基于违约相关性的商业银行经济资本计量研究
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摘要
银行信用风险管理的核心之一是在信用风险量化的基础上确定其应持有的经济资本。经济资本是指在一定容忍度下商业银行覆盖非预期损失所需要的资本,经济资本管理方法已成为现代商业银行的重要的风险管理手段。而对商业银行的贷款组合来说,贷款之间的违约相关性对贷款的损失分布和经济资本有很大的影响,因此,本文提出了基于违约相关性的商业银行经济资本计量方法。
本文主要是利用单因素模型和加权平均频带划分方法,给出了一种计量商业银行经济资本的新方法。单因素模型在内部评级法中主要被用来求单笔贷款的监管资本,在有的文献中还被用来对贷款组合的损失分布做理论化的分析;频带划分方法是CreditRisk+模型的一种方法,针对该方法在数据分布不均匀时计算结果误差较大的缺陷,我们采用了加权平均频带划分方法。本文首先通过加权平均频带划分方法,把同质贷款放到一个频带中,然后利用单因素模型分别求同频带内贷款的违约比例的分布,再转换成损失分布,最终求得经济资本。
本文采用我国某个城市商业银行的贷款数据对我们所提出的方法进行了分析。计算结果表明:本文提出的基于违约相关性的经济资本计量方法可以用来求贷款组合的经济资本,扩大了单因素模型的应用范围;且利用该方法计算的经济资本与违约相关性成正相关关系;在贷款笔数多,贷款之间相关性很小的情况下,通过本文模型也可以得到与CreditRisk+模型相近的经济资本,说明本文提出的基于违约相关性的经济资本计量方法是有效的;本文提出的方法只适用于贷款笔数多的组合,不适用于贷款笔数少的的组合,有一定的局限性。
本文提出的基于违约相关性的经济资本计量方法在实际中应用还需要更多的配套措施。具体措施包括:加强各类相关数据库的建立及其完善;完善我国商业银行经济资本管理方法及建设良好的风险管理环境等。
The core of credit risk management in commercial banks is to quantizate the economic capital on the basis of quantization to the credit risk. Economic capital (Economic Capital, EC) refers to the capital which is used to coverage unexpected loss of loans in the commercial banks under a certain tolerance. Economic capital management has become an important tool of risk management in modern commercial banks. The correlation between loans has a great impact on the loss of loan portfolio of commercial banks. Therefore, we build an economic capital measurement model based on the default correlation.
In this paper, we bring forward a new method of economic capital measurement using the single-factor model and the weighted average of band classification. Single-factor model has been mainly used to get the supervision capital of a single loan in the Internal Ratings-Based Approach, and also been used to analyse the loss distribution of the loan portfolio theoretically in some literatures. Band classification is a method of CreditRisk + model and the error of it’s result is very big when data distribution is not uniform, so we have adopted a weighted average of band classification. In this paper,we first put homogeneous loans into a band through the weighted average of band classification, and then get of loans’portfolio in the same band by using single-factor model,and then transform the default percentange distribution into the loss distribution, and ultimately get the economic capital.
We use some loans’data of a city commercial bank in our country to illustrate our method.Through the calculation ,we found that the economic capital measurement model based on the default correlation can be used to calculate the economic capital of loan portfolio,and expand the application scope of the single-factor model. The economic capital calculated through the model is positively correlated.At the same time, we found that we can get the economic capital of loan portfolio using the method which is similar to CreditRisk + model’s when the number of loans are quite big and the correlation between the loans are small.So it shows that the model is effective. Lastly,we explaine that our method is only applicable to the portfolios which have a lot of loans, and not to portfolios containing few loans,So it has some limitations.
It needs more measures when the economic capital measurement method based on the default correlation is applied in practice. Specific measures include: strengthening the establishment and perfection of various types of database; perfecting the economic capital management of our country’s commercial banks and building good environment of the risk management.
本文主要是利用单因素模型和加权平均频带划分方法,给出了一种计量商业银行经济资本的新方法。单因素模型在内部评级法中主要被用来求单笔贷款的监管资本,在有的文献中还被用来对贷款组合的损失分布做理论化的分析;频带划分方法是CreditRisk+模型的一种方法,针对该方法在数据分布不均匀时计算结果误差较大的缺陷,我们采用了加权平均频带划分方法。本文首先通过加权平均频带划分方法,把同质贷款放到一个频带中,然后利用单因素模型分别求同频带内贷款的违约比例的分布,再转换成损失分布,最终求得经济资本。
本文采用我国某个城市商业银行的贷款数据对我们所提出的方法进行了分析。计算结果表明:本文提出的基于违约相关性的经济资本计量方法可以用来求贷款组合的经济资本,扩大了单因素模型的应用范围;且利用该方法计算的经济资本与违约相关性成正相关关系;在贷款笔数多,贷款之间相关性很小的情况下,通过本文模型也可以得到与CreditRisk+模型相近的经济资本,说明本文提出的基于违约相关性的经济资本计量方法是有效的;本文提出的方法只适用于贷款笔数多的组合,不适用于贷款笔数少的的组合,有一定的局限性。
本文提出的基于违约相关性的经济资本计量方法在实际中应用还需要更多的配套措施。具体措施包括:加强各类相关数据库的建立及其完善;完善我国商业银行经济资本管理方法及建设良好的风险管理环境等。
The core of credit risk management in commercial banks is to quantizate the economic capital on the basis of quantization to the credit risk. Economic capital (Economic Capital, EC) refers to the capital which is used to coverage unexpected loss of loans in the commercial banks under a certain tolerance. Economic capital management has become an important tool of risk management in modern commercial banks. The correlation between loans has a great impact on the loss of loan portfolio of commercial banks. Therefore, we build an economic capital measurement model based on the default correlation.
In this paper, we bring forward a new method of economic capital measurement using the single-factor model and the weighted average of band classification. Single-factor model has been mainly used to get the supervision capital of a single loan in the Internal Ratings-Based Approach, and also been used to analyse the loss distribution of the loan portfolio theoretically in some literatures. Band classification is a method of CreditRisk + model and the error of it’s result is very big when data distribution is not uniform, so we have adopted a weighted average of band classification. In this paper,we first put homogeneous loans into a band through the weighted average of band classification, and then get of loans’portfolio in the same band by using single-factor model,and then transform the default percentange distribution into the loss distribution, and ultimately get the economic capital.
We use some loans’data of a city commercial bank in our country to illustrate our method.Through the calculation ,we found that the economic capital measurement model based on the default correlation can be used to calculate the economic capital of loan portfolio,and expand the application scope of the single-factor model. The economic capital calculated through the model is positively correlated.At the same time, we found that we can get the economic capital of loan portfolio using the method which is similar to CreditRisk + model’s when the number of loans are quite big and the correlation between the loans are small.So it shows that the model is effective. Lastly,we explaine that our method is only applicable to the portfolios which have a lot of loans, and not to portfolios containing few loans,So it has some limitations.
It needs more measures when the economic capital measurement method based on the default correlation is applied in practice. Specific measures include: strengthening the establishment and perfection of various types of database; perfecting the economic capital management of our country’s commercial banks and building good environment of the risk management.
引文
[1] Araten, Michel. Current Issues in Estimating Econonmic Capital for Credit Risk. RMA Journal, 2004,86(6):38-43
[2] Kupiec, Paul. Estimating economic capital allocations for market and credit risk. Journal of Risk, 2004,6(4):11-31
[3] Jeremy Scott. Economic capital: at the heart of managing risk and value. Balance Sheet, 2002,10(3):10-13
[4] David R., Dean J., Richard R. BaselⅡand Economic Capital. New York:US Banker, 2004: 72-75
[5] Oldrich Vasicek. Loan portfolio value.Risk, 2002,(12):160-162
[6] Gupton G., C. Finger, M. Bhatia. CreditMetrics technical document. New York: Mergan Guaranty Trust Company, 199:56-63
[7]安东尼桑德斯.信用风险度量:风险估值的新方法与其他范式.刘宇飞译.北京:机械工业出版社, 2000:80-85
[8] Credit Suisse First Boston.Credit risk+: A Credit Risk Management Framework. London:Credit Suisse First Boston International,1997:18-56
[9] Altman E.I., Saunders A. Credit risk measurement developments over the last 20 years. Journal of Banking &Finance, 1998,(21):1724-1742
[10] Didier C., Hugues P. Advanced credit risk analysis: Financal approaches and machematical models to assess, price, and manage credit risk. Australia:John Wiley &Sons Ltd, 2001,(20):56-60
[11] Gordy Michael. A comparative anatomy of credit risk models. Journal of Banking&Finance, 2000,(24):119-149
[12] Burgisser P., Alexandre K., Armin W. Incorporating Severity variations into credit risk, Risk, 2001,(4):5-31
[13] Susanne E., Dirk T. Calculating credit risks capital charges with the one-factor model. Journal of Risk, 2003,7(2):85-103
[14] Giesecke, Kay. Credit Risk Modeling and Valuation: An Introduction. London: Cornell University,2003:15-16
[15] Vandendorpe et al. On the parameterization of the CreditRisk model forestimating credit portfolio risk. Insurance:Mathematics and Economics, 2008,(42):736-745
[16]彭建刚,张丽寒,刘波,屠海波.聚合信用风险模型在我国商业银行应用的方法论探讨.金融研究, 2008, (8): 72-85
[17]韩平,席酉民.违约相关性分析.统计研究, 2001,(5):52-56
[18]张玲,曹艳春.对违约相关性计量模型的研究.湖南大学学报(自然科学版), 2002,(6):118-122
[19]张尧庭.连接函数(copula)技术与金融风险分析.统计研究, 2002,(4):48-51
[20]韦艳华,张世英,孟利锋. Copula理论在金融上的应用.西北农林科技大学学报(社会科学版), 2003,(5):97-101
[21]朱世武.基于Copula函数度量违约相关性.统计研究, 2005,(4):61-64
[22]叶永刚,朱堰徽.违约相关性理论文献综述.经济学动态, 2006,(4):97-101
[23] Lucas D.J.Default correlation and credit analysis. Journal of Fixed Income,1995,(11):76-87
[24] Black F.,Scholes M.The Pricing of Options and Corporate Liabilities.Journal of Political Economy,1973,81(3):631-654
[25] Merton, R.On the Pricing of Corporate Debt:The Risk Structure of Interest Rates. Journal of Finance, 1974,29(2):449-470
[26] Black F., Cox J.C. Valuing corporate securities:Some effects of bond indenture provisions.Journal of Finance,1976,31(2)351-367
[27] Darrel D., Kenneth S.l. Simulating Correlated defaults. California:Stanford University, 1998:90-93
[28] Nelsen, Roger B. An Introduction to Copulas.New York:Springer Verlag, 1997:86-112
[29] Edward Frees, Emiliano Valdez. Understanding relationships using copulas. Journal of North Americal Actuarial, 1998,(2):59-63
[30]杨晓光.经济资本及其在我国商业银行中的应用.金融视线, 2002,(3):22-23
[31] The Basel Committee. Internantional Convergence of Capital measurement and Capital Standards:A Revised Framework. www.bis.com,1999:65-68
[32] Michael Kong.内部信用风险模型:资本分配和绩效度量.李智辉译.南开大学出版社, 2004,153-159
[33]章彰.商业银行信用风险管理—兼论巴塞尔新资本协议.北京:中国人民大学出版社, 2002:67-72
[34]詹原瑞.银行信用风险的现代度量与管理.北京:经济科学出版社, 2004:189-192
[35]武剑.论商业银行资本的配置与管理.新金融,2004,(4):14-16
[36]赵先信.银行内部模型和监管模型:风险计量与资本分配.上海:上海人民出版社, 2004:196-255
[37] Jarrow, Robert A.,Stuart M. Turnbull.The intersection of market and creditrisk.Journal of Bankin&Finance,2000,24(1):271-299
[38] Crouhy M, Galai D, Mark R. A comparative analysis of TM current creditrisk models.Journal of Banking&Finance,2000,24 (1 ) :59-67
[39]克里斯·马滕.银行资本管理:资本配置和绩效评估.王洪,漆艰明等译.北京:机械工业出版社, 2004:195
[40] Marvin S. Captial Allocation: A Study of Current and Evolving Practices in Selected Banks. Washington: OCC Staff ,1996:22-24
[2] Kupiec, Paul. Estimating economic capital allocations for market and credit risk. Journal of Risk, 2004,6(4):11-31
[3] Jeremy Scott. Economic capital: at the heart of managing risk and value. Balance Sheet, 2002,10(3):10-13
[4] David R., Dean J., Richard R. BaselⅡand Economic Capital. New York:US Banker, 2004: 72-75
[5] Oldrich Vasicek. Loan portfolio value.Risk, 2002,(12):160-162
[6] Gupton G., C. Finger, M. Bhatia. CreditMetrics technical document. New York: Mergan Guaranty Trust Company, 199:56-63
[7]安东尼桑德斯.信用风险度量:风险估值的新方法与其他范式.刘宇飞译.北京:机械工业出版社, 2000:80-85
[8] Credit Suisse First Boston.Credit risk+: A Credit Risk Management Framework. London:Credit Suisse First Boston International,1997:18-56
[9] Altman E.I., Saunders A. Credit risk measurement developments over the last 20 years. Journal of Banking &Finance, 1998,(21):1724-1742
[10] Didier C., Hugues P. Advanced credit risk analysis: Financal approaches and machematical models to assess, price, and manage credit risk. Australia:John Wiley &Sons Ltd, 2001,(20):56-60
[11] Gordy Michael. A comparative anatomy of credit risk models. Journal of Banking&Finance, 2000,(24):119-149
[12] Burgisser P., Alexandre K., Armin W. Incorporating Severity variations into credit risk, Risk, 2001,(4):5-31
[13] Susanne E., Dirk T. Calculating credit risks capital charges with the one-factor model. Journal of Risk, 2003,7(2):85-103
[14] Giesecke, Kay. Credit Risk Modeling and Valuation: An Introduction. London: Cornell University,2003:15-16
[15] Vandendorpe et al. On the parameterization of the CreditRisk model forestimating credit portfolio risk. Insurance:Mathematics and Economics, 2008,(42):736-745
[16]彭建刚,张丽寒,刘波,屠海波.聚合信用风险模型在我国商业银行应用的方法论探讨.金融研究, 2008, (8): 72-85
[17]韩平,席酉民.违约相关性分析.统计研究, 2001,(5):52-56
[18]张玲,曹艳春.对违约相关性计量模型的研究.湖南大学学报(自然科学版), 2002,(6):118-122
[19]张尧庭.连接函数(copula)技术与金融风险分析.统计研究, 2002,(4):48-51
[20]韦艳华,张世英,孟利锋. Copula理论在金融上的应用.西北农林科技大学学报(社会科学版), 2003,(5):97-101
[21]朱世武.基于Copula函数度量违约相关性.统计研究, 2005,(4):61-64
[22]叶永刚,朱堰徽.违约相关性理论文献综述.经济学动态, 2006,(4):97-101
[23] Lucas D.J.Default correlation and credit analysis. Journal of Fixed Income,1995,(11):76-87
[24] Black F.,Scholes M.The Pricing of Options and Corporate Liabilities.Journal of Political Economy,1973,81(3):631-654
[25] Merton, R.On the Pricing of Corporate Debt:The Risk Structure of Interest Rates. Journal of Finance, 1974,29(2):449-470
[26] Black F., Cox J.C. Valuing corporate securities:Some effects of bond indenture provisions.Journal of Finance,1976,31(2)351-367
[27] Darrel D., Kenneth S.l. Simulating Correlated defaults. California:Stanford University, 1998:90-93
[28] Nelsen, Roger B. An Introduction to Copulas.New York:Springer Verlag, 1997:86-112
[29] Edward Frees, Emiliano Valdez. Understanding relationships using copulas. Journal of North Americal Actuarial, 1998,(2):59-63
[30]杨晓光.经济资本及其在我国商业银行中的应用.金融视线, 2002,(3):22-23
[31] The Basel Committee. Internantional Convergence of Capital measurement and Capital Standards:A Revised Framework. www.bis.com,1999:65-68
[32] Michael Kong.内部信用风险模型:资本分配和绩效度量.李智辉译.南开大学出版社, 2004,153-159
[33]章彰.商业银行信用风险管理—兼论巴塞尔新资本协议.北京:中国人民大学出版社, 2002:67-72
[34]詹原瑞.银行信用风险的现代度量与管理.北京:经济科学出版社, 2004:189-192
[35]武剑.论商业银行资本的配置与管理.新金融,2004,(4):14-16
[36]赵先信.银行内部模型和监管模型:风险计量与资本分配.上海:上海人民出版社, 2004:196-255
[37] Jarrow, Robert A.,Stuart M. Turnbull.The intersection of market and creditrisk.Journal of Bankin&Finance,2000,24(1):271-299
[38] Crouhy M, Galai D, Mark R. A comparative analysis of TM current creditrisk models.Journal of Banking&Finance,2000,24 (1 ) :59-67
[39]克里斯·马滕.银行资本管理:资本配置和绩效评估.王洪,漆艰明等译.北京:机械工业出版社, 2004:195
[40] Marvin S. Captial Allocation: A Study of Current and Evolving Practices in Selected Banks. Washington: OCC Staff ,1996:22-24