摘要
近20年来，世界范围的金融危机的频繁爆发，给整个世界经济带来了深刻的影响，造成了巨大的损失。综观几次大的金融危机的成因，不难发现，由于信用风险而引发的危机对经济的破坏力是最大的，经济能力的恢复期最长。这不能不引起学术界和实业界对信用风险研究的高度重视。虽然我国金融体系在强管制下还没有出现较大的信用风险，但是随着中国的金融体系的日益市场化和国际化，由于金融体系自身运行而出现较大的风险的可能性是在增强的。所以，对金融体系的信用风险的关注度也会越来越高。
1974年，默顿基于期权思想提出了或有要求权理论，建立了最早的结构信用风险模型。从此，有关信用风险模型的研究在几十年内有了长足的进展。结构信用风险模型也逐渐完善成外生性的和内生性的两种。LT模型是目前发展比较成熟的内生的结构信用风险模型，它认为，违约边界的决定受到很多因素的影响，如经济主体的资本结构，资产与负债比率，税率，违约（破产）成本，资产收益及收益波动率等，而最根本的，是由微观经济主体在经济运行过程中追求股权最大化动机所决定。如何将包括很多复杂经济变量的理论模型应用于实际，以检验其优劣，是学术研究中面临的难题。
本文首先利用该LT模型，结合使用极大似然法，将模型中的资产价值通过股权的市场价值提取出来，进而估计上市企业的预期违约概率，在解决该类模型存在的资产与债务价值不易观察和度量的不足方面进行了有益的尝试。结合我国资本市场的实际情况，给出了模型其它参数的具体设定方法，筛选一定的上市公司，包括特别处理的样本公司和评级样本公司利用2008－2009年的实际数据进行违约风险的度量，主要通过预期违约率的测算，对其信用状况进行了全面的估计。
分别使用两类结构模型如Merton模型和LT模型进一步对银行自身的信用风险进行度量。除了上市企业的违约行为会给银行带来损失以外，银行自身也会发生违约行为，进而产生违约风险。由于我国银行上市比较晚，样本量比较少，所以在使用上述两种结构模型时，对银行资产价值及其波动率的估计方面采用了受限波动率方法，其它参数，也结合我国银行业的相关规定进行了符合我国实际的合理的设定。针对我国宏观经济形势的变化，及其股市走势，选择了2008年和2009年的数据进行对比实证分析，一方面试图发现不同模型的优势或不足，另一方面，希望能更精确地测算商业银行的违约风险。
无论是对上市企业，还是对上市银行来说，在某个个体违约的同时，也就必然会影响其它个体，从现实的角度看，违约存在相关性。也就是整个金融体系存在着系统性风险。在对上市企业与上市银行的违约风险进行度量的基础上，本文又进一步对违约相关性进行了研究。并根据数据可得性，引入COPULA函数，通过股权收益率的相关性考察研究不同经济主体的违约相关性。考察的步骤依次是单个银行与整个银行业的资产相关性；单个银行间的资产相关性；金融行业与其它行业的资产相关性。
本文通过引入CEV模型，将默顿模型进行了扩展，认为银行的系统性违约风险也表现为跳扩展的特征；同时，针对银行同业市场的结构特征，引入清算支付向量因子，构建了银行体系违约风险系数（概率）函数，提出一个定量管理系统性风险的新的理论方法，最后提出了相应的防范违约风险的对策。
总之，本文基于经典结构式违约风险模型——默顿模型，以及其最新发展的内生性构模型—LT模型对我国上市公司与银行的违约风险进行全面的度量，并在此基础上构建了银行体系的违约风险概率函数。本文的研究成果，对推进我国对信用风险理论模型的研究，并将信用风险理论模型结合我国实际数据进行实证研究，以及提高金融监管水平方面都具有重要的学术价值和实践意义。
During the past20years, financial crises which have frequently broken outaround the world have brought great effect on the world economic and causedheavy damage to the world. Studying the reasons of several big financial crises,it’s not difficult to find that the crisis caused by credit risks has destroyed theeconomy most and the recovery of the economic capacity is the longest. Thishas no alternative but to cause a highlight by academe and business circles.Although our country’s financial system has not presented the big credit risksunder the strong control, with day-by-day marketability and internationalizationof Chinese financial system the possibility owing to presenting the big risk as aresult of financial system own operation is in the enhancement. From this, weshould think highly of the credit risk of financial system.
In1974, Merton proposed the Contingent Claims Model based on theOption Pricing Theory and has established the earliest credit risks model. Fromthis, the related research about credit risks model had the considerable progressin several decades. And also the structural model gradually improves exogenousand endogenous model. LT model is the endogenous structure credit risks modelwhich develops maturely currently. LT model believed that the default boundarywas affected by many factors, like capital structure of economic subject, theratio of assets and liabilities, tax rate, default (bankruptcy) cost, the returnvolatility and so on, but ultimately, the microscopic economic subjects pursuitof the stockholder's rights maximization in economic operation. How to puttheoretical model include a number of complex variables into practice so as totest its merits, is an academic problem.
The paper first uses the endogenous structure credit risks model, integratesuse of maximum likelihood method, extracts the value of asset through the marketvalue of equity and then estimates the expected default probability of listed companies,makes a good attempt on the problem that the value of assets and liabilities are difficultto observed and measured in the model. With the actual situation of our countrycapital market, the paper gives the set methods of other specific parameters in the model, screens certain listed companies, including special treatment samplecompanies and rating sample companies, and then uses actual data of the year2008-2009to measure default risk, makes a comprehensive estimate of its creditby the expected default rate.
The paper measures the bank credit risks uses the structural model likeMerton model and LT model. In addition to the breach of listed companieswould cause losses to banks, the banks themselves will be the case of default,thereby creating the risk of default. As banks of our country were listedrelatively late, the sample was relatively low, so when using either model, weuse volatility restricted method to estimate the value of bank assets and theterms of the volatility, other parameters also are accord with the relevantprovisions of China's banking industry. Taken the changes of macroeconomicsituation and the trend the stock market into consideration, we select actual dataof the year2008-2009to do empirical analysis, one hand, trying to findadvantage and disadvantage among different models, on the other hand, hopingto measure default risk of commercial banks more accurately.
Both for listed companies and listed banks, a breach of one individual isbound to other individuals, so default correlation does exist from a practicalpoint of view. That is to say systemic risk does exist in the entire financialsystem. On the basis of measurement the default risk of listed companies andlisted banks, this article further studies default correlation. According to dataavailability, by introduction of COPULA function, we investigate the defaultcorrelation between different economic agents through correlation betweenequity returns. The steps followed by studying assets correlation between onesingle bank and the entire banking industry; assets correlation of single bank;assets correlation of financial industry and other industries.
Merton model was extended by introducing of CEV model in this paper, thesystemic risk of bank default performance of the extended features of jump. Atthe same time, consider the inter-bank market structure, this paper constructsbanking system default risk factor (probability) function by introduction ofclearing payment vector factor, and proposes a new theoretical method ofquantitative management in systemic risk and finally proposes thecorresponding countermeasures of guarding default risks.
To sum up, this paper carries on the comprehensive measure to default riskof listed companies and listed banks of our country based on the classicalstructural default risk model——Merton model, as well as the endogenousstructure credit risks model which was developed rapidly recently——LTmodel，and then constructs banking system default risk probability function. Theresults of this paper has an important academic value and practical significancein the aspect of advancing our theoretical models of credit risk research andmaking empirical study combining theoretical models of credit risk with theactual data of our country, as well as enhancing the level of financialsupervision.
引文
[1] Huberto M. Ennis and H. S. Malek. Bank Risk of Failure and the Too-Big-to-FailPolicy. Economic Quarterly,2005,(91):21-44
[2] Hui Tong, Shang-Jin Wei. Real Effects of the Subprime Mortgage Crisis: Is It aDemand or a Finance Shock? NBER working paper14205,2008,(6)
[3] Jeffrey marshall and Grdgory J. Millman. Lessons from the Abyss. FinancialExecutive,2008,(24):36-43
[4] Rachel Parker and Michelle Wilkes. Subprime Fallout: Investing in DataManagement. Risk Manage,2008,(55):30-33
[5] Danielle DiMartino and John V. Duca. The Rise and Fall of Subprime Mortgages.EconomicLetter,2007(2):1-8
[6]李国平，黄国勇.新巴塞尔资本协议研究动态.东南大学学报（哲学社会科学版），2007,（3）73-77
[7] Myung-Jig Kim. Downturn LGD，Best Estimate of Expected Loss，and PotentialLGD under Basel II. Journal of Economic Research,2006(11):203-223
[8]王志强,齐佩金,刘丽巍.解读巴塞尔协议II中内部评级法关于资本的计算.数理统计与管理,2007,(1):125-131
[9] Hugh Thomas; Zhiqiang Wang. Interpreting the internal ratings-based capitalrequirements in Basel II. Journal of BcznkinQ ReRulcztion.2005,(6):274-289
[10] David Jones and John Mingo. Industry Practices in Credit Risk Modeling andInternal Capital Allocations: Implications for a Model-Based Regulatory CapitalStandard. FRBNY Economic Policy Review,1998,(10):53-60
[11] Edward I Altman. Effects of the New Basel Capital Accord on Bank CapitalRequirements for SMEs. Journal of Financial Services Research.2005,(28):15-42
[12] Allen N Berger. Potential Competitive Effects of Basel II on Banks in SMECredit Markets in the United States. Journal of Financial Services Research,2006,(29):5-36
[13] Altman E I. Financial Ratios，Discriminate Analysis，and the Prediction of CorporateBankruptcy.Journal of Finance,1968,(24):589-609
[14] Efron, B. The Efficiency of Logistic Regression Compared to Normal DiscriminantAnalysis. Journal of the American Statistical Association,1975,(70):892-898
[15] Anderson, J.A. Quadratic Logistic Discrimination. Biometrika,1975,(62):149-154
[16] Kaplan, R. and U. Urwitz. Statistical Model of Bond Ratings: A MethodologicalInquiry, Journal of Business,1979,(52):231-261
[17] Shumway, T. Forecasting Bankruptcy More Accurately: A Simple Hazard Model.The Journal of Business，2001，（74）:101-124
[18] Vanessa, Gail Perry. Is Ignorance Bliss? Consumer Accuracy in Judgments aboutCredit Ratings. The Journal of Consumer Affair,2008,(42),189-205
[19]王春峰，万海晖，张维.商业银行信用风险评估及其实证研究.管理科学学报，1998,(1):68-72
[20]李萌. Logit模型在商业银行信用风险评估中的应用研究.管理科学,2005(18):33-38
[21]卫韦.基于Logit的商业银行信用风险识别模型.经济师，2007（11）：238-239
[22]倪泽强.基于多元判别方法的商业银行信用风险度量研究.广西金融研究.2008(2):47-49
[23]于立勇，詹捷辉.基于Logistic回归分析的违约概率预测研究.财经研究，2004，(9)：15-23
[24]刘方根.违约风险模型对违约定义的敏感性研究.国际金融研究,2008(2):32-38
[25]黄波，王楚明.基于排序Logit模型的城镇就业风险的分析和预测.中国软科学,2010(4):146-154
[26] Merton R. On the pricing of corporate debt: The risk structure of interestrate.Journal of Finance，1974，29:449-470
[27]Falkenstein, E. and A. Boral. Some empirical results on the Merton Model.RiskProfessional,2001,(4)
[28] Sanjiv R. Das, Laurence Freed, Gary Geng, and Nikunjkapadia. Correlated DefaultRisk.The Journal of Fixed Income, Fall,2006:7-32
[29]Campbell, Hilscher, and Szilagyi.in. In Search of Distress Risk.NBER WorkingPaper No.12362,2006,(7)
[30] Sreedhar T. Bharath. Forecasting Default with the Merton Distance to DefaultModel. The Review of Financial Studies,2008,(21):1339-1369
[31]李舜蛟,王文胜. EDF模型在中国商业银行信用风险管理中的应用.金融论坛.2008(1):22-26
[32]张能福,张佳.改进的KMV模型在我国上市公司信用风险度量中的应用.预测，2010,(5):48-52
[33]Black, Fischer and John C. Cox. Valuing Corporate Securities: Some Effects of BondIndenture Provisions. Journal of Finance,1976,(31):351-367.
[34] Leland, H.E. Corporate Debt Value, Bond Covenants, and Optimal Capital Structure.The Journal of Finance,1994,(49):1213-1252
[35]Anderson, Ronald and Suresh Sundaresan. A Comparative Study of StructuralModels of Corporate Bond Yields: An exploratory investigation. Journal of Banking&Finance,2000,(24):255-269
[36]Mella-Barral, Pierre. The Dynamics of Default and Debt Reorganization. Review ofFinancial Studies,1999,(12):535–578
[37]Duffie and Lando. Term Structures of Credit Spreads with Incomplete AccountingInformation. Econometrica,2001,(69):633-664
[38]Nikola A. Tarashev. An Empirical Evaluation of Structural Credit-Risk Models.International Journal of Central Banking,2008,(4):1-57
[39]Longstaff, Francis A. and Eduardo S. Schwartz. A Simple Approach to Valuing RiskyFixed and Floating Rate Debt. Journal of Finance,1995,(50):789-819
[40]Collin-Dufresne, Pierre, Robert S. Goldstein, and J. Spencer Martin. TheDeterminants of Credit Spread Changes. Journal of Finance,2001,(56):2177-2207
[41] Huang, J. Z. and M. Huang. How Much of the Corporate Treasury Yield Spread isdue to Credit Risk. Working Paper, Penn. State University and Stanford University,2003
[42] Anderson, R. W., S. M. Sundaresan, and P. Tychon. Strategic Analysis of ContingentClaims. European Economic Review,1996,(40):871-881
[43] Leland, H. E., and K. B. Toft. Optimal Capital Structure, Endogenous Bankruptcy,and the Term Structure of Credit Spreads. The Journal of Finance,1996,(51):987-1019
[44] Jarrow, Robert A. and Stuart M. Turnbull. Pricing Derivatives on FinancialSecurities Subject to Credit Risk. Journal of Finance,1995,(50),53-85
[45] Duffie, Darrell and Kenneth J. Singleton. An Econometric Model of the TermStructure of Interest-Rate Swap Yields. Journal of Finance,1997,(52):1287-1321
[46] John Hull Alan White. Valuing Credit Default Swaps II: Modeling DefaulCorrelations. Journal of Derivatives,2001,(8):12-22
[47] Robert A. Jarrow and Fan Yu. Counterparty Risk and the Pricing of DefaultableSecurities. Journal of Finance,2001,(56):1765-1799
[48] John Hull Alan White Valuing Credit Default Swaps I: No Counterparty DefaultRisk. Journal of Derivatives,2000,(8):29-40
[49]Tibor Janosi. Estimating Default Probabilities Implicit in Equity Price. Journal ofInvestment Management,2003,(1):1-30
[50] Jarrow, Robert A. and Stuart M. Turnbull. The Intersection of Market and CreditRisk. Journal of Banking&Finance,2000,(24):271-299
[51] Mi Ae Kim; Tong Suk Kim Default Correlation Dynamics with Business Cycle andCredit Quality Changes The Journal of Derivatives, Fall2005
[52]Brent W. Ambrose, Yildiray Yildirim. Credit Risk and the Term Structure of LeaseRates: A Reduced Form Approach. Journal of Real Estate Finance Economics.2008,(37):281-298
[53]Rainer Jankowitsch, Rainer Pullirsch, Tanja Veza. The delivery option in creditdefault swaps.Journal of Banking&Finance,2008,(32):1269-1285
[54]Gupton,Greg M. The New Talk of the Town: CreditMetrics. A CreditValue-at-Risk Approach. Journal of Lending&Credit Risk Management,1997,(79):44-54
[55] A1tman E I，Saunders A. Credit Risk Measurement：Development Over the Last20Years.Journal of Banking and Finance，1998,(20):1721-1742
[56]Michael Cmuhy,Dan Galai, Robert Mark. A comparative Analysis of Current RiskModels. Journal of Banking&Finance,2000,(24):59-117
[57]范南.CreditMetric模型及其对我国银行信用风险管理的借鉴.金融论坛，2002，(5)：12-17
[58]吴军，张继宝.信用风险量化模型比较分析.国际金融研究，2004,(8)
[59]张海燕. CreditRisk+模型与中国商业银行信用风险管理.吉林大学学报,2007(5):119-122
[60]韩岗.国外信用风险度量方法及其适用性研究.国际金融研究,2008(2):43-47
[61]龚澄.信用风险主流模型与RCM模型的比较及借鉴.国际金融研究,2008(2):47-51
[62]Dutta, S. and Shekhar, S.`Bond rating: a non-conservative application of neuralnetworks', IEEE International Conference on Neural Networks, II,1988:443-450
[63]Surkan, A. And J. Singleton. Neural Networks for Bond Rating Improved byMultiple Hidden Layers. Proceedings of the1990International Joint Conferenceon Neural Networks,4,1990:157-162
[64]王春峰万海晖.基于神经网络技术的商业银行信用风险评估.系统工程科理论与实践.1999,(9):34-43
[65]吴冲,吕静杰,潘启树,刘云焘.基于模糊神经网络的商业银行信用风险评估模型研究.系统工程理论与实践,2004，(11)：1-8
[66]张玲，陈收，张晰.基于多元判别分析和神经网络技术的公司财务困境预警.系统工程.2005,(11):45-54
[67]宋雪枫，杨朝军，徐任重.商业银行信用风险评估的生存分析模型及实证研究.金融论坛，2006（11）：37-42
[68] Altman, E., and Katz, S. Statistical bond rating classification using financial andaccounting data. In Michael Schiff and George Sorter (eds.), Proceedings of theConference on Topical Research in Accounting. New York: New York UniversitySchools of Business,1976
[69] Saunders, A. Credit Risk Measurement, J. Wiley, New York.1999:35-87
[70] Caouette, J., E. Altman and P. Narayana nManaging Credit Risk. John Wiley&Sons, New York,1998:132-143
[71]沈沛龙，任若恩.现代信用风险管理模型和方法的比较研究.经济科学2002(3):34-38
[72]陈建华，唐立波.浅析我国银行内部评级体系的建立.金融研究，2002,(9):88-93
[73]刘莉亚.商业银行内部评级系统研究综述.外国经济与管理，2004,(8):40-44
[74]王小明.银行信用风险评级测度方法研究.财经研究,2005,(5):73-82
[75]武剑.内部评级法中的违约损失率（LGD）模型——新资本协议核心技术研究.国际金融研究，2005,(2):15-22
[76]沈沛龙,崔捷.内部评级法中违约损失率的研究.金融研究,2005,(12):86-95
[77]蔡艳华.压力测试在商业银行风险管理中应用探讨.河南商业高等专科学校学报,2007(11):43-46
[78]徐明东,刘晓星.金融系统稳定性估计:基于宏观压力测试方法的国际比较.国际金融研究,2008(2):39-46
[79]王胜帮,陈影.新资本协议内部评级法对宏观经济运行的影响:亲经济周期效应研究.金融研究,2008(5):48-59
[80] Altman E I，Haldeman R G.，Narayanan P. Zeta Analysis: A New Model to IdentifyBankruptcy Risk of Corporations. Journal of Banking and Finance.1977,(1):29-54
[81] Altman E I， F Varetto. Corporate Distress Diagnosis: Comparisons UsingLinearDiscriminant Analysis and Neural Networks. Journal of Banking andFinance.1994,(18):405-529
[82] Fledelius, Peter, David Lando, and Jens Perch Nielson. Non-Parametric Analysis ofRating Transition and Default Data. Journal of Investment Management,2004,(2):71-85
[83] Mark B. Wise and Vineer Bhansali.Implications of Correlated Default for PortfolioAllocation to Corporate Bonds. The Credit Market Handbook:Advanced ModelingIssues, John Wiley&Sons, inc.,2006:165-185
[84]Thomas S.Y. Ho and Sang Bin Lee. Valuing High-Yield Bonds: ABusinessModeling Approach. The Credit Market Handbook: AdvancedModeling Issues, John Wiley&Sons, inc.,2006:101-117
[85] Wolfgang H ardle, Yuh-Jye Lee, Dorothea Sch afer, Yi-Ren Yeh. The DefaultRisk of Firms Examined with Smooth Support Vector Machines. SFB649Discussion Paper,2008-005
[86] Altman E.I. and Saunders A. Credit Rating and the BIS reform agenda. Journal ofBanking and Finance,2002,(26):909-921
[87] Halina Frydman, Til Schuermann. Credit rating dynamics and Markov mixturemodels. Journal of Banking&Finance,2008(32),1062-1075
[88] Myung-Jig Kim. Downturn LGD, Best Estimate of Expected Loss, and PotentialLGD under Basel II: Korean Experience. Journal of Economic Research,2006,(11):203-223
[89] Hayne E. Leland.Predictions of Default Probabilities in Structural Models of Debt.Journal of Investment Management,2004,(2):5-20
[90] Siem Jan Koopman, Andr′e Lucas, Andr′e Monteiro. The Multi-State Latent FactorIntensity Model for Credit Rating Transitions. Tinbergen Institute DiscussionPaper, TI2005-071/4
[91] Heber Farnsworth and Tao Li. The Dynamics of Credit Spreads and RatingsMigrations. Journal of Financial and Quantitative Analysis,2007,(42):595-620
[92] Yu-Chiang Hu, Jake Ansell. Measuring retail company performance using creditscoring techniques. European Journal of Operational Research,2007,(183):1595–1606
[93] Navneet Arora, Jeffrey R. bohn, and Fanlin Zhu. Reduced Form vs StructuralModels of Credit. Risk: A Case Study of Three Models, Journal of InvestmentManagement,2005,(3):43-67
[94] Jan Ericsson and Joel Reneby. An Empirical Study of Structural Credit Risk ModelsUsing Stock and Bond Prices. The Journal of Fixed Income,2004,(3):38-49
[95] D. Feng, C. Gourieroux, J. Jasiak. The ordered qualitative model for credit ratingtransitions. Journal of Empirical Finance,2008,(15):111-130
[96] Ericsson, Jan&Reneby, Joel. Valuing Corporate Liabilities.SIFR ResearchReport Series15, Swedish Institute for Financial Research,2003
[97] Robert A. Jarrow and Philip Protter. Structural versus Reduced-Form Models: ANew Information-Based Perspective. The Credit Market Handbook: AdvancedModeling Issues, John Wiley&Sons, inc.,2006:118-131
[98] Boness,A.James.Elements of a Theory of Dtock-Option Values.Journal of PoliticalEconomy,1964,(72):163-175
[99] Samuelson,Paul A.Ration theory of Warrant Pricing.Industrial ManagementReview,1965,(6):13-31
[100] Robert C. Merton. On the Pricing of Corporate Debt: The Risk Structure of InterestRates. Journal of Finance,1974,(29):499-470
[101] John Trussel. Default Probability on Corporate Bonds:A Contingent ClaimsModel.Review of Financial Economics,1997,(6):199-209
[102]郭其友张晖萍.2001年诺贝尔经济学奖得主——乔治·阿克洛夫经济学思想述评.外国经济与管理,2001,(11):45-48
[103]徐伯华.概率论诞生的思想历程.咸阳师范学院学报,2006,(8):16-19
[104]柳金甫,孙洪祥,王军,应用随机过程.北京:清华大学出版社,北京交通大学出版社,2006，76-83
[105]孙洪祥.随机过程.北京:北京机械工业出版社,2007，194-200
[106] Steven E.Shreve.金融随机分析.上海:上海财经大学出版社,2008，213-216
[107]张维功,何建敏,丁德臣.企业全面风险管理研究综述.软科学,2008,(12):40-43
[108] Jin Chuan Duan,Jean Guy Simonato. Maximum Likelihood Estimation of DepositInsurance Value with Interest Rate Risk. Journal of Empirical Finance,2002(9):109-132
[109] Ronald Anderson, suresh Sundaresan. A Comparative Study of Structural Modelsof Corporate Bond Yields: An Exploratory Investigation. Journal of Banking&Finance,2000,(24):255-269
[110] Ka Leung Li, Hoi Ying Wong. Structural Models of Corporate Bond Pricing withMaximum Likelihood Estimation. Journal of Empirical Finance,2008,(15):751-777
[111] Jan Ericsson,Joel Reneby. Estimating Structual Bond Pricing Models. Journal ofBusiness,2005,78(2):707-735
[112] Kanak Patel&Ricardo Pereira. Expected Default Probabilities in StructuralModels: Empirical Evidence. Journal of Real Estate Financial Economy,2007(34):107–133
[113] Sreedhar T. Bharath, Tyler Shumway.Forecasting Default with the MertonDistance to Default Model.The Review of FinancialStudies,2008,21(3):1339-1639
[114] David Lando,Mads Stenbo Nielsen. Correlation in corporate defaults: Contagion orconditional independence(Accepted Manuscript). Journal of FinancialIntermediation,2010,19(3):355-372
[115] Klaus Düllmann, Jonathan Küll, Michael Kunisch. Estimating asset correlationsfrom stock prices or default rates–which method is superior?. Journal of EconomicDynamics&Control,2010,34(11):2341-2357
[116] Larry Eisenberg,Thomas H.Noe.Systemic Risk in Financial Systems. ManagementsScience,2001,47(2):236-249
[117] Chunsheng Zhou. An Analysis of Default Correlations and Multiple Defaults. TheReview of Financial Studies,2001,14(2):555-576
[118]于波，陈希镇，杜江. Copula函数的选择方法与应用.数理统计与管理，2008，27（6）：1027-1033.
[119]余孝军. copula理论在商业银行风险管理中的应用.经济与管理，2009：64-68.
[120]朱新玲.相关系数与Copula函数相关性比较研究.武汉科技大学学报，2009，32（6）：664-668.
[121] Franklin Allen, ana Babus, Elena Carletti. Financial Connections and SystemicRisk. NBER working paper,2010.7
[122] Douglas W. Diamond. Bank Runs, Deposit Insurance, and Liquidity. FederalReserve Bank of Minneapolis Quarterly Review,2000,24(1):14-23
[123] Helmut Elsinger, Alfred Lehar,Martin Summer.Using Market Information forBanking System Risk Assessment. International Journal of Central Banking,2006(3):137-165
[124] Xavier Freixas. Systemic Risk, Interbank Relation and Liquidity Provision by theCentral Bank. Journal of Money,Credit and Banking,2000,32(3):611-38(Part2)
[125] Douglas W. Diamond. Bank and Liquidity Creation:A Simple Exposition of theDiamond-Dybvig Model. Wconomic Quarterly,93(2):189-200
[126] Robert C. Merton. Option Pricing When Underlying Stock Returns AreDiscontinuous. Journal of Financial Economics,1976,(3):125-144
[127] Peter Carr,Vadim Linetsky. A Jump to Default Extended CEV Models: AnApplication of Bessel Processes.Finance Stoch,2006(10):303-330
[128] Stan Beckers. The Constant Elasticity of Variance Model and Its Implications forOption Pricing. The Journal of Finance,1980,XXXV(3):661-673
[129] Mark Schroder. Computing the Constant Elasticity of Variance Option PricingFormula. The Journal of Finance,1989,XLIV(1):211-219
[130] Luciano Campi, Simon Polbennikov, Alessandro Sbuelz. Systematic equity-basedcredit risk: A CEV Model with Jump to Default. Journal of Economic Dynamics&Control,2009(33):93-108
[131] Alfred Lehar. Measuring Systemic risk: a Risk Management approach. Journal ofBanking&Finance,2005,29(10):2577-2603