商业银行贷款定价的简化型模型研究
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摘要
贷款是商业银行的核心业务。在我国利率市场化以及巴塞尔新资本协议实施的双重背景下,应用国际上先进的信用风险定价技术,研究贷款定价模型,是当前商业银行经营决策中面临的一项重大挑战。由于贷款所面临的信用风险的基本要素——违约概率、违约损失率、贷款暴露和年期等因素存在着不确定性和相关性,以及贷款客户历史违约数据稀缺、我国间接融资比例高等现实因素,加之研究的主要工具——随机分析和鞅方法需要较为艰深的数学知识,使得这一问题的研究具有重要的理论和现实意义。
本文采用了金融工程学的研究方法,在风险中性的研究环境和简化型模型的框架下,运用随机分析和鞅方法的有关技术,数学推导出在不同假设背景下商业银行贷款的定价模型,建立了三大类、共七个贷款定价模型。本文的核心内容及研究成果,可以概括为:
采用扩散过程刻画无风险利率过程以及违约强度过程的运动趋势。数学推导出了无风险利率过程和违约强度过程独立,无风险利率过程与违约强度过程相关,无风险利率过程与违约强度过程和回收率过程三者相关,三种假设条件下的定价模型,解释了模型的经济含义和应用范围。
研究两个贷款客户违约相关条件下的贷款定价模型。将研究背景设定为两种情况,一种是两个贷款客户在风险中性测度下违约相关,另一种情景是两个贷款客户在真实测度下违约相关。解释了在两种情景下,模型的现实意义和应用范围。数学推导出了推导出了两个贷款客户在真实测度和风险中性测度下的联合违约分布和密度函数,并推导出了定价模型,解释了模型的经济含义。
按照信用等级细分贷款客户的无违约状态,利用离散状态空间的连续时间G -Markov链,以及离散状态空间的连续时间F -条件的G -Markov链,刻画贷款客户信用等级迁移过程。假设无风险利率过程与信用等级迁移过程独立,以及无风险利率过程与信用等级迁移过程两者相关两种情景,数学推导出了贷款定价模型,解释了模型的现实意义和应用范围。
列举了实际的分析算例,运用Monte Carlo随机模拟的方法,计算出了风险价差和商业银行盈亏平衡利率,分析了模型中参数的变动对风险价差的影响。
The loan business is the core of operations in the commercial banks. Under the circumstances of interest rate adopted of the market principle and the implementation BaselⅡ, it is an important challenge for the commercial bank to study the pricing models by using advanced credit risk pricing technology. Since the basic credit risk elements of the loan : default probability, recovery rate, exposure and term are uncertain and correlated, and historic default data of the borrowers are scarce, and indirect financing plays an important role, and stochastic analysis and martingale methods are difficult to be learnt , which have made it being meaningful to study the questions both in theory and reality.
The paper uses the research approaches in financial engineering. In the framework of the risk neutral measures and reduced form models, by applying the technology of stochastic analysis and martingale methods, the mathematic models of pricing the loan are deduced under the circumstances of different assumptions in this paper. Seven models belonging to three classes are built in the paper.
The core and achievements of the paper can be generalized as follows:
The processes of risk-free interest rate and hazard rate are drawn by the diffusion process. The mathematic models of pricing the loan are deduced on the circumstance of the risk-free interest rate process and the hazard rate being independent, the risk-free interest rate process and the hazard rate being dependent, the risk-free interest rate process and the hazard rate and recovery rate being dependent. The economic meaning and application of the model are illustrated.
The paper builds the two pricing models considering the correlated defaults. The study backgrounds are set as follow: one is the two clients are default correlated on the physical measurement, the other is the two clients are default correlated on the martingale measurement. The real meaning and the field of application are explained. The joint default distribution function and the density function of the two clients are deduced under the physical measurement and the neutral-risk measurement. The models of pricing the loan are deduced.
The states of default-free of the client are divided by credit classes. By adopting continuous time G -Markov chains and F -conditioned G -Markov chain in the discrete state space, the migration process of credit classes are drown. The study backgrounds are set as follow: one is the risk-free interest rate is correlated with the migration process of credit classes, the other is the two processes are independent. The economic meaning and application of the model are illustrated. The models of pricing the loan are deduced.
Some examples are given. Through the Monte Carlo simulation the break-even interest rate and risk premium are calculated. The paper analyses the influence on the risk premium by changing parameters in the model.
本文采用了金融工程学的研究方法,在风险中性的研究环境和简化型模型的框架下,运用随机分析和鞅方法的有关技术,数学推导出在不同假设背景下商业银行贷款的定价模型,建立了三大类、共七个贷款定价模型。本文的核心内容及研究成果,可以概括为:
采用扩散过程刻画无风险利率过程以及违约强度过程的运动趋势。数学推导出了无风险利率过程和违约强度过程独立,无风险利率过程与违约强度过程相关,无风险利率过程与违约强度过程和回收率过程三者相关,三种假设条件下的定价模型,解释了模型的经济含义和应用范围。
研究两个贷款客户违约相关条件下的贷款定价模型。将研究背景设定为两种情况,一种是两个贷款客户在风险中性测度下违约相关,另一种情景是两个贷款客户在真实测度下违约相关。解释了在两种情景下,模型的现实意义和应用范围。数学推导出了推导出了两个贷款客户在真实测度和风险中性测度下的联合违约分布和密度函数,并推导出了定价模型,解释了模型的经济含义。
按照信用等级细分贷款客户的无违约状态,利用离散状态空间的连续时间G -Markov链,以及离散状态空间的连续时间F -条件的G -Markov链,刻画贷款客户信用等级迁移过程。假设无风险利率过程与信用等级迁移过程独立,以及无风险利率过程与信用等级迁移过程两者相关两种情景,数学推导出了贷款定价模型,解释了模型的现实意义和应用范围。
列举了实际的分析算例,运用Monte Carlo随机模拟的方法,计算出了风险价差和商业银行盈亏平衡利率,分析了模型中参数的变动对风险价差的影响。
The loan business is the core of operations in the commercial banks. Under the circumstances of interest rate adopted of the market principle and the implementation BaselⅡ, it is an important challenge for the commercial bank to study the pricing models by using advanced credit risk pricing technology. Since the basic credit risk elements of the loan : default probability, recovery rate, exposure and term are uncertain and correlated, and historic default data of the borrowers are scarce, and indirect financing plays an important role, and stochastic analysis and martingale methods are difficult to be learnt , which have made it being meaningful to study the questions both in theory and reality.
The paper uses the research approaches in financial engineering. In the framework of the risk neutral measures and reduced form models, by applying the technology of stochastic analysis and martingale methods, the mathematic models of pricing the loan are deduced under the circumstances of different assumptions in this paper. Seven models belonging to three classes are built in the paper.
The core and achievements of the paper can be generalized as follows:
The processes of risk-free interest rate and hazard rate are drawn by the diffusion process. The mathematic models of pricing the loan are deduced on the circumstance of the risk-free interest rate process and the hazard rate being independent, the risk-free interest rate process and the hazard rate being dependent, the risk-free interest rate process and the hazard rate and recovery rate being dependent. The economic meaning and application of the model are illustrated.
The paper builds the two pricing models considering the correlated defaults. The study backgrounds are set as follow: one is the two clients are default correlated on the physical measurement, the other is the two clients are default correlated on the martingale measurement. The real meaning and the field of application are explained. The joint default distribution function and the density function of the two clients are deduced under the physical measurement and the neutral-risk measurement. The models of pricing the loan are deduced.
The states of default-free of the client are divided by credit classes. By adopting continuous time G -Markov chains and F -conditioned G -Markov chain in the discrete state space, the migration process of credit classes are drown. The study backgrounds are set as follow: one is the risk-free interest rate is correlated with the migration process of credit classes, the other is the two processes are independent. The economic meaning and application of the model are illustrated. The models of pricing the loan are deduced.
Some examples are given. Through the Monte Carlo simulation the break-even interest rate and risk premium are calculated. The paper analyses the influence on the risk premium by changing parameters in the model.
引文
[1] Acharya V., Carpenter J., Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy [J], Review of Financial Studies, 2002 , 15:1355-1383.
[2] Alessandrini F., Credit Risk, Interest Rate Risk and the Business Cycle:[Master Thesis], HEC, Lausanne University, 1998
[3] Altman E. I., Measuring Corporate Bond Mortality and Performance[J], Journal of Finance,1989, 44:909-922.
[4] Altman E. I., High Yield Bond and Default Study, Salomon Smith Barney, U.S. Fixed Income High Yield Report, 2001, July.
[5] Anderson R., Sundaresan S., Design and Valuation of Debt Contracts [J], Review of Financial Studies, 1996, 9:37-68.
[6] Arvanitis A, Getting the Pricing Right [J], Risk, 1998, 13(9):115-119
[7] Athavale M. , Edmister R.O., The Pricing of Sequential Bank Loans[J], The Financial review, 2004, (39):231-253.
[8] Bakshi G., Madan D., Zhang F., Understanding the Role of Recovery in Default Risk Models : Empirical Comparisons and Implied Recovery Rates, working paper, 2001,
[9]Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards:A Revised Framework.,2004,Basel Committee Publications, No.107
[10] Bernnan M. J., Schwartz E.S., A Continuous Time Approach to the Pricing of Bonds, Journal of Banking and Finance, 1979, 3: 133-155
[11] Bielecki T. R., Rutkowski M., Multiple Ratings Model of Defaultable Term Structure [J], Mathematical Finance,2000, (10):125-139
[12] Bielecki T.R., Rutkowski M., Credit Risk: Modeling, Valuation and Hedging[M], Berlin Heidelberg New York, Springer-Verlag, 2002
[13] Black, Fischer, Scholes M., The Pricing of Options and Corporate Liabilities [J], Journal of Political Economy, 1973, 81: 637–564
[14] Black F.,Cox, J C., Valuing Corporate Securities: Some Effects of Bond Indenture Provisions[J],Journal of Finance, 1976, 2(31): 351-367
[15] Blackwell D.W., Winters D.B., Banking Relationships and the Effect of Monitoring on Loan Pricing [J],The Journal of Financial Research, 1997, Summer, 275-289
[16] Blanchet-Scalliet C., Jeanblanc M., Hazard Rate for Credit Risk and Hedging Defaultable Contingent , Working Paper, 2000
[17] Briys E., de Varenne, Valuing Risky Fixed Rate Debt: An Extension [J],Journal of Financial and Quantitative Analysis, 1997, 31(2):239-248.
[18] Briys E., de Varenne F., Options, Futures and Exotic Derivatives: Theory, Application and Practice, [M], John Wiley, 1998
[19] Carey M., Credit Risk in Private Debt Portfolios [J], Journal of Finance,1998, Vol.53,August.
[20] Cooper, Ian, Mello A , The Default Risk of Swaps [J], Journal of Finance, 1991, 46:597–620.
[21] Cox J. C., Ingersoll J.E., Ross S. A., An Analysis of Variable Rate Loan Contact [J], Journal of Finance, 1980, 35:389-403
[22] Crouhy M., Galai D., Credit Risk Revisited: An Option Pricing Approach [J], working paper , 1997
[23] Crougy M., Galai D., Mark R., Prototype Risk Rating System[J], Journal of Banking & Finance, 2001,(25):47-95
[24] Das S. R., Tufano P., Pricing Credit-Sensitive Debt When Interest Rates, Credit Rating and Credit Spread Are Stochastic[J], Journal of Finance ,1996, 5(2):161-198
[25] Delbaen F.,Schachermayer W,A General Version of the Fundamental Theorem of Asset Pricing[J], Math. Ann,1994, 46: 300-520
[26]Duffie D., Dynamic Asset Pricing Theory [M], Princeton University Press,1996
[27] Duffie D., Garleanu N., Risk and Valuation of Collateralized Debt Obligations [J], Financial Analysis’ Journal, 2001, 57(1):41-59.
[28] Duffie D., Singleton K., Modeling Term Structures of Default Risky Bonds[J], Review of Financial Studies, 1999,12:687-720
[29] Duffie D., Lando D., Term Structures of Credit Spreads with Incomplete Accounting Information[J], Econometrica, 2001,.69:633–664.
[30] Duffie, D.,. Singleton, Modelling Term Structures of Defaultable Bonds[J], The Review of Financial Studies, 1999,12(4): 687-720.
[31] Duffie, D., Pedersen L. H., Singleton K. J., Modeling Sovereign Yield Spreads: A Case Study of Russian Debt [J], Journal of Finance, 2003, 58(1):119-159
[32] Ericsson, Asset Substitution, Debt pricing, Optimal Leverage and Maturity[J], Working Paper, 2000, McGill University
[33] Finger C. C., Conditional Approaches for CreditMetrics Portfolio Distributions, Working Paper, RiskMetrics Group,1999,
[34] Frey R., McNeil A. J., Nyfeler M. A., Modelling Dependent Defaults: Asset Correlations Are Not Enough!, Working Paper, Department of Mathematics, ETHZ, Zurich, 2001
[35] Galai D., Masulis R. W., The Option Pricing Model and the Risk Factor of Stock [J], J. Finan. Econom, 1976, 3:5-81
[36] Geske R., The Valuation of Corporate Liabilities as Compound Options [J],Journal of Financial and Quantitative Analysis, 1977, 12:541-552.
[37]Giesecke K., Correlated Default with Incomplete Information [J], Journal of Banking and Finance,2004,28:1521-1545
[38]Giesecke K., Goldberg L., Calibrating Credit with Incomplete Information, 2004, working paper, Cornell University
[39] Gordy M. B.,A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules[J],. Journal of Financial Intermediation, 2003, 12:199-232.
[40] Greenfield Y. Hedging of Credit risk Embedded in Derivative Transactions : [Ph.D. dissertation], Carnegie Mellon University, 2000
[41] Gupton G. M., Gates D., Carty L.V., Bank Loan Loss Given Default, Moody’s Investors Service, Global Credit Research, 2000, November.
[42] Harrison J. M,Pliska S., Martingales and Stochastic Integrals in the Theory of Continuous Trading[J], Stochastic Processes and Their Applications, 1981, (11): 215-260.
[43] Hilberink B., Rogers L., Optimal Capital Structure and Endogenous Default[J], Financial and Stochastics , 2002, 6:237-263
[44] Ho T., Singer R., Bond Indenture Provisions and the Risk of Corporate Debt [J], Journal of Financial Economics, 1982, 10:375-406
[45] Huge B., Lando D., Swap pricing with two-side default risk in a rating-based model [J], European Finance Review, 1999, 3: 239-268
[46] Hull John ,Alan White, The Impact of Default Risk on the Prices of Options and Other Derivative Securities[J], Journal of Banking and Finance, 1995, 19: 299-322.
[47] Hull J., Predescu M., White A., The Relationship Between Credit Default Swap Spreads, Bond Yields, and Credit Rating Announcements [J], Journal of Banking and Finance, 2004, 28(11): 2789-2811
[48] Jarrow R., Lando D., Turnbull S. M., A Markov Model for the Term Structure of Credit Risk Spread[J], Rev. Financial Stud, 1997,10:481-523
[49] Jarrow R.A ,Protter P., Structural versus Reduced Form Models: A New Information Based Perspective[J], Journal of investment management,2004, 2(2):1-10
[50] Jarrow R., Turnbull S., Pricing Derivatives on Financial Securities Subject to Credit Risk [J], Journal of Finance,1995,50: 53–85.
[51] Jarrow R., Lando D., Yu F., Default Risk and Diversification: Theory and Applications, working paper, 1999, Cornell University
[52] Jarrow R.A., Yu F., Counterparty Risk and the Pricing of Defaultable Securities [J],Journal of Finance, 2001,56(5):1765-1799.
[53] Jeanblanc M., Rutkowski M., Modelling Default Risk: An Overview, Mathematical Finance: Theory and Practice, Beijing, Higher Education Press, 2000
[54] Jeanblanc M., Rutkowski M., Default Risk and Hazard Process, Mathematical Finance -- Bachelier Congress, 2000
[55] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus [M], BerlinHeidelberg New York, Springer-Verlag, 1991
[56] Kijima M., Monotonicities in a Markov Chain Model for Valuing Corporate Bonds Subject to Credit Risk[J], Mathematical Finance, 1998, 8(3): 229-247
[57] Kim I. J., Ramaswamy K., Sundaresan S. M., “Valuation of Corporate Fixed- Income Securities [J],Financial Management, 1993,Autumn, 117-131.
[58] Kim, Ramaswamy , Sundaresan, Does Default Risk in Coupons Affect the Valuation of Corporate Bonds?: A Contingent Claims Model[J], Financial Management, 1993, 22 (3): 117-131.
[59] Krahnen J. P., Weber M., Generally Accepted Rating Principles: A Primer [J], Journal of Banking & Finance, 2001, (3):3-23
[60] Kreps D.M, Arbitrage and Equilibrium in Economics with infinitely Commodities [J], Journal of mathematical economics,1981,3(8):15-35.
[61] Kusuoka S., A Remark on Default Risk Models [J],Advances in Mathematical Economics,1999,1:69-82,
[62] Lando D., On Cox Process and Credit Risk Bond, working paper, University of Copenhagen, 1994
[63] Lando D., Modeling Bonds and Derivatives with Credit Risk[M],Cambridge University Press,1997
[64] Lando D., On Cox Processes and Credit Risky Securities [J], Review of DerivativesResearch, 1998, 2(2/3): 99-120.
[65] Laurent J. P. Default Swap and Credit Spread Options, Working paper, BNP Paribas, London, 2000
[66] Leland H., Risky Debt, Bond Covenants and Optimal Capital Structure [J], Journal of Finance, 1994, 49:1213-1252.
[67] Leland H., Toft K., “Optimal Capital Structure, Endogenous Bankruptcy and the Term Structure of Credit Spreads[J], Journal of Finance, 1996,50:789-819.
[68] Litterman R., Iben T., Corporate Bond Valuation and the Term Structure of Credit Spreads[J], Journal of Portfolio Management, 1991,Spring, 52–64.
[69] Longstaff, F. and E. Schwartz (1995), “A Simple Approach to Valuing Risky Fixed and Floating Rate Debt,” Journal of Finance, 50:789-819
[70] Madan D., Unal H., Pricing the Risks of Default [J], Review of Derivatives Research,1998,2:121–160
[71] Merton R., On the Pricing of Corporate Debt: the Risk Structure of Interest Rates [J],Journal of Finance,1974,29:449-470
[72] Merton R., The Theory of Rational Option Pricing[J], Bell Journal of Economics and Management Science,1973,4:141–183
[73] Modigliani. F., Miller M. H, The Costs of Capital, Corporation Finance,and the Theory of Investment [J],American Economic Review, 1958, 6(48): 261-297
[74]Monkkonen H., Modeling Default Risk: Theory and Empirical Evidence:[Ph.D. dissertation ], Queens’ University, 1997
[75] Nielsen L. T., Saá-Requejo J., Santa-Clara P., Default Risk and Interest RateRisk: The Term Structure of Default Spreads, Working Paper, Insead, 1993
[76] Pitts, Selby,The Pricing of Corporate Debt: A Further Note[J], Journal of Finance, 1983, 38: 1311-1313
[77] Philip P., Stochastic Integration and Differential Equations [M], Springer-Verlag, New York, 2004
[78] Pye G., Gauging the Default Premium[J], Finan. Analysts J., 1974, 30(1): 49-52
[79]Ramaswamy K., Sundaresan S. M., The Valuation of Floating-rate Instruments, Theory and Evidence [J], J. Finan. Econom., 1986, (17):251-272
[80] Rendleman,How Risk are Shared in Interest Rates Swaps[J], J. Finan. Services Res. ,1992,5-34
[81] Repullo R. & Suarez J., Loan Pricing under Basel Capital Requirement[J], Journal of Financial Intermediation, 2004,13:496-521
[82] Ronn E. I., Verma A. K., Pricing Risk-Adjusted Deposit Insurance: An Option Based Model [J], Journal of Finance, 1986, 41(4):871-895.
[83] Santa Clara P., Bond Pricing with Default Risk, Working Paper, John E. Anderson Graduate School of Management, UCLA, 1997
[84] Sch?nbucher P. J., Factor Models for Portfolio Credit Risk, Working Paper, Department of Statistics, Bonn University,2000
[85]Sch?nbucher P., Term Stucture Modelling of Defaultable Bonds[J], Review of Derivatives Research, 1998, 2: 161–192
[86] Shimko D., Tejima H., van Deventer D., The Pricing of Risky Debt When Interest Rates are Stochastic[J], Journal of fixed income, 1993,September, 58-66
[87] Turnbull S. M., Pricing Loans using Default Probabilities[J], Economic notes by Banca Monte dei Paschi di Siena Spa, 2003,.32(2):197-217
[88] Vasicek. O, An Equilibrium Characterization of the Term Structure [J], The Journal of Financial Economics, 1977, 5:177-188
[89] Wang D. F., Pricing Defaultable Debt: Some Exact Results [J], Internat. J. Theor. Appl. Finance, 1999, 2: 95-99
[90] Yu F., Accounting Transparency and the Term Structure of Credit Spreads[J], The Journal of Financial Economics, 2005, 75(1):53-84.
[91] Zhou C., An Analysis of Default Correlations and Multiple Defaults[J], Review of Financial Studies, 2001, 14(2):555-576
[92]Zhou C., A Jump-Diffusion Approach to Modelling Credit Risk and Valuing Defaultable Secturities, working paper, Federal Reserve Board, Washington, 1997
[93] Zhou C., The Term Structure of Credit Spreads with Jump Risk [J], Journal of Banking & Finance, 2001, 25:2015-2040
[94] 毕明强,基于贡献度分析和客户关系的商业银行贷款定价方法研究[J],金融论坛,2004,(7):44-51
[95] 彼得.S.罗斯著,唐旭等译,商业银行管理(第三版)[M],北京:经济科学出版社,1999
[96] 曹清山 等,商业银行贷款定价策略和模型设计[J],金融论坛,2005,(2):33-37
[97]陈丽霞,陈玉祥,商业银行贷款定价方法研究[J],工业技术经济,2002,121(3):117-118
[98] 陈燕玲,贷款定价模式比较与利率市场化后的模式选择[J],华南金融 研究,2002,17(2):24-27
[99] 陈忠阳,金融风险分析与管理研究——市场与机构的理论、模型与技术[M],北京,中国人民大学出版社,2001
[100] 程希骏,周晖,武义青,对无套利定价理论中的完备性问题的研究[J],预测,2002,2(21):47-50
[101] 迪迪埃.科森,于格.皮罗特著,殷剑锋等译,高级信用风险分析:评估、定价和管理信用风险的金融方法和数学模型[M],北京,机械工业出版社,2005
[102] 戴国强,吴许均,基于违约概率和违约损失率的贷款定价研究[J],国际金融研究,2005,(10):43-48
[103] 胡丹,商业银行贷款定价体系探讨[J],农村金融研究,2004,(10):32-34
[104] 吉晓辉,国有商业银行人民币贷款定价机制研究[J],上海社会科学院学术季刊,1999,(1):33-36
[105] 蒋东明,论国外贷款定价模式及其对我国商业银行的启示[J],北京理工大学学报(社会科学版),2005,6(5):83-85
[106] 蒋东明,基于信用评级和违约概率的贷款定价研究:[博士学位论文],天津,天津大学,2005
[107] 金雪军,李红坤,解读新旧巴塞尔协议演绎途径[J],北京科技大学学报(社会科学版),2005,21(3):51-55
[108] 李瑞梅,我国商业银行贷款定价研究[J],上海金融,2005,(6):18-20
[109] 刘忠燕,娄树本,商业银行经营管理学[M],中国金融出版社,北京,2002
[110] 苗运铎,积极应对利率市场化改革建立商业银行存贷款定价机制[J],中国金融,2003,(13):38-39
[111] Manuel Ammann著,杨玉明译,信用风险评估——方法?模型?应用,北京,清华大学出版社,2004
[112] 牛锡明,我国商业银行实行贷款定价之研究[J],金融研究,1997,(10): 15-20.
[113] 牛锡明,国有商业银行实行贷款定价的几点设想[J],城市金融论坛,1998,(10):41-44.
[114] 乔埃尔.贝西斯著,许世清等译,商业银行风险管理——现代理论与方法 [M]. 深圳:海天出版社,2001
[115] 邱军,我国商业银行贷款定价问题的研究:硕士学位论文,天津,天津大学,2001
[116] 史泽友 等,关于利率市场化进程中人民币贷款定价的探讨[J],金融论坛,2002,(11):8-13
[117] 宋逢明,金融工程原理[M],北京:清华大学出版社,1999
[118] 孙晓成主编. 金融风险及其防范[M],北京,中国发展出版社,2000
[119] Thomas Stanley,贷款定价――期望收益与基于风险的收益[J],经济译文,1996,(2):41-43
[120] 王春发,金融资产定价的方法论评述[J],财经论丛,2001,92(6):53-59
[121] 王俊寿,商业银行贷款定价模型的比较研究[J],南开经济研究,2004 (2):99-102
[122] 王琼,陈金贤,信用风险定价方法与模型研究[J],现代财经,2002,22(4):14-16
[123] 席红辉,新巴塞尔协议框架下的风险分类和控制:银行和保险 [J],商业研究,2005,第 313 期:144-146
[124] 徐百兴,现代金融学中的无套利均衡分析研究进展概述[J],云南财经大学学报,2004,6(18):65-67
[125]杨婷蓉,利率市场化下的商业银行贷款定价管理:硕士学位论文,济南,山东大学,2002
[126] 叶中行,林建忠,数理金融――资产定价与金融决策理论[M],北京:科 学出版社,1998
[127]袁桂秋,姜礼尚,罗俊,固定支付利率的抵押贷款定价理论――限于在 支付日提前支付或违约[J],系统工程理论与实践,2003,(9):48-5.
[128] 袁桂秋,金能,无违约风险的可调支付利率抵押贷款定价原理[J],系 统工程学报,2004,19(2):135-140
[129]约翰.B.考埃特,爱德华.I.爱特曼,保罗.纳拉亚南, 演进着的信 用风险管理—— 金融领域面临的巨大挑战,北京,机械工业出版社,2000
[130] 赵银祥,刘瑞霞,新巴塞尔协议及国外商业银行内部评级体系研究[J] ,金融论坛,2003,第二期:2-9
[131] 詹原瑞,银行信用风险的现代度量与管理[M],北京,经济科学出版社, 2004
[132] 张金良,贷款定价模式研究[J],金融会计,2000,(9):11-15
[133] 中国人民银行. 中国货币政策报告(2002). http://www.pbc.gov.cn/
[134] 周爱民,刘乃岳,金融风险的实时检测——汇率偏差估计与风险价值量测 算,北京,经济管理出版社,2000
[135] 周四军,商业银行贷款定价方法研究[J],统计与决策,2002,149(5):11-12
[136] 周燕明,商业银行贷款定价研究:[硕士学位论文],天津,天津大学,2006
[137] 庄新田,黄小原,基于信息不对称的银行贷款定价策略分析[J],系统 工程,2002,20(3):20-23
[2] Alessandrini F., Credit Risk, Interest Rate Risk and the Business Cycle:[Master Thesis], HEC, Lausanne University, 1998
[3] Altman E. I., Measuring Corporate Bond Mortality and Performance[J], Journal of Finance,1989, 44:909-922.
[4] Altman E. I., High Yield Bond and Default Study, Salomon Smith Barney, U.S. Fixed Income High Yield Report, 2001, July.
[5] Anderson R., Sundaresan S., Design and Valuation of Debt Contracts [J], Review of Financial Studies, 1996, 9:37-68.
[6] Arvanitis A, Getting the Pricing Right [J], Risk, 1998, 13(9):115-119
[7] Athavale M. , Edmister R.O., The Pricing of Sequential Bank Loans[J], The Financial review, 2004, (39):231-253.
[8] Bakshi G., Madan D., Zhang F., Understanding the Role of Recovery in Default Risk Models : Empirical Comparisons and Implied Recovery Rates, working paper, 2001,
[9]Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards:A Revised Framework.,2004,Basel Committee Publications, No.107
[10] Bernnan M. J., Schwartz E.S., A Continuous Time Approach to the Pricing of Bonds, Journal of Banking and Finance, 1979, 3: 133-155
[11] Bielecki T. R., Rutkowski M., Multiple Ratings Model of Defaultable Term Structure [J], Mathematical Finance,2000, (10):125-139
[12] Bielecki T.R., Rutkowski M., Credit Risk: Modeling, Valuation and Hedging[M], Berlin Heidelberg New York, Springer-Verlag, 2002
[13] Black, Fischer, Scholes M., The Pricing of Options and Corporate Liabilities [J], Journal of Political Economy, 1973, 81: 637–564
[14] Black F.,Cox, J C., Valuing Corporate Securities: Some Effects of Bond Indenture Provisions[J],Journal of Finance, 1976, 2(31): 351-367
[15] Blackwell D.W., Winters D.B., Banking Relationships and the Effect of Monitoring on Loan Pricing [J],The Journal of Financial Research, 1997, Summer, 275-289
[16] Blanchet-Scalliet C., Jeanblanc M., Hazard Rate for Credit Risk and Hedging Defaultable Contingent , Working Paper, 2000
[17] Briys E., de Varenne, Valuing Risky Fixed Rate Debt: An Extension [J],Journal of Financial and Quantitative Analysis, 1997, 31(2):239-248.
[18] Briys E., de Varenne F., Options, Futures and Exotic Derivatives: Theory, Application and Practice, [M], John Wiley, 1998
[19] Carey M., Credit Risk in Private Debt Portfolios [J], Journal of Finance,1998, Vol.53,August.
[20] Cooper, Ian, Mello A , The Default Risk of Swaps [J], Journal of Finance, 1991, 46:597–620.
[21] Cox J. C., Ingersoll J.E., Ross S. A., An Analysis of Variable Rate Loan Contact [J], Journal of Finance, 1980, 35:389-403
[22] Crouhy M., Galai D., Credit Risk Revisited: An Option Pricing Approach [J], working paper , 1997
[23] Crougy M., Galai D., Mark R., Prototype Risk Rating System[J], Journal of Banking & Finance, 2001,(25):47-95
[24] Das S. R., Tufano P., Pricing Credit-Sensitive Debt When Interest Rates, Credit Rating and Credit Spread Are Stochastic[J], Journal of Finance ,1996, 5(2):161-198
[25] Delbaen F.,Schachermayer W,A General Version of the Fundamental Theorem of Asset Pricing[J], Math. Ann,1994, 46: 300-520
[26]Duffie D., Dynamic Asset Pricing Theory [M], Princeton University Press,1996
[27] Duffie D., Garleanu N., Risk and Valuation of Collateralized Debt Obligations [J], Financial Analysis’ Journal, 2001, 57(1):41-59.
[28] Duffie D., Singleton K., Modeling Term Structures of Default Risky Bonds[J], Review of Financial Studies, 1999,12:687-720
[29] Duffie D., Lando D., Term Structures of Credit Spreads with Incomplete Accounting Information[J], Econometrica, 2001,.69:633–664.
[30] Duffie, D.,. Singleton, Modelling Term Structures of Defaultable Bonds[J], The Review of Financial Studies, 1999,12(4): 687-720.
[31] Duffie, D., Pedersen L. H., Singleton K. J., Modeling Sovereign Yield Spreads: A Case Study of Russian Debt [J], Journal of Finance, 2003, 58(1):119-159
[32] Ericsson, Asset Substitution, Debt pricing, Optimal Leverage and Maturity[J], Working Paper, 2000, McGill University
[33] Finger C. C., Conditional Approaches for CreditMetrics Portfolio Distributions, Working Paper, RiskMetrics Group,1999,
[34] Frey R., McNeil A. J., Nyfeler M. A., Modelling Dependent Defaults: Asset Correlations Are Not Enough!, Working Paper, Department of Mathematics, ETHZ, Zurich, 2001
[35] Galai D., Masulis R. W., The Option Pricing Model and the Risk Factor of Stock [J], J. Finan. Econom, 1976, 3:5-81
[36] Geske R., The Valuation of Corporate Liabilities as Compound Options [J],Journal of Financial and Quantitative Analysis, 1977, 12:541-552.
[37]Giesecke K., Correlated Default with Incomplete Information [J], Journal of Banking and Finance,2004,28:1521-1545
[38]Giesecke K., Goldberg L., Calibrating Credit with Incomplete Information, 2004, working paper, Cornell University
[39] Gordy M. B.,A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules[J],. Journal of Financial Intermediation, 2003, 12:199-232.
[40] Greenfield Y. Hedging of Credit risk Embedded in Derivative Transactions : [Ph.D. dissertation], Carnegie Mellon University, 2000
[41] Gupton G. M., Gates D., Carty L.V., Bank Loan Loss Given Default, Moody’s Investors Service, Global Credit Research, 2000, November.
[42] Harrison J. M,Pliska S., Martingales and Stochastic Integrals in the Theory of Continuous Trading[J], Stochastic Processes and Their Applications, 1981, (11): 215-260.
[43] Hilberink B., Rogers L., Optimal Capital Structure and Endogenous Default[J], Financial and Stochastics , 2002, 6:237-263
[44] Ho T., Singer R., Bond Indenture Provisions and the Risk of Corporate Debt [J], Journal of Financial Economics, 1982, 10:375-406
[45] Huge B., Lando D., Swap pricing with two-side default risk in a rating-based model [J], European Finance Review, 1999, 3: 239-268
[46] Hull John ,Alan White, The Impact of Default Risk on the Prices of Options and Other Derivative Securities[J], Journal of Banking and Finance, 1995, 19: 299-322.
[47] Hull J., Predescu M., White A., The Relationship Between Credit Default Swap Spreads, Bond Yields, and Credit Rating Announcements [J], Journal of Banking and Finance, 2004, 28(11): 2789-2811
[48] Jarrow R., Lando D., Turnbull S. M., A Markov Model for the Term Structure of Credit Risk Spread[J], Rev. Financial Stud, 1997,10:481-523
[49] Jarrow R.A ,Protter P., Structural versus Reduced Form Models: A New Information Based Perspective[J], Journal of investment management,2004, 2(2):1-10
[50] Jarrow R., Turnbull S., Pricing Derivatives on Financial Securities Subject to Credit Risk [J], Journal of Finance,1995,50: 53–85.
[51] Jarrow R., Lando D., Yu F., Default Risk and Diversification: Theory and Applications, working paper, 1999, Cornell University
[52] Jarrow R.A., Yu F., Counterparty Risk and the Pricing of Defaultable Securities [J],Journal of Finance, 2001,56(5):1765-1799.
[53] Jeanblanc M., Rutkowski M., Modelling Default Risk: An Overview, Mathematical Finance: Theory and Practice, Beijing, Higher Education Press, 2000
[54] Jeanblanc M., Rutkowski M., Default Risk and Hazard Process, Mathematical Finance -- Bachelier Congress, 2000
[55] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus [M], BerlinHeidelberg New York, Springer-Verlag, 1991
[56] Kijima M., Monotonicities in a Markov Chain Model for Valuing Corporate Bonds Subject to Credit Risk[J], Mathematical Finance, 1998, 8(3): 229-247
[57] Kim I. J., Ramaswamy K., Sundaresan S. M., “Valuation of Corporate Fixed- Income Securities [J],Financial Management, 1993,Autumn, 117-131.
[58] Kim, Ramaswamy , Sundaresan, Does Default Risk in Coupons Affect the Valuation of Corporate Bonds?: A Contingent Claims Model[J], Financial Management, 1993, 22 (3): 117-131.
[59] Krahnen J. P., Weber M., Generally Accepted Rating Principles: A Primer [J], Journal of Banking & Finance, 2001, (3):3-23
[60] Kreps D.M, Arbitrage and Equilibrium in Economics with infinitely Commodities [J], Journal of mathematical economics,1981,3(8):15-35.
[61] Kusuoka S., A Remark on Default Risk Models [J],Advances in Mathematical Economics,1999,1:69-82,
[62] Lando D., On Cox Process and Credit Risk Bond, working paper, University of Copenhagen, 1994
[63] Lando D., Modeling Bonds and Derivatives with Credit Risk[M],Cambridge University Press,1997
[64] Lando D., On Cox Processes and Credit Risky Securities [J], Review of DerivativesResearch, 1998, 2(2/3): 99-120.
[65] Laurent J. P. Default Swap and Credit Spread Options, Working paper, BNP Paribas, London, 2000
[66] Leland H., Risky Debt, Bond Covenants and Optimal Capital Structure [J], Journal of Finance, 1994, 49:1213-1252.
[67] Leland H., Toft K., “Optimal Capital Structure, Endogenous Bankruptcy and the Term Structure of Credit Spreads[J], Journal of Finance, 1996,50:789-819.
[68] Litterman R., Iben T., Corporate Bond Valuation and the Term Structure of Credit Spreads[J], Journal of Portfolio Management, 1991,Spring, 52–64.
[69] Longstaff, F. and E. Schwartz (1995), “A Simple Approach to Valuing Risky Fixed and Floating Rate Debt,” Journal of Finance, 50:789-819
[70] Madan D., Unal H., Pricing the Risks of Default [J], Review of Derivatives Research,1998,2:121–160
[71] Merton R., On the Pricing of Corporate Debt: the Risk Structure of Interest Rates [J],Journal of Finance,1974,29:449-470
[72] Merton R., The Theory of Rational Option Pricing[J], Bell Journal of Economics and Management Science,1973,4:141–183
[73] Modigliani. F., Miller M. H, The Costs of Capital, Corporation Finance,and the Theory of Investment [J],American Economic Review, 1958, 6(48): 261-297
[74]Monkkonen H., Modeling Default Risk: Theory and Empirical Evidence:[Ph.D. dissertation ], Queens’ University, 1997
[75] Nielsen L. T., Saá-Requejo J., Santa-Clara P., Default Risk and Interest RateRisk: The Term Structure of Default Spreads, Working Paper, Insead, 1993
[76] Pitts, Selby,The Pricing of Corporate Debt: A Further Note[J], Journal of Finance, 1983, 38: 1311-1313
[77] Philip P., Stochastic Integration and Differential Equations [M], Springer-Verlag, New York, 2004
[78] Pye G., Gauging the Default Premium[J], Finan. Analysts J., 1974, 30(1): 49-52
[79]Ramaswamy K., Sundaresan S. M., The Valuation of Floating-rate Instruments, Theory and Evidence [J], J. Finan. Econom., 1986, (17):251-272
[80] Rendleman,How Risk are Shared in Interest Rates Swaps[J], J. Finan. Services Res. ,1992,5-34
[81] Repullo R. & Suarez J., Loan Pricing under Basel Capital Requirement[J], Journal of Financial Intermediation, 2004,13:496-521
[82] Ronn E. I., Verma A. K., Pricing Risk-Adjusted Deposit Insurance: An Option Based Model [J], Journal of Finance, 1986, 41(4):871-895.
[83] Santa Clara P., Bond Pricing with Default Risk, Working Paper, John E. Anderson Graduate School of Management, UCLA, 1997
[84] Sch?nbucher P. J., Factor Models for Portfolio Credit Risk, Working Paper, Department of Statistics, Bonn University,2000
[85]Sch?nbucher P., Term Stucture Modelling of Defaultable Bonds[J], Review of Derivatives Research, 1998, 2: 161–192
[86] Shimko D., Tejima H., van Deventer D., The Pricing of Risky Debt When Interest Rates are Stochastic[J], Journal of fixed income, 1993,September, 58-66
[87] Turnbull S. M., Pricing Loans using Default Probabilities[J], Economic notes by Banca Monte dei Paschi di Siena Spa, 2003,.32(2):197-217
[88] Vasicek. O, An Equilibrium Characterization of the Term Structure [J], The Journal of Financial Economics, 1977, 5:177-188
[89] Wang D. F., Pricing Defaultable Debt: Some Exact Results [J], Internat. J. Theor. Appl. Finance, 1999, 2: 95-99
[90] Yu F., Accounting Transparency and the Term Structure of Credit Spreads[J], The Journal of Financial Economics, 2005, 75(1):53-84.
[91] Zhou C., An Analysis of Default Correlations and Multiple Defaults[J], Review of Financial Studies, 2001, 14(2):555-576
[92]Zhou C., A Jump-Diffusion Approach to Modelling Credit Risk and Valuing Defaultable Secturities, working paper, Federal Reserve Board, Washington, 1997
[93] Zhou C., The Term Structure of Credit Spreads with Jump Risk [J], Journal of Banking & Finance, 2001, 25:2015-2040
[94] 毕明强,基于贡献度分析和客户关系的商业银行贷款定价方法研究[J],金融论坛,2004,(7):44-51
[95] 彼得.S.罗斯著,唐旭等译,商业银行管理(第三版)[M],北京:经济科学出版社,1999
[96] 曹清山 等,商业银行贷款定价策略和模型设计[J],金融论坛,2005,(2):33-37
[97]陈丽霞,陈玉祥,商业银行贷款定价方法研究[J],工业技术经济,2002,121(3):117-118
[98] 陈燕玲,贷款定价模式比较与利率市场化后的模式选择[J],华南金融 研究,2002,17(2):24-27
[99] 陈忠阳,金融风险分析与管理研究——市场与机构的理论、模型与技术[M],北京,中国人民大学出版社,2001
[100] 程希骏,周晖,武义青,对无套利定价理论中的完备性问题的研究[J],预测,2002,2(21):47-50
[101] 迪迪埃.科森,于格.皮罗特著,殷剑锋等译,高级信用风险分析:评估、定价和管理信用风险的金融方法和数学模型[M],北京,机械工业出版社,2005
[102] 戴国强,吴许均,基于违约概率和违约损失率的贷款定价研究[J],国际金融研究,2005,(10):43-48
[103] 胡丹,商业银行贷款定价体系探讨[J],农村金融研究,2004,(10):32-34
[104] 吉晓辉,国有商业银行人民币贷款定价机制研究[J],上海社会科学院学术季刊,1999,(1):33-36
[105] 蒋东明,论国外贷款定价模式及其对我国商业银行的启示[J],北京理工大学学报(社会科学版),2005,6(5):83-85
[106] 蒋东明,基于信用评级和违约概率的贷款定价研究:[博士学位论文],天津,天津大学,2005
[107] 金雪军,李红坤,解读新旧巴塞尔协议演绎途径[J],北京科技大学学报(社会科学版),2005,21(3):51-55
[108] 李瑞梅,我国商业银行贷款定价研究[J],上海金融,2005,(6):18-20
[109] 刘忠燕,娄树本,商业银行经营管理学[M],中国金融出版社,北京,2002
[110] 苗运铎,积极应对利率市场化改革建立商业银行存贷款定价机制[J],中国金融,2003,(13):38-39
[111] Manuel Ammann著,杨玉明译,信用风险评估——方法?模型?应用,北京,清华大学出版社,2004
[112] 牛锡明,我国商业银行实行贷款定价之研究[J],金融研究,1997,(10): 15-20.
[113] 牛锡明,国有商业银行实行贷款定价的几点设想[J],城市金融论坛,1998,(10):41-44.
[114] 乔埃尔.贝西斯著,许世清等译,商业银行风险管理——现代理论与方法 [M]. 深圳:海天出版社,2001
[115] 邱军,我国商业银行贷款定价问题的研究:硕士学位论文,天津,天津大学,2001
[116] 史泽友 等,关于利率市场化进程中人民币贷款定价的探讨[J],金融论坛,2002,(11):8-13
[117] 宋逢明,金融工程原理[M],北京:清华大学出版社,1999
[118] 孙晓成主编. 金融风险及其防范[M],北京,中国发展出版社,2000
[119] Thomas Stanley,贷款定价――期望收益与基于风险的收益[J],经济译文,1996,(2):41-43
[120] 王春发,金融资产定价的方法论评述[J],财经论丛,2001,92(6):53-59
[121] 王俊寿,商业银行贷款定价模型的比较研究[J],南开经济研究,2004 (2):99-102
[122] 王琼,陈金贤,信用风险定价方法与模型研究[J],现代财经,2002,22(4):14-16
[123] 席红辉,新巴塞尔协议框架下的风险分类和控制:银行和保险 [J],商业研究,2005,第 313 期:144-146
[124] 徐百兴,现代金融学中的无套利均衡分析研究进展概述[J],云南财经大学学报,2004,6(18):65-67
[125]杨婷蓉,利率市场化下的商业银行贷款定价管理:硕士学位论文,济南,山东大学,2002
[126] 叶中行,林建忠,数理金融――资产定价与金融决策理论[M],北京:科 学出版社,1998
[127]袁桂秋,姜礼尚,罗俊,固定支付利率的抵押贷款定价理论――限于在 支付日提前支付或违约[J],系统工程理论与实践,2003,(9):48-5.
[128] 袁桂秋,金能,无违约风险的可调支付利率抵押贷款定价原理[J],系 统工程学报,2004,19(2):135-140
[129]约翰.B.考埃特,爱德华.I.爱特曼,保罗.纳拉亚南, 演进着的信 用风险管理—— 金融领域面临的巨大挑战,北京,机械工业出版社,2000
[130] 赵银祥,刘瑞霞,新巴塞尔协议及国外商业银行内部评级体系研究[J] ,金融论坛,2003,第二期:2-9
[131] 詹原瑞,银行信用风险的现代度量与管理[M],北京,经济科学出版社, 2004
[132] 张金良,贷款定价模式研究[J],金融会计,2000,(9):11-15
[133] 中国人民银行. 中国货币政策报告(2002). http://www.pbc.gov.cn/
[134] 周爱民,刘乃岳,金融风险的实时检测——汇率偏差估计与风险价值量测 算,北京,经济管理出版社,2000
[135] 周四军,商业银行贷款定价方法研究[J],统计与决策,2002,149(5):11-12
[136] 周燕明,商业银行贷款定价研究:[硕士学位论文],天津,天津大学,2006
[137] 庄新田,黄小原,基于信息不对称的银行贷款定价策略分析[J],系统 工程,2002,20(3):20-23