of historical data and empirical research, this paper constructs a LGD mixed-model system, with the establishment of quantitative models as the core, supplemented by experts, the model's construction ideas and build technology for the development of domestic banks provide LGD models useful reference and specific examples.
2. For the calculation of LGD are explored in this key link, based on the actual situation of domestic banks, this paper give the definition of relevant concepts and specific LGD calculation scheme, with a strong operational; the same time, LGD of the Beta fit and normality Distribution conversion method, for domestic LGD Model of a breakthrough technical problems.
3. As to the type of variable factors of LGD, according to the different types of the average LGD to be re-classified, and on this basis, setting the dummy variable approach is the first time in the domestic banking industry, this method effectively solves the problems of more types of factors and the difficult to carry out the virtual variable for LGD facts, and the method is simple and proven results is higher.
The main inadquance of this paper is:
1. The data used in model is the information of public loan defaults on dabt from Bank of China, Jiangsu Branch between2002and July2010. During this period, as to the stocks were listed, part of non-performing assets were stripped, resulting some data absence, it may have some impact on the result of model.
2. This paper used expert adjustment method on the base of LGD statistical model, when constructing the hybrid LGD model. Since this method requires exploration on practice, therefore, this paper just proposes an adjustment program by expert, but how to fall in the real world do not systematically discussed.
本文通过借鉴国内外违约损失率计量的研究成果,结合新资本协议有关要求和我国银行业的实际情况,基于中国银行江苏省分行2002年至2010年7月间的违约贷款债项信息数据,尝试对国内银行LGD估计模型的构建方法进行研究。
围绕LGD模型的开发,本文在对LGD的相关理论、文献,现有LGD建模方法以及国内开发LGD模型的难点和约束条件等进行研究分析的基础上,提出了以统计计量模型为核心,辅之以专家调整的LGD混合模型体系的模型构建思路。
为构建LGD统计模型,本文重点对两个关键环节进行突破：一是历史债项LGD的计算及其转换；二是模型自变量的确定。
围绕第一个环节,本文首先从违约和损失的概念界定、清收结束时间的确定、清收中回收部分的计算、清收中成本部分的计算、LGD计算中贴现率的设定和EAD的计算等六个方面入手,突破LGD计算过程中存在的技术难题,完成历史违约债项LGD的计算；在此基础上,通过对样本LGD分布的观察分析,发现该分布与Beta分布较为相似,基于此,对样本LGD分布进行了Beta拟合,并通过Beta分布与正态分布之间转换,将LGD数据序列转换成服从正态分布、可用于统计模型建模的Y序列,而Y值与LGD值之间可以相互转换,从而解决了LGD统计模型的因变量问题。
围绕第二个环节,本文首先梳理出可能影响LGD的潜在因素,其次,对梳理出的潜在影响因素逐个进行单因素分析,鉴于潜在影响因素均为类型变量,采用设定虚拟变量的方式对类型变量进行处理,在单因素分析的过程中,以统计显著性、经济含义等为约束条件,对部分不符合条件的变量做放弃处理,从而筛选出LGD统计模型的备选变量；第三,采用逐步回归的方法进行模型优化和变量选择,最终确定LGD统计模型；第四,从模型的拟合效果、可靠性和准确性三个纬度进行模型检验。通过上述步骤,本文建立了一个包括地区、行业、企业性质、企业规模、贷款占比、贷款溯源、风险缓释类型7个LGD影响因素,共11个虚拟自变量的LGD统计模型。
考虑到在LGD统计模型之外还存在着一些因素可能会对LGD产生较大影响,以及统计模型本身的局限性、数据基础的缺陷性等方面因素,本文在LGD统计模型的基础上引入专家调整法,提出了可用于实践的LGD“混合模型”方案。该方案包括两个层面,第一个层面是：通过专家调整的方式对LGD统计模型中没有考虑到的宏观经济周期因素、借款人的还款顺序、借款人的资产负债率、债项的抵押情况、债项的质押情况、债项的担保情况六个因素进行考虑,形成LGD调整方案,从而使得LGD的预测值能够尽可能多地包含影响LGD因素的信息；第二个层面是,对于由LGD统计模型加上专家调整方案共同组成的LGD混合模型确定的LGD预测值,与传统专家模型下的LGD范围边界值进行比照,一旦突破边界,则启动专家整体复议方案,从而避免模型预测结果出现较大偏差的情况。通过在统计计量模型的基础上引入专家判断调整和人工复议,弥补了单纯LGD统计模型的局限,保证了LGD模型预测结果的准确度和合理性,为LGD模型由理论走向具体实践提供了一个现实可行的方案。
本文可能的创新之处在于：
第一,受LGD影响因素复杂、合格数据缺乏、建模技术要求高等方面因素的影响,国内LGD估计模型的研究还处于起步阶段。本文不仅提出了一个较为完整的LGD估计模型,对模型构建过程中的关键技术也有创新突破,构建的以统计计量模型为核心、辅之以专家调整的LGD混合模型体系,在国内尚属首次。
第二,根据对中国银行江苏省分行历史LGD数据分布的观察,采用Beta拟合技术和Beta分布与正态分布的转换技术,实现了LGD实际数据向LGD统计模型应用数据的转换,解决了LGD模型构建过程中的一个技术难题。此外,针对LGD计算上的难点,基于国内银行实际情况给出了相关概念的界定和具体的LGD计算方案,具有较强的可操作性,为LGD模型的建立奠定了基础。
第三,根据LGD统计模型的潜在自变量多为类型变量、且类型较多的特点,采取了根据不同类型下的平均LGD情况进行重新分类,并在此基础上设定虚拟变量的处理方法,这是本文在探索LGD建模方法中的一个创新,有效解决了LGD影响因素的定性信息向LGD统计模型可用的定量信息的转化难题。
本文的不足之处在于：
第一,本文建模所使用的数据是中国银行江苏省分行2002年至2010年7月间的对公贷款违约债项信息,其间,由于股改上市因素,对一部分不良资产进行了剥离,导致该部分数据的缺失,这可能会对模型的结果产生一定的影响。
第二,在构建LGD混合模型时,本文在LGD统计模型的基础上引入了专家调整法。由于该方法需要基于实践进行探索。因此,本文仅仅是提出了一个专家调整的方案,具体如何在现实中落地未能进行系统的研究。
Loss given default (LGD) is an important parameter for the calculation of regulatory capital, also the parameter must be estimated by banks of their own according the implementation of Basel II internal ratings-based (IRB) Advanced law. With the domestic banking sector to promote the implementation of Basel II to speed up the process, the development of LGD model becomes the focus of tackling domestic banks. However, due to complex factors of LGD, lack of qualified data and modeling requirements of advanced factors, either domestic academia, regulatory authorities or the bank's internal, both lack of proven methods and techniques.
By LGD home and abroad measured research, combining with the relevant requirements of the new Capital Accord and the actual situation of China's banking industry, this paper try to construct the quantitative modeling method for domestic banks'LGD, based on the Bank of China Jiangsu Branch from2002to July2010of default loans debt information.
Around the development of LGD quantitative models, on the base of system analysis of the relevant article in the LGD theory, literature, the existing modeling methods and the domestic development of LGD models such as the difficulties and constraints of research and analysis, this paper propose a construction method of LGD mixed-model system, with the establishment of quantitative models as the core, supplemented by experts.
In order to construction the LGD quantitative models, this paper focus on two key aspects of a breakthrough:The first is to complete calculation and conversion of history debt LGD; and the second is to determine the model variables.
Around the first link, from the six aspects, including the concept of default and loss from the definition of the end of the clear closing time determination, clear recovery of part of the calculation of income, the cost of clearing some of the calculation of income, LGD setting the discount rate calculation and the calculation of EAD, this paper break the technical problems exist to complete the historical default LGD calculation of the debt for LGD calculation; On this basis, by observing and analyzing the distribution of LGD samples, it found that the distribution was similar with the Beta distribution, based on this, through the distribution of LGD Beta fitting, and by switching between Beta distribution and normal distribution, the data sequence into a subject LGD Normal distribution, then it can be used for statistical modeling of the Y sequence, also the Y value and the LGD value can be interchangeable, thus the problem of the dependent variable for LGD statistical model was solved.
Around the second aspect, firstly, this paper teases out the underlying factors that may affect the LGD; Secondly, the potential fators was caome out one by one by single factor analysis. Given the potential influence factors are type variables, this paper set the dummy variable approach to the type variable handling, in the course of a single factor analysis to statistical significance, economic implications such as the constraints on the part of the variables do.not meet the conditions to give up processing to filter out options for variable statistical model LGD:Third, through the use of stepwise regression approach to model optimization and variable selection, the final LGD quantitative models was identified; Fourth, checking the quantitative model from the three dimensions of the fitting results, the reliability and accuracy. Through the above steps, this paper builds the LGD virtual statistical model including11independent variables, such as egion, industry, ownership, firm size, loan accounting, loan source, type of risk mitigation factors.
Base on the LGD statistical model, this paper propose a "hybrid model" program on the base of adjusted by experts. The program includes two aspects, the first, taking into accounting the important factors that do not considered by expert adjustment, including six fators such as macroeconomic cycle factors, the borrower's repayment order, the borrower's debt ratio, mortgage debt situation, pledge debt situation, debt guarantees. By this way. the predictive value of LGD can contain as much as possible factors affect LGD information. The second, comparing the predictive value of LGD mixed model with the traditional expert model of LGD, once breaking the boundary, then starting the whole review experts Program, thus avoiding the predicted results to the case of larger deviations. Statistical measurement model through the introduction of expert judgments on the basis of adjustment and manual review to make up the limitations of purely statistical models LGD, ensuring the accuracy and reasonableness of the LGD model, thus, providing a realistic feasible method of theory to pratice.
The main contribution of this paper is:
1. On the base of historical data and empirical research, this paper constructs a LGD mixed-model system, with the establishment of quantitative models as the core, supplemented by experts, the model's construction ideas and build technology for the development of domestic banks provide LGD models useful reference and specific examples.
2. For the calculation of LGD are explored in this key link, based on the actual situation of domestic banks, this paper give the definition of relevant concepts and specific LGD calculation scheme, with a strong operational; the same time, LGD of the Beta fit and normality Distribution conversion method, for domestic LGD Model of a breakthrough technical problems.
3. As to the type of variable factors of LGD, according to the different types of the average LGD to be re-classified, and on this basis, setting the dummy variable approach is the first time in the domestic banking industry, this method effectively solves the problems of more types of factors and the difficult to carry out the virtual variable for LGD facts, and the method is simple and proven results is higher.
The main inadquance of this paper is:
1. The data used in model is the information of public loan defaults on dabt from Bank of China, Jiangsu Branch between2002and July2010. During this period, as to the stocks were listed, part of non-performing assets were stripped, resulting some data absence, it may have some impact on the result of model.
2. This paper used expert adjustment method on the base of LGD statistical model, when constructing the hybrid LGD model. Since this method requires exploration on practice, therefore, this paper just proposes an adjustment program by expert, but how to fall in the real world do not systematically discussed.
引文
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6 Altman, Resti and Sironi. Analyzing and Explaining Default Recovery Rates. ISDA report. 2001,12.
7 Amihud, Yakov, Kenneth Garhade and Marcel Kahan. An institutional innovation to reduce agency costs of public corporate bonds [J]. Journal of Applied Corporate Finance, 2000(l):114-121.
8 Araten, M., Jacobs, Jr., and Varshney, P. Measuring LGD on commercial loans:An 18-year internal study [J]. The Journal of the Risk Management Association,2004, May,28-35.
9 Asarnow E., Edwards D. Measuring Loss on Defaulted Bank Loans:a 24-Year Study [J]. The Journal of Commercial Lending,1995, Vol.77, No.7. pp.11-23.
10 Basel Committee. Modifications to the Capital Treatment for Expected and Unexpected Credit Losses in the New Basel Accord,2004.
11 Benett R.L., Catarineu E., Moral G. Loss Given Default Validation [R]. In:Basel Committee on Banking Supervision, Studies on the Validation of Internal Rating Systems. Working Paper No.14, Bank for International Settlement,2005, pp.60-93.
12 Basel Committee. New Basel Capital Accord CP2 [M], Jan,2001.
13 Basel Committee. New Basel Capital Accord CP3 [M], Jan,2003.
14 Carey, Mark and Michael Gordy. Systematic Risk in Recoveries on Defaulted Debt. Mimeo, Federal Reserve Board, Washington,2003.
15 Carty and Hamilton, et.al. Bankrupt Bank Load Recoveries [J]. Moody's Special Report. 1998(6).
16 Carty. I. and D. Lieberman. Defaulted bank load recoveries [R]. Moody's Special Comment. 1996:1-12.
17 Christopher James. RAROC Based Capital Budgeting and Performance Evaluation:A Case Study of Bank Capital Allocation. Wharton Financial Institutions Center's conference on Risk Management in Banking, Working Paper.2003,8-15.
18 Crouhy, M. and D. Gaiai, D. Mark. Evaluating Credit Risk:An Option Pricing Approach [J]. Risk Management and Regulation in Banking,1997(11).
19 David T Hamilton and Lea V Carty. Debt recoveries for corporate bankruptcies [R]. Moody's Investors Service, Global Credit Research, June,1999:1-16.
20 Dermine J and Caralho C. Bank loan losses-Given-Default:A Case Study [J]. Journal of Banking and Finance,2006, Vol.30, pp.1219-1243.
21 D-Fine. LGD-Rating for a Portfolio of Retail Loans. A diploma thesis.2004,5.
22 Dimities N.Chorafas. Economic Capital. Allocation with Basel II Cost benefit and implementation procedures.2004.
23 Dullmann, K., and M. Trapp. Systematic Risk in Recovery Rates-An Empirical Analysis of U.S. Corporate Credit Exposures, in E. I. Altman, A. Resti and A. Sironi (eds), Recovery Risk: The Next Challenge in Credit Risk Management. Risk Books, London,2005:235-252.
24 Eales, R. and Bosworth. Severity of loss in the event of default in small business and larger consumer loans [J]. Journal of Leading and Credit Risk Management,1998,27(4):58-65.
25 Franks, J., de Servigny, A., Davdenko, S. A Comparative Analysis of the Recovery Process and Recovery Rate for private Companies in the U.K., France, and Germany. Standard and Poor's Risk Solutions, July,2004.
26 Froot,.K.A., and J.C.Stein. A New Approach to Capital Budgeting for Financial Institutions. HarVARd Business School, Working Paper, July,2006.
27 Froot, K.A., and J.C.Stein., Risk Management, capital budgeting, and capital structure policy for financial institutions:an integrated approach. Journal of Financial Economics, Vol.47, No.l,1998
28 Frye, J. Collateral damage detected [R]. Federal Reserve Bank of Chicago, Working Paper, Emerging Issues Series, October,2000:1-14.
29 Frye, J. Depressing recoveries [J]. Risk.2000,13(11):106-111.
30 G. Bakshi, D. Madan, Zhang Frank. Understanding the Role of Recory in Default Risk Models:Empirical Comparisons and Implied Recovery Rate. [J]. Finance and Economics Disscssion Series. Federal Reserve Board of Governors, Washington D.C.,2001(37).
31 Greg M. Gupton, Daniel Gates and Lea V. Carty. Bank-loan loss given default [R]. Moody's Investors Service, Global Credit Research, November,2000:1-24.
32 Greg M. Gupton, Roger M. Stein, LossCalcTM:Moody's Models for Prediting Loss Given Default, http://www.moodyskmv.com/products/LGD.html.
33 Grossman, R, S O Shea, and S. Bonelii. Bank load and bond recovery study:1997-2000 [R]. Fitch Load Products Special Report, March,2001:1-23.
34 Gupton, G. and Stein, R. Losscalc:Model for predicting loss given default (LGD), Moody's Investors Service,2002,2.
35 Gupton, G., Finger, C. and Bhatia, M. CreditMetrics-Technical document, J.P. Morgan,1997.
36 Gupton, Gates and Carty. Bank-loan loss given default. [R]. Moody's Investor's Service, Global Credit Research,2000(11):1-24.
37 Hamilton, David T., Greg M. Gupton and Alexandra Berhault, Default and Recovery Rates of Corporate Bond Issuers:2000 [R]. Moody's Special Comment,2001.
38 Harris, M.and A. Aviv. The Capital Budgeting Process:Incentives and Information. Journal of Finance,1996.
39 Hartmannn-Wendels, T.&M Honal. Do Economic Downturns Have an Impact on the Loss Given Default of Mobile Lease Contracts. Working Paper,2006.
40 Helmut Grundl, Hato Schmeiser. Risk-adjusted Performance Measurement and Capital Allocation in Insurance Firms. July,2002.
41 Hu, Y.&T, W. Perraudin. The Dependence of Recovery Rates and Defaults, Working Paper, Birkbeck College and Bank of England,2002.
42 Hui Li. Downturn LGD:A Spot Recovery Approach [R]. MPRA Working Paper No.20375, 2010.
43 Hurt I. and Felsovalyi A. Measuring loss on latin American defaulted bank loans, a 27 year Study of 27 Country [J]. The Journal of Leading and Credit Risk Management,1998, 81(11):41-46.
44 James, C. RAROC based Capital Budgeting and Performance Evaluation:A Case Study of Bank Capital Allocation. Working Paper#96-40, Wharton Financial Institutions Center,1996.
45 Jens Grunert and Martin Weber. Recovery Rate of Bank Loans:Empirical Evidence for Germany [R]. Working Paper, March,2005.
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4 Altman, E. and V. Kishore. Almost everything you wanted to know about recovery on defaulted bonds [J]. Financial Analysts Journal,1996(6):57-64.
5 Altman, Edward I. and Eberhart, Allan C. Do Seniority Provisions Protect Bondholders' Inestment? [R]. A New York University Salomon Center Working Paper, Series S-94-12, 1994.
6 Altman, Resti and Sironi. Analyzing and Explaining Default Recovery Rates. ISDA report. 2001,12.
7 Amihud, Yakov, Kenneth Garhade and Marcel Kahan. An institutional innovation to reduce agency costs of public corporate bonds [J]. Journal of Applied Corporate Finance, 2000(l):114-121.
8 Araten, M., Jacobs, Jr., and Varshney, P. Measuring LGD on commercial loans:An 18-year internal study [J]. The Journal of the Risk Management Association,2004, May,28-35.
9 Asarnow E., Edwards D. Measuring Loss on Defaulted Bank Loans:a 24-Year Study [J]. The Journal of Commercial Lending,1995, Vol.77, No.7. pp.11-23.
10 Basel Committee. Modifications to the Capital Treatment for Expected and Unexpected Credit Losses in the New Basel Accord,2004.
11 Benett R.L., Catarineu E., Moral G. Loss Given Default Validation [R]. In:Basel Committee on Banking Supervision, Studies on the Validation of Internal Rating Systems. Working Paper No.14, Bank for International Settlement,2005, pp.60-93.
12 Basel Committee. New Basel Capital Accord CP2 [M], Jan,2001.
13 Basel Committee. New Basel Capital Accord CP3 [M], Jan,2003.
14 Carey, Mark and Michael Gordy. Systematic Risk in Recoveries on Defaulted Debt. Mimeo, Federal Reserve Board, Washington,2003.
15 Carty and Hamilton, et.al. Bankrupt Bank Load Recoveries [J]. Moody's Special Report. 1998(6).
16 Carty. I. and D. Lieberman. Defaulted bank load recoveries [R]. Moody's Special Comment. 1996:1-12.
17 Christopher James. RAROC Based Capital Budgeting and Performance Evaluation:A Case Study of Bank Capital Allocation. Wharton Financial Institutions Center's conference on Risk Management in Banking, Working Paper.2003,8-15.
18 Crouhy, M. and D. Gaiai, D. Mark. Evaluating Credit Risk:An Option Pricing Approach [J]. Risk Management and Regulation in Banking,1997(11).
19 David T Hamilton and Lea V Carty. Debt recoveries for corporate bankruptcies [R]. Moody's Investors Service, Global Credit Research, June,1999:1-16.
20 Dermine J and Caralho C. Bank loan losses-Given-Default:A Case Study [J]. Journal of Banking and Finance,2006, Vol.30, pp.1219-1243.
21 D-Fine. LGD-Rating for a Portfolio of Retail Loans. A diploma thesis.2004,5.
22 Dimities N.Chorafas. Economic Capital. Allocation with Basel II Cost benefit and implementation procedures.2004.
23 Dullmann, K., and M. Trapp. Systematic Risk in Recovery Rates-An Empirical Analysis of U.S. Corporate Credit Exposures, in E. I. Altman, A. Resti and A. Sironi (eds), Recovery Risk: The Next Challenge in Credit Risk Management. Risk Books, London,2005:235-252.
24 Eales, R. and Bosworth. Severity of loss in the event of default in small business and larger consumer loans [J]. Journal of Leading and Credit Risk Management,1998,27(4):58-65.
25 Franks, J., de Servigny, A., Davdenko, S. A Comparative Analysis of the Recovery Process and Recovery Rate for private Companies in the U.K., France, and Germany. Standard and Poor's Risk Solutions, July,2004.
26 Froot,.K.A., and J.C.Stein. A New Approach to Capital Budgeting for Financial Institutions. HarVARd Business School, Working Paper, July,2006.
27 Froot, K.A., and J.C.Stein., Risk Management, capital budgeting, and capital structure policy for financial institutions:an integrated approach. Journal of Financial Economics, Vol.47, No.l,1998
28 Frye, J. Collateral damage detected [R]. Federal Reserve Bank of Chicago, Working Paper, Emerging Issues Series, October,2000:1-14.
29 Frye, J. Depressing recoveries [J]. Risk.2000,13(11):106-111.
30 G. Bakshi, D. Madan, Zhang Frank. Understanding the Role of Recory in Default Risk Models:Empirical Comparisons and Implied Recovery Rate. [J]. Finance and Economics Disscssion Series. Federal Reserve Board of Governors, Washington D.C.,2001(37).
31 Greg M. Gupton, Daniel Gates and Lea V. Carty. Bank-loan loss given default [R]. Moody's Investors Service, Global Credit Research, November,2000:1-24.
32 Greg M. Gupton, Roger M. Stein, LossCalcTM:Moody's Models for Prediting Loss Given Default, http://www.moodyskmv.com/products/LGD.html.
33 Grossman, R, S O Shea, and S. Bonelii. Bank load and bond recovery study:1997-2000 [R]. Fitch Load Products Special Report, March,2001:1-23.
34 Gupton, G. and Stein, R. Losscalc:Model for predicting loss given default (LGD), Moody's Investors Service,2002,2.
35 Gupton, G., Finger, C. and Bhatia, M. CreditMetrics-Technical document, J.P. Morgan,1997.
36 Gupton, Gates and Carty. Bank-loan loss given default. [R]. Moody's Investor's Service, Global Credit Research,2000(11):1-24.
37 Hamilton, David T., Greg M. Gupton and Alexandra Berhault, Default and Recovery Rates of Corporate Bond Issuers:2000 [R]. Moody's Special Comment,2001.
38 Harris, M.and A. Aviv. The Capital Budgeting Process:Incentives and Information. Journal of Finance,1996.
39 Hartmannn-Wendels, T.&M Honal. Do Economic Downturns Have an Impact on the Loss Given Default of Mobile Lease Contracts. Working Paper,2006.
40 Helmut Grundl, Hato Schmeiser. Risk-adjusted Performance Measurement and Capital Allocation in Insurance Firms. July,2002.
41 Hu, Y.&T, W. Perraudin. The Dependence of Recovery Rates and Defaults, Working Paper, Birkbeck College and Bank of England,2002.
42 Hui Li. Downturn LGD:A Spot Recovery Approach [R]. MPRA Working Paper No.20375, 2010.
43 Hurt I. and Felsovalyi A. Measuring loss on latin American defaulted bank loans, a 27 year Study of 27 Country [J]. The Journal of Leading and Credit Risk Management,1998, 81(11):41-46.
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