违约率与回收率关系及其对信用风险管理的影响
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摘要
最近,许多的研究表明,抵押品价值及违约时的回收率呈现波动性。当经济处于低迷时期,在违约数量上升的同时,抵押品价值和回收率呈现下降趋势。这种现象表明违约率与回收率之间或许存在某种关联性,但目前大多数信用风险模型均假定二者相互独立,他们只关注于违约概率,将违约时的回收率看成是一个常数参数或者是独立于违约概率的一个随机变量。对回收率的这种假定会对管理信用风险产生怎样的影响呢?显然,要分析这种影响程度就需要考察违约率与回收率之间实际存在的关系,因此,本文的研究内容是：首先在理论模型中考察系统风险对违约风险与回收风险的影响,探讨违约率与回收率之间是如何产生联系的,然后实证检验二者之间的关系,接下来考察这种关系对信用风险度量和管理的影响,为了清楚的展示其影响程度,运用蒙特卡洛模拟技术,比较了在不同假设条件下二者之间的关系对信用风险管理的影响,结果表明如果忽略二者之间的关系,仅仅只假设二者之间相互独立,则会低估信用风险水平,将会导致银行储备不充足,甚至会对金融市场产生不必要的冲击。
准确地度量信用风险水平对信用风险管控和监管是非常重要的,因此,本文以穆迪全球公司债券违约与回收数据为实证分析资料,探讨了违约率与回收率之间关系及其影响,全文可分为四大部分,一是对现有信用风险模型的评述,系统梳理了违约率与回收率相关关系研究的理论成果和模型；二是介绍了单因子系统风险模型；三是应用穆迪数据进行实证分析；四是运用蒙特卡洛模拟技术考察违约率与回收率相关性对信用风险管理的影响。具体内容如下。
第一章绪论。系统地研究阐述了信用风险的理论基础、构成要素、信用风险模型以及这些模型是如何处理违约率与回收率之间的关系,并对近年来违约率与回收率相关关系研究的新进展进行梳理。
第二章探讨违约率与回收率之间的关系。当前大多数信用风险模型假设违约率和回收率之间相互独立,但是近年来更多的实证分析显示二者之间存在负相关关系,由于现阶段对二者关系的研究还处在初步阶段,因此在众多考察二者关系的理论模型中,还没有形成一致的认识。目前有关两者负相关关系成因的理论解释主要有系统风险(经济周期)影响论和违约债券供需关系影响论。本文基于单因子模型,从系统风险的角度研究违约率和回收率之间相互关系,阐述了单因子模型的理论基础和逻辑结构,给出了模型框架和极大似然估计函数。
第三章实证分析。首先基于穆迪全球公司违约数据对单因子模型进行实证分析,并研究了不同行业、不同评级企业其资产收益与系统风险因子的相关性。然后计量分析回收率与违约率之间的关系,.由于在经济衰退阶段,违约率高,回收率低,而在经济高涨阶段违约率低,回收率高,因此在回归分析中,除了违约率之外,还引入了一系列能反映宏观经济运行状态的经济指标来解释回收率。
第四章考察了PD与RR负相关关系的影响。我们考察二者之间的负相关关系对信用风险度量及管理的影响,具体说来,就是考察这种关系对经济资本计算、监管资本配置的影响。银行的资本是银行在经营过程中所需持有或被要求持有的一定数量的资本金,用来抵御在风险暴露和银行运作中可能面临的损失风险。银行内部为抵御风险而主动配备的资本属于经济资本,而由外部监管当局所要求银行必须持有的资本属于监管资本。显然,这种对银行资本的影响会直接作用于银行的资本收益甚至于银行机构本身的存续。
论文的主要观点、贡献及不足之处：
1.本文基于穆迪全球公司违约数据对单因子模型进行实证分析,考察违约风险与系统风险的相关性以及回收风险与系统风险的相关性。发现资产收益与系统风险相关系数具有相对稳定性,即在某一较短时期内,相关系数相对保持不变,尽管从长时间来看,相关系数随时间而波动。相关系数的相对不变性或许对违约率的预测有一定的意义。因为,如果已知当前时期的相关系数,只需估计有哪些因素影响以及是如何影响宏观系统因子,就能对违约率进行粗略估计。我们进一步分析了不同行业、不同评级企业资产收益与系统风险的相关系数,发现除Aa级外,企业信用等级越低,其与系统风险的绝对相关系数越高,即相对于信用等级高的公司,信用等级低的公司更加容易受到系统风险的影响。
2.在经济高涨时期,违约率降低,回收率升高,而在经济低迷时期,违约率升高,回收率则降低,但这并不意味违约率与回收率之间具有对称的关系。而恰恰相反,它们之间存在非对称的关系,因为是违约事件的发生才导致了回收的存在,如果不发生违约事件,回收率则始终等于100%。同时由于违约率在一定程度上反映了宏观经济运行状态,因此可以这样说违约率部分反应了回收的系统风险(回收率同时要受到担保、抵押等特有因素影响)。所以本文以违约率为解释变量,回收率为被解释变量来检验二者之间的关系。在回归分析中,除违约率之外,我们引入了相关的宏观经济变量来解释回收率。
3.为了清楚的显示违约率与回收率的负相关关系对信用风险管理的影响程度,运用蒙特卡洛模拟技术,比较了在不同假设条件下二者之间关系对信用风险度量的影响。蒙特卡洛模拟结果显示：在计入相关性影响之后的预期损失、标准差和VaR值均明显高于独立假设情况约30%。这意味着如果忽略二者之间的负相关关系,仅仅假设二者之间相互独立,则会低估信用风险水平,将会导致银行储备相对不足,严重时甚至会对金融市场产生不必要的冲击。
4.本文的不足,主要表现在：一是仅仅基于单因子模型作了实证分析,而没有提出理论模型来考察违约率与回收率之间的相关性；二是只运用蒙特卡洛模拟技术考察违约率与回收率相关关系对信用风险管理的影响,而未分析这种关系对信用风险定价的影响；三是本文未对信用风险管理技术的一些问题加以研究,如信用衍生产品定价模型、信用风险管理模型等,而这些问题将成为作者今后进一步研究的重点工作,从而不断完善信用风险研究体系。此外,由于数据获取限制等因素,未能对有些问题进行深入研究,如回收率等问题。穆迪的公开数据只是对全球违约与回收的统计性描述,而未有更详细的数据。
Recently, many studies have shown that collateral values and default recovery rate showed volatility. Moreover, when the economic is in a downturn, the increase in default rate at the same time, collateral values and recovery rates show a downward trend. This phenomenon shows that default rates and recovery rate may be show some correlation. But most of the credit risk models assume default rate and recovery rate independent of each other, they only focus on the probability of default, the recovery rate as a constant parameters or a random variable which is independent of the probability of default. This assumption would have impact on credit risk management. Obviously, if we analyze the impact we need to look at the relationship between default rates and recovery. Main contents of in the paper as follow:First, from the perspective of theoretical analyze how did systemic risk effect default process and recovery process to explore how the default rate and recovery are linked. Second.from the perspective of empirical analysis tests the relationship between the default rate and recovery rate.Once the relationship between default rates and recovery specified, in order to clearly demonstrate the extent of this affect, uses Monte Carlo simulation techniques to compare the different assumptions of the relationship between default rates and recovery rate, and found that if ignored the relations between default rate and recovery rate only just assumed independent of each other, it will underestimate the credit risk level, it will lead to insufficient bank reserves and even the financial markets would suffer unnecessary shocks.
Insufficient place, contribution and the major viewpoint of paper:
1. Based on Moody's global corporate default data for empirical analysis of single-factor model to study default risk and systematic risk correlation and recovery risk and systematic risk relevance. We found that the relationship between asset returns and systematic risk has a relative stable relationship over time, which is in a relatively short period of time, the correlation coefficient remained relatively unchanged, from the long term, while the correlation coefficient fluctuates over time, but the relative invariance of the correlation coefficient may be used to predict default rate. Second, analysis of the correlation coefficient of different rating companies and found that except Aa rating, Rating the lower with the absolute correlation coefficient higher, i.e. companies with lower ratings than higher companies more dependent on systemic risk.
2. In the economic boom periods to reduce default rates, recovery rates rise, while in the economic downturn, default rates rise, the recovery rate is lower, but this does not mean that the relationship is symmetry. On the contrary, it is non-symmetrical relationship the reason is that recovery exists is because of the events of default, In different economic states has different default rates, at the economic boom periods default rates lower, recovery rates higher, and vice versa, to a certain extent, the default rate as reflected the macro-economy status, it can be said that default rate decide the systemic the recovery rate, which led to defaults and recovery rates between the non-symmetric relation. With default rates as the explanatory variable, the recovery rate as the dependent variable to test the relationship between them. In the regression analysis, besides default rates, we incorporate a number of macroeconomic variables as independent variables to explain the recovery rate.
3. This paper analyses the impact of various assumptions on which most credit risk measurement models are presently based:namely, it analyses the association between default rate and the loss given default on bank loans and corporate bonds, and seeks to empirically explain this critical relationship. Moreover, it simulates the effects of this relationship on credit VaR models, as well as on the procyclicality effects of the new capital requirements proposed in 2001 by the Basel Committee. Summing up, if PD and LGD were driven by some common factors, then not only the risk measures based on standard errors and percentiles (i.e. the unexpected losses usually covered with bank capital), but even the amount of "normal" losses to be expected on a given loan (and to be shielded through charge-offs and reserves) could be seriously underestimated by most credit risk models.
4. There are still some deficiencies in this paper. Firstly, single-factor model was based solely on empirical analysis, but made no new theoretical model to examine the correlation between default rates and recovery rate. Secondly, we only applied Moody's data to regression analysis, but not more economic variables on the recovery of empirical analysis.
准确地度量信用风险水平对信用风险管控和监管是非常重要的,因此,本文以穆迪全球公司债券违约与回收数据为实证分析资料,探讨了违约率与回收率之间关系及其影响,全文可分为四大部分,一是对现有信用风险模型的评述,系统梳理了违约率与回收率相关关系研究的理论成果和模型；二是介绍了单因子系统风险模型；三是应用穆迪数据进行实证分析；四是运用蒙特卡洛模拟技术考察违约率与回收率相关性对信用风险管理的影响。具体内容如下。
第一章绪论。系统地研究阐述了信用风险的理论基础、构成要素、信用风险模型以及这些模型是如何处理违约率与回收率之间的关系,并对近年来违约率与回收率相关关系研究的新进展进行梳理。
第二章探讨违约率与回收率之间的关系。当前大多数信用风险模型假设违约率和回收率之间相互独立,但是近年来更多的实证分析显示二者之间存在负相关关系,由于现阶段对二者关系的研究还处在初步阶段,因此在众多考察二者关系的理论模型中,还没有形成一致的认识。目前有关两者负相关关系成因的理论解释主要有系统风险(经济周期)影响论和违约债券供需关系影响论。本文基于单因子模型,从系统风险的角度研究违约率和回收率之间相互关系,阐述了单因子模型的理论基础和逻辑结构,给出了模型框架和极大似然估计函数。
第三章实证分析。首先基于穆迪全球公司违约数据对单因子模型进行实证分析,并研究了不同行业、不同评级企业其资产收益与系统风险因子的相关性。然后计量分析回收率与违约率之间的关系,.由于在经济衰退阶段,违约率高,回收率低,而在经济高涨阶段违约率低,回收率高,因此在回归分析中,除了违约率之外,还引入了一系列能反映宏观经济运行状态的经济指标来解释回收率。
第四章考察了PD与RR负相关关系的影响。我们考察二者之间的负相关关系对信用风险度量及管理的影响,具体说来,就是考察这种关系对经济资本计算、监管资本配置的影响。银行的资本是银行在经营过程中所需持有或被要求持有的一定数量的资本金,用来抵御在风险暴露和银行运作中可能面临的损失风险。银行内部为抵御风险而主动配备的资本属于经济资本,而由外部监管当局所要求银行必须持有的资本属于监管资本。显然,这种对银行资本的影响会直接作用于银行的资本收益甚至于银行机构本身的存续。
论文的主要观点、贡献及不足之处：
1.本文基于穆迪全球公司违约数据对单因子模型进行实证分析,考察违约风险与系统风险的相关性以及回收风险与系统风险的相关性。发现资产收益与系统风险相关系数具有相对稳定性,即在某一较短时期内,相关系数相对保持不变,尽管从长时间来看,相关系数随时间而波动。相关系数的相对不变性或许对违约率的预测有一定的意义。因为,如果已知当前时期的相关系数,只需估计有哪些因素影响以及是如何影响宏观系统因子,就能对违约率进行粗略估计。我们进一步分析了不同行业、不同评级企业资产收益与系统风险的相关系数,发现除Aa级外,企业信用等级越低,其与系统风险的绝对相关系数越高,即相对于信用等级高的公司,信用等级低的公司更加容易受到系统风险的影响。
2.在经济高涨时期,违约率降低,回收率升高,而在经济低迷时期,违约率升高,回收率则降低,但这并不意味违约率与回收率之间具有对称的关系。而恰恰相反,它们之间存在非对称的关系,因为是违约事件的发生才导致了回收的存在,如果不发生违约事件,回收率则始终等于100%。同时由于违约率在一定程度上反映了宏观经济运行状态,因此可以这样说违约率部分反应了回收的系统风险(回收率同时要受到担保、抵押等特有因素影响)。所以本文以违约率为解释变量,回收率为被解释变量来检验二者之间的关系。在回归分析中,除违约率之外,我们引入了相关的宏观经济变量来解释回收率。
3.为了清楚的显示违约率与回收率的负相关关系对信用风险管理的影响程度,运用蒙特卡洛模拟技术,比较了在不同假设条件下二者之间关系对信用风险度量的影响。蒙特卡洛模拟结果显示：在计入相关性影响之后的预期损失、标准差和VaR值均明显高于独立假设情况约30%。这意味着如果忽略二者之间的负相关关系,仅仅假设二者之间相互独立,则会低估信用风险水平,将会导致银行储备相对不足,严重时甚至会对金融市场产生不必要的冲击。
4.本文的不足,主要表现在：一是仅仅基于单因子模型作了实证分析,而没有提出理论模型来考察违约率与回收率之间的相关性；二是只运用蒙特卡洛模拟技术考察违约率与回收率相关关系对信用风险管理的影响,而未分析这种关系对信用风险定价的影响；三是本文未对信用风险管理技术的一些问题加以研究,如信用衍生产品定价模型、信用风险管理模型等,而这些问题将成为作者今后进一步研究的重点工作,从而不断完善信用风险研究体系。此外,由于数据获取限制等因素,未能对有些问题进行深入研究,如回收率等问题。穆迪的公开数据只是对全球违约与回收的统计性描述,而未有更详细的数据。
Recently, many studies have shown that collateral values and default recovery rate showed volatility. Moreover, when the economic is in a downturn, the increase in default rate at the same time, collateral values and recovery rates show a downward trend. This phenomenon shows that default rates and recovery rate may be show some correlation. But most of the credit risk models assume default rate and recovery rate independent of each other, they only focus on the probability of default, the recovery rate as a constant parameters or a random variable which is independent of the probability of default. This assumption would have impact on credit risk management. Obviously, if we analyze the impact we need to look at the relationship between default rates and recovery. Main contents of in the paper as follow:First, from the perspective of theoretical analyze how did systemic risk effect default process and recovery process to explore how the default rate and recovery are linked. Second.from the perspective of empirical analysis tests the relationship between the default rate and recovery rate.Once the relationship between default rates and recovery specified, in order to clearly demonstrate the extent of this affect, uses Monte Carlo simulation techniques to compare the different assumptions of the relationship between default rates and recovery rate, and found that if ignored the relations between default rate and recovery rate only just assumed independent of each other, it will underestimate the credit risk level, it will lead to insufficient bank reserves and even the financial markets would suffer unnecessary shocks.
Insufficient place, contribution and the major viewpoint of paper:
1. Based on Moody's global corporate default data for empirical analysis of single-factor model to study default risk and systematic risk correlation and recovery risk and systematic risk relevance. We found that the relationship between asset returns and systematic risk has a relative stable relationship over time, which is in a relatively short period of time, the correlation coefficient remained relatively unchanged, from the long term, while the correlation coefficient fluctuates over time, but the relative invariance of the correlation coefficient may be used to predict default rate. Second, analysis of the correlation coefficient of different rating companies and found that except Aa rating, Rating the lower with the absolute correlation coefficient higher, i.e. companies with lower ratings than higher companies more dependent on systemic risk.
2. In the economic boom periods to reduce default rates, recovery rates rise, while in the economic downturn, default rates rise, the recovery rate is lower, but this does not mean that the relationship is symmetry. On the contrary, it is non-symmetrical relationship the reason is that recovery exists is because of the events of default, In different economic states has different default rates, at the economic boom periods default rates lower, recovery rates higher, and vice versa, to a certain extent, the default rate as reflected the macro-economy status, it can be said that default rate decide the systemic the recovery rate, which led to defaults and recovery rates between the non-symmetric relation. With default rates as the explanatory variable, the recovery rate as the dependent variable to test the relationship between them. In the regression analysis, besides default rates, we incorporate a number of macroeconomic variables as independent variables to explain the recovery rate.
3. This paper analyses the impact of various assumptions on which most credit risk measurement models are presently based:namely, it analyses the association between default rate and the loss given default on bank loans and corporate bonds, and seeks to empirically explain this critical relationship. Moreover, it simulates the effects of this relationship on credit VaR models, as well as on the procyclicality effects of the new capital requirements proposed in 2001 by the Basel Committee. Summing up, if PD and LGD were driven by some common factors, then not only the risk measures based on standard errors and percentiles (i.e. the unexpected losses usually covered with bank capital), but even the amount of "normal" losses to be expected on a given loan (and to be shielded through charge-offs and reserves) could be seriously underestimated by most credit risk models.
4. There are still some deficiencies in this paper. Firstly, single-factor model was based solely on empirical analysis, but made no new theoretical model to examine the correlation between default rates and recovery rate. Secondly, we only applied Moody's data to regression analysis, but not more economic variables on the recovery of empirical analysis.
引文
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20. E. Jokivuolle, S. Peura. Incorporating Collateral Value Ratios. European Financial Management.2003,9(3):299-314
21. M. Carey, M. Gordy. Systematic Risk in Recoveries on Defaulted Debt Working Paper Presented at the 2001 Financial Management Association Meeting, Toronto,20 October
22. G. Bakshi, D. Madan, Zhang Frank, Understanding the Roles of Recovery in Default Risk Models:Empirical Comparisons and Implied Recovery Rates. Finance and Economics Discussion series,2001-37, Federal Reserve Board of Governors, Washington D.C.
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35. Moody's,2008. Default and Recovery Rates of Corporate Bond Issuers 1920-2008.
36. Schuermann, T.,2003. What Do We Know About Loss-Given-Default? Working Paper, Federal Reserve Bank of New York.
37.刘志刚.银行信用风险、资本要求和经济问题周期研究[D].长春：吉林大学数量经济学,2008.
38.麦强.基于违约概率和回收率负相关假设的信用风险模型研究[D].哈尔滨：哈尔滨工业大学管理学院,2006.
39.李晓庆,郑垂勇.违约率：理论方法及实证研究综述[J].经济评论,2006,(5)：153-160.
40.曹道胜,何明升.商业银行信用风险模型的比较及其借鉴[J].金融研究,2006,(10).
41.陈忠阳.违约损失率(LGD)研究[J].国际金融研究.2004,5.
42.刘志刚等.违约损失率数据库与预测模型的构建,金融研究(实务版),2007,5.
43.伍舟宏.信用风险定价模型综述[J].商业时代,2007,09.
44.阎庆民.我国商业银行信用风险VaR的实证分析[J].金融研究,2004,10.
45.张维,李玉霜.商业银行信用风险分析综述[J].管理科学学报,1998,03.
46.章政,田侃,吴宏.现代信用风险度量技术在我国的应用方向研究[J].金融研究,2006,07.
47.刘国光,上市公司违约率研究[D],南京：河海大学商学院.2006.
48.李晓庆,郝丽风,郑垂勇,试析违约回收率与违约率相关关系研究的新进展[J].外国经济与管理,2006,(12)：32-39.
49.李晓庆,郑垂勇,违约率：理论方法及实证研究综述[J].经济评论,2006,(5)：153-160.
50.冯谦, 信用风险测度和信用衍生产品定价—Copula函数的非参数估计与应用[D].上海：上海交通大学管理学院.2006.
51.李姗姗,吴涛,信用风险度量——VaR值的计算方法研究[J],问题探讨,2009,(7)：70-73.
52.纪婧,信用风险度量模型的评述与比较[EB/OL].http://www.cnki.net.
53.文忠桥,曾刚,王芳,郭卫文.信用风险度量与管理一违约率研究[J].国际金融研究,2002(11)：20-24.
54.李兴法.信用风险理论、模型及应用研究[D].沈阳：东北财经大学数量经济学.2007.
55.梁世栋,李勇,方兆本.信用风险模型比较分析[J],中国管理科学,2002,(2)：17-22.
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9. D. Madan, H. Unal. Pricing, the Risk of Default. Review of Derivatives Research,1995,2:121-160.
10. T. Wilson. Portfolio credit risk Ⅰ.Risk,10(9),1997, Sep.
11. T.Wilson. Portfolio credit risk Ⅱ.Risk,10(9),1997, Sep.
12. Altman, E., Brady, B., Resti, A., Sironi, A.,2003. "The Link between Default and Recovery Rates:Theory. Empirical Evidence and Implications, " Journal of Business,2005, vol.78, no.6.
13. Basel Committee on Banking Supervision,2004. International Convergence of Capital Measurement and Capital Standards-A Revised Framework, Consultative Document, Bank for International Settlements, June.
14. Cantor, R., Varma, P.,2005. Determinants of Recovery Rates on Defaulted Bonds and Loans for North American Corporate Issuers: 1983-2003, Journal of Fixed Income 14(4),29-44.
15. Dullmann, K., Trapp, M.,2004. Systematic Risk in Recovery Rates-An Empirical Analysis of U.S. Corporate Credit Exposures, Discussion Paper, Series 2:Banking and Financial Supervision, No 02/2004.
16. R. Jarrow, S. Turnbull. Pricing Derivatives on Financial Securities Subject to Deafult Risk.JournalofFinance,1995,50:53-86
17. D. Madan, H.Unal. Pricing the Risk of Deafult Risk. Review of Derivatives Research,1995,2:121-160
18. J. Kim, K. Ramaswamy and S. Sundaresan. Does Deafult Risk in Coupons Affect the Valuation of Corporate Bonds:a Contingent Claim Model. Financial Management,1993,22(3):117-131
19. Hu Yen-Ting, W. Perraudin. The Dependence of Recovery Rates and Defaults. BirkBeck College, mimeo, February,2002
20. E. Jokivuolle, S. Peura. Incorporating Collateral Value Ratios. European Financial Management.2003,9(3):299-314
21. M. Carey, M. Gordy. Systematic Risk in Recoveries on Defaulted Debt Working Paper Presented at the 2001 Financial Management Association Meeting, Toronto,20 October
22. G. Bakshi, D. Madan, Zhang Frank, Understanding the Roles of Recovery in Default Risk Models:Empirical Comparisons and Implied Recovery Rates. Finance and Economics Discussion series,2001-37, Federal Reserve Board of Governors, Washington D.C.
23. Frye J.2000. Depressing Recoveries, Risk 3(11),106-111.
24. Frye J. Collateral damage [J] Risk,2000,13 (4):91-941.
25. Frye J. Collateral damage detected, Federal Reserve Bank of Chicago [R]. Working Paper, Emerging Issues Series, Octo2ber,2000.
26. Gupton, Greg M Hamilton, David T, and Alexandra Berthault. Default and recovery rates of corporate bond issuers:2000
27. Bakshi, G, Dilip Madan, and Frank Zhang. Understanding the role of recovery in default risk models:empirical comparisons and implied recovery rates[R]. Working Paper, Finance and Economics Discussion Series,2001037, FEDS, Washington DC.,2001.
28. Yen-Ting Hu, and W Perraudin. The dependence of recovery rate and default s[R].CEPR Working Paper,2002.
29. Cantor, R, D T Hamilton, and S Ou. Default and recovery rates of corporate bond issuers[R].Working Paper, Moody's Investors Services, February,2002.
30. Carey, Mark, and Michael Gordy. Systematic risk in recoveries on defaulted debt [R].Working Paper, Mimeo, Federal Reserve Board, Washington D. C., 2003.
31. Yen-Ting Hu, and Extreme. Correlation of defaults and LGDs [R].Working Paper, University of London, August,2005.
32. Sanjiv R Das, and Paul Hanouna. Implied recovery [R]. Http://wwwl defaultrisklcom/pp_recov_73.htm,July,2006.
33. [R]1Working Paper, Moody's Investors Service, New York February,2001
34. Gordy, M.B.,2003. A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules, Journal of Financial Intermediation 12,199-232.
35. Moody's,2008. Default and Recovery Rates of Corporate Bond Issuers 1920-2008.
36. Schuermann, T.,2003. What Do We Know About Loss-Given-Default? Working Paper, Federal Reserve Bank of New York.
37.刘志刚.银行信用风险、资本要求和经济问题周期研究[D].长春：吉林大学数量经济学,2008.
38.麦强.基于违约概率和回收率负相关假设的信用风险模型研究[D].哈尔滨：哈尔滨工业大学管理学院,2006.
39.李晓庆,郑垂勇.违约率：理论方法及实证研究综述[J].经济评论,2006,(5)：153-160.
40.曹道胜,何明升.商业银行信用风险模型的比较及其借鉴[J].金融研究,2006,(10).
41.陈忠阳.违约损失率(LGD)研究[J].国际金融研究.2004,5.
42.刘志刚等.违约损失率数据库与预测模型的构建,金融研究(实务版),2007,5.
43.伍舟宏.信用风险定价模型综述[J].商业时代,2007,09.
44.阎庆民.我国商业银行信用风险VaR的实证分析[J].金融研究,2004,10.
45.张维,李玉霜.商业银行信用风险分析综述[J].管理科学学报,1998,03.
46.章政,田侃,吴宏.现代信用风险度量技术在我国的应用方向研究[J].金融研究,2006,07.
47.刘国光,上市公司违约率研究[D],南京：河海大学商学院.2006.
48.李晓庆,郝丽风,郑垂勇,试析违约回收率与违约率相关关系研究的新进展[J].外国经济与管理,2006,(12)：32-39.
49.李晓庆,郑垂勇,违约率：理论方法及实证研究综述[J].经济评论,2006,(5)：153-160.
50.冯谦, 信用风险测度和信用衍生产品定价—Copula函数的非参数估计与应用[D].上海：上海交通大学管理学院.2006.
51.李姗姗,吴涛,信用风险度量——VaR值的计算方法研究[J],问题探讨,2009,(7)：70-73.
52.纪婧,信用风险度量模型的评述与比较[EB/OL].http://www.cnki.net.
53.文忠桥,曾刚,王芳,郭卫文.信用风险度量与管理一违约率研究[J].国际金融研究,2002(11)：20-24.
54.李兴法.信用风险理论、模型及应用研究[D].沈阳：东北财经大学数量经济学.2007.
55.梁世栋,李勇,方兆本.信用风险模型比较分析[J],中国管理科学,2002,(2)：17-22.