浮动利率住房抵押贷款隐含期权定价
摘要
我国金融市场尚处于发育和形成之中,全国统一的金融市场还没有完全建立起来,没有形成利率市场化,利率是受央行管制的。统计数据显示,我国的贷款利率一年平均至少调整一次,当利率上升时,就会提高借款人的每月还款额,作为理性的还款人会根据自己的利益最大化,选择履约还是提前还款或违约,如果选择提前还款或违约就会给商业银行带来损失。近年来,一些商业银行为了规避损失的发生,相继制定了提前还款违约金制度。所以,无论是站在贷款人还是借款人角度,合理的抵押贷款定价显得非常重要。
本文以期权定价理论为基础,探讨了我国住房抵押贷款隐含期权定价及参数的估计。文章共分为6章,大致可以分为三个部分。第一部分包含第一章,简述我国个人住房抵押贷款的发展现状及商业银行错误定价对社会造成的影响,并对近期关于个人住房抵押贷款隐含期权的相关研究文献进行了回顾与简要评价。第二部分包括第二章到第四章,是对住房抵押贷款隐含期权的定价,其主要特点是在浮动利率及美式期权条件下进行探讨的,得出了隐含期权的表达式。第三部分是第五章,主要是对期权的模型进行求解,并估计了模型中的各个参数。第六章是本文的结论、建议及进一步研究的方向。
现有研究文献,要么着眼于固定利率贷款,要么限于在支付日进行提前还款或违约,而且现金流的贴现率被假定为在整个时间段是不变的。有鉴于此,本文在浮动贷款利率的基础上,对住房抵押贷款隐含的期权进行研究,且假设贷款利率服从跳跃过程；假设住房抵押贷款隐含的期权是美式期权；市场利率(贴现率)是随机变化的,且服从CIR模型；由于期权的表达式中含有随机项贷款利率,所以利用数学期望的方法得出隐含期权的价值。
不可否认,本文的研究是探索性的,所得到的住房抵押贷款隐含期权的定价表达式及其中的参数估计是否更为合理都有待于今后进一步的检验和研究。
China's financial market is still in the process of development and formation; unified national financial market has not been fully established. Interest rate market has not formed, interest rate is controlled by the central bank. Statistical data show that the adjustment of loan rates at least once a year on average. When interest rates rise, it will increase the borrower's monthly repayment, at this time, as a rational person would select compliance or prepayment or default based on their own maximized benefits. If borrower chooses prepayment or default, it will result in losses to commercial banks. Some commercial banks in order to avoid losses, have developed the system of prepayment penalty. Therefore, standing on the position of view of the lender and the borrower, reasonable pricing of mortgage is very important.
This article discussed that option pricing and parameter estimation of housing mortgage loans. The paper can be divided into three parts. The first part is the first chapter, outlined the development status of housing mortgage loans and the impact on the commercial banks error pricing to the society. After review the recent related research literature on the mortgage of implied option, we discuss the issues of the literature. The second part including ChapterⅡto Chapter IV is the pricing of implied option to mortgage; Its main feature is base on the floating rate and American options to explore. The third part is the fifth chapter.It mainly solve the model, and estimate the parameter of the model. ChapterⅥis the conclusion, recommendations and further research.
The existing research literatures, either based on the assume of fixed rate loan, or on determinant payment date to prepayment or default. And the discount rate of cash flow is a constant at defferent terms. The innovations of this paper are that base on a floating interest rate, assuming loan interest rate follow a jump process, underlying mortgage options are American options, market interest rate (discount rate) is a random variable as in the CIR model on the implied option mortgage study. Because expressions of options with random item, we use the method of mathematical expectation to solve implied option value.
Undeniable, study of this article is tentative. Weather the result of implicit option pricing expressions and parameters estimation is more reasonable, needing further research.
本文以期权定价理论为基础,探讨了我国住房抵押贷款隐含期权定价及参数的估计。文章共分为6章,大致可以分为三个部分。第一部分包含第一章,简述我国个人住房抵押贷款的发展现状及商业银行错误定价对社会造成的影响,并对近期关于个人住房抵押贷款隐含期权的相关研究文献进行了回顾与简要评价。第二部分包括第二章到第四章,是对住房抵押贷款隐含期权的定价,其主要特点是在浮动利率及美式期权条件下进行探讨的,得出了隐含期权的表达式。第三部分是第五章,主要是对期权的模型进行求解,并估计了模型中的各个参数。第六章是本文的结论、建议及进一步研究的方向。
现有研究文献,要么着眼于固定利率贷款,要么限于在支付日进行提前还款或违约,而且现金流的贴现率被假定为在整个时间段是不变的。有鉴于此,本文在浮动贷款利率的基础上,对住房抵押贷款隐含的期权进行研究,且假设贷款利率服从跳跃过程；假设住房抵押贷款隐含的期权是美式期权；市场利率(贴现率)是随机变化的,且服从CIR模型；由于期权的表达式中含有随机项贷款利率,所以利用数学期望的方法得出隐含期权的价值。
不可否认,本文的研究是探索性的,所得到的住房抵押贷款隐含期权的定价表达式及其中的参数估计是否更为合理都有待于今后进一步的检验和研究。
China's financial market is still in the process of development and formation; unified national financial market has not been fully established. Interest rate market has not formed, interest rate is controlled by the central bank. Statistical data show that the adjustment of loan rates at least once a year on average. When interest rates rise, it will increase the borrower's monthly repayment, at this time, as a rational person would select compliance or prepayment or default based on their own maximized benefits. If borrower chooses prepayment or default, it will result in losses to commercial banks. Some commercial banks in order to avoid losses, have developed the system of prepayment penalty. Therefore, standing on the position of view of the lender and the borrower, reasonable pricing of mortgage is very important.
This article discussed that option pricing and parameter estimation of housing mortgage loans. The paper can be divided into three parts. The first part is the first chapter, outlined the development status of housing mortgage loans and the impact on the commercial banks error pricing to the society. After review the recent related research literature on the mortgage of implied option, we discuss the issues of the literature. The second part including ChapterⅡto Chapter IV is the pricing of implied option to mortgage; Its main feature is base on the floating rate and American options to explore. The third part is the fifth chapter.It mainly solve the model, and estimate the parameter of the model. ChapterⅥis the conclusion, recommendations and further research.
The existing research literatures, either based on the assume of fixed rate loan, or on determinant payment date to prepayment or default. And the discount rate of cash flow is a constant at defferent terms. The innovations of this paper are that base on a floating interest rate, assuming loan interest rate follow a jump process, underlying mortgage options are American options, market interest rate (discount rate) is a random variable as in the CIR model on the implied option mortgage study. Because expressions of options with random item, we use the method of mathematical expectation to solve implied option value.
Undeniable, study of this article is tentative. Weather the result of implicit option pricing expressions and parameters estimation is more reasonable, needing further research.
引文
[1]蔡晓春,住房贷款的风险及其控制,北京：金融与经济,1999(3)；
[2]程艳琴,韩文秀,抵押贷款提前偿付率的非参数估计,天津理工学院学报,2003(4)18；
[3]陈颖,住房抵押贷款偿还过程中的博弈分析,哈尔滨工业大学学报,2007(39)；
[4]陈为涛,杨晓庄,加息对我国住房抵押贷款影响的实证研究,商业研究,2005(11)；
[5]个人住房抵押贷款风险分析[J].重庆大学学报(社会科学版),2002,(3)：26-29；
[6]戴建国,黄培清,住房抵押贷款的提前支付特性及其定价,系统工程理论方法应用,2001,10(2),21-124；
[7]段胜军,个人住房抵押贷款违约风险影响因素研究[D],昆明理工大学,2006；
[8]付小玲.住房抵押贷款提前偿付的风险分析[J],经济研究导刊,2007(10)；
[9]傅强,张宜松.住房抵押贷款证券化信用制度的博弈分析[J].重庆大学学报.2004(5)：111-115；
[10]何晓晴,谢赤,吴晓,住房按揭贷款违约风险及其防范机制,社会科学家,2005(11)；
[11]约翰.赫尔,John C. Hull期权、期货和其他衍生产品,华夏出版社,1999：
[12]黄玉霜,周清佳,林哲群,应用动态提前清偿模型评价住宅抵押贷款证券[J],商场现代化,2005(7)12-19；
[13]姜礼尚,期权定价的数学模型和方法,高等教育出版社,2002；
[14]孔刘柳,业银行信贷合约行为理论[M],上海：上海财经大学出版社, 2001：
[15]李静,商业银行住房抵押贷款风险管理研究,西南财经大学硕士论文,2008,11：
[16]李鹏雁,王雅林,基于层次分析法的住房抵押贷款风险评价,哈尔滨工业大学学报,2006(11)；
[17]李鹏雁,住房抵押贷款风险规避研究[D],哈尔滨,哈尔滨工业大学,2006；
[18]林建华,方翊,冯敬海,随机利率下提前还贷的优劣分析,运筹与管理,2003(4),6-9；
[19]林海.股利政策与上市公司收益的实证研究[EB/OL],华财会网(WWW. e521.com),2002-04-15；
[20]刘春红,上海市个人住房抵押贷款违约因素实证分析,《上海金融》,2000(1)；
[21]刘疆,游江,个人住房抵押贷款提前还款行为分析[J].西南金融,2006,(10)；
[22]刘畅,徐承龙,谢志华,提前还款及隐含期权的研究,应用数学与计算数学学报,2006(12)；
[23]刘川巍.不对称信息条件下商业银行信贷风险的博弈分析[J],上海财经大学学报,2004(5)：31-36；
[24]罗力力,我国个人住房抵押贷款风险控制问题研究,经济管理,2009；
[25]马宇,韩存,申亮,美国次级债危机影响为何如此之大—基于风险分担视角的解释[J],经济学家,2008(3)92-98；
[26]买建国,住房抵押贷款被动违约风险控制方略,货币银行,2005(9)；
[27]牛凤瑞,2007房地产蓝皮书,中国房地产发展报告N0.4[M],北京,社会科学文献出版社.
[28]卜壮志,徐成贤,浮动利率房贷提前还款的损失度量,金融论坛,2008.2；
[29]孙冰,刘洪玉,个人住房抵押贷款提前还款风险因素实证研究,同济大学学报,自然科学版,2007(1)35；
[30]施方,俞自由,黄保佳,住房抵押贷款的比例提前偿付模型,数理统计与管理,2003(3),36-40；
[31]施锡铨,张淼,我国住房抵押贷款提前还款的博弈分析,财经研究,2002 (10),35-42；
[32]尚耀华,国外个人住房抵押贷款违约问题的研究概述,环球经济,2006,1；
[33]石晓军.试析我国信用风险产生的原因[J],财经科学(增刊),2003,(5)
[34]田启伟,肖凯,住房抵押贷款理性违约的博弈分析,郑州航空工业管理学院学报,(管理科学版),2004(6)；
[35]王福林,个人住房抵押贷款违约风险影响因素实证研究,浙江大学博士论文,2004；
[36]吴冲锋、王海成,吴文锋,金融工程研究[M],上海,上海交通大学出版社,2000；
[37]王重润,赵冬暖,王浩润.信息非对称对住房抵押市场的影响[J],中国房地产金融,2003,(11)；
[38]王建红,陈松,郑志明.住房抵押贷款的理性违约及其风险的规避[J],重庆建筑大学学报,2002,(5)：80-85；
[39]吴晨,蒋晓枫,黄卫国.个人住房抵押贷款风险的博弈分析[J],中国纺织大学学报.1999(6)：9-12；
[40]肖任凤,杨明,银行对抗住房抵押贷款提前还贷的合同设计,应用数学,2005(18增),167-170；
[41]谢赤,一个动态化的利率期限结构模型群[J],预测,2000,19(3)：49-52：
[42]杨健青,马万智,如何规避和降低房地产抵押贷款风险,中国房地信息,2000(2)；
[43]杨德才.我国个人住房贷款发展的制约因素与对策,中国房地产,2000,(7)
[44]袁贵秋,姜礼尚,罗俊,固定支付利率的抵押贷款定价理论,系统工程理论与实践,2004；
[45]姚捷,我国住房抵押贷款借款人提前还款行为分析,商业研究,2005(23),120；
[46]张尧庭,金融市场的统计分析[M]南宁,广西师范大学出版社,1998,175-230；
[47]张红,娜,房抵押贷款理性违约风险及其规避[J],庆建筑大学学报(增刊),2001：84-8；
[48]张劲,滑翔,我国目前住房个人按揭贷款风险分析及对策[J],西南金融,2003(1)：58-9；
[49]郑作标.浅谈个人住房贷款风险防范[J]海南金融,2003,(7)：50-51；
[50]Brent W Ambrose, Ricardo J but timer J r. Embedded options in the mortgage contract [J],Journal of Real Estate Finance and Economics,2000,21 (2):95-111;
[51]Cox J, Ingersoll J, Ross R, A Re-examination of traditional hypotheses about the term structure of interest rates [J]. Journal of Finance,1981,36:769-799;
[52]Cox J, Ingersoll J, Ross R.A theory of the term structure of interest rates [J]. Econometrica,1985,53 (2):302-363;
[53]Chan, K. C., G.A. Karolin, F. A. Long staff and A. B. Sanders. An Empirical Comparison of Alternative Models of the Short tern Interest Rate [J]. Journal of Finance,1992,47:1209-1227;
[54]Chen, R. and L. Scott. Maximum Likelihood Estimation of a Multifactor Equilibrium Model of the Term Structure of Interest Rates [J]. Journal of Fixed Income,1993,3 (3):14-32;
[55]Deng Y, Zhen D, Ling C. An early assessment of residential mortgage performance in China [J]. Forthcoming in Journal of Real Estate Finance and Economics,2005,31 (2);
[56]Deng, Y.H., J.M. Quigley, R. Van Order. Mortgage terminations [D],Center for Real Estate Finance and Urban Economics Working Paper 95-230, University of California at Berkeley,1995;
[57]Fabozzi F, Fabozzi T. Prepayment, Default, and the Valuation of Mortgage Pass-Through Securitization, Journal of Business,1992 (2) 221-239;
[58]Foster, Chester, Robert Van Oder, An Option-Based Model of Mortgage default, Housing Finance Review,1984,3,351-3721;
[59]Gau, A Taxonomic Model for The Risk-Rating of Residential Mortgages, Journal of Business,1978,51:687-7061;
[60]Hilliard Jimmy E, Kau J B, Kennan D C. Valuing prepayment and default in a fixed-rate mortgage, abivariate binomial options pricing technique [J].Real Estate Economics,1998,26 (3):431-468;
[62]Henderson Patrice H, Robert V an Order. Pricing mortgages:an interpretation of the models and results [J]. Journal of Financial Services Research,1987,1: 77-111;
[62]Jung, Allen F., Terms of Conventional Mortgage Loans on Existing Houses Journal of Finance,1962,432-443;
[63]James B Kau, and Donald C. Keenan. A n overview of the option theoretic pricing of mortgages [J] Journal of Housing Research, Fannie M ac,1995,6 (Issue2):217-244;
[64]Kau J B, Kennan D C. An overview of the option-theoretic pricing of mortgages [J]. Journal of Housing Research,1995,6 (2):217-244;
[65]Kenneth B. Rational Prepayment and Valuation of Mortgage Backed Securitization, Review of Finance Studies,1995 (3):673-685;
[66]Quercia, Roberto G. and Michael A. Stegman, Residential Mortgage Default:A Review of the Literature[J], Journal of Housing Research, 1992,3,341-379;
[67]Quigley John M, Robert Van Oder, Yong heng Deng, The Competing Risks for Mortgage Termination by Default and Prepayment in the Residential Housing Market, paper presented at the NBER Summer Institute, Mimeo11 9931;
[68]Robert F. Cotterman, Neighborhood effects in mortgage default risk March, Unicom Research Corporation,2000;
[69]Sunil G. M BS structuring:Concepts and techniques [J]. The Securitization Conduit,1998,1(3):77 82;
[70]Von Furstenberg, George M., Default Risk on FHA2Insured Home Mortgages as a Function of the Terms of Financing:A Quantitative Analysis [J]. Journal of Finance,1969,24,459-477;
[71]Vasicek O A. An equilibrium characterization of the Term Structure [J] Journal of Financial Economics,1977,5:177-88;
[2]程艳琴,韩文秀,抵押贷款提前偿付率的非参数估计,天津理工学院学报,2003(4)18；
[3]陈颖,住房抵押贷款偿还过程中的博弈分析,哈尔滨工业大学学报,2007(39)；
[4]陈为涛,杨晓庄,加息对我国住房抵押贷款影响的实证研究,商业研究,2005(11)；
[5]个人住房抵押贷款风险分析[J].重庆大学学报(社会科学版),2002,(3)：26-29；
[6]戴建国,黄培清,住房抵押贷款的提前支付特性及其定价,系统工程理论方法应用,2001,10(2),21-124；
[7]段胜军,个人住房抵押贷款违约风险影响因素研究[D],昆明理工大学,2006；
[8]付小玲.住房抵押贷款提前偿付的风险分析[J],经济研究导刊,2007(10)；
[9]傅强,张宜松.住房抵押贷款证券化信用制度的博弈分析[J].重庆大学学报.2004(5)：111-115；
[10]何晓晴,谢赤,吴晓,住房按揭贷款违约风险及其防范机制,社会科学家,2005(11)；
[11]约翰.赫尔,John C. Hull期权、期货和其他衍生产品,华夏出版社,1999：
[12]黄玉霜,周清佳,林哲群,应用动态提前清偿模型评价住宅抵押贷款证券[J],商场现代化,2005(7)12-19；
[13]姜礼尚,期权定价的数学模型和方法,高等教育出版社,2002；
[14]孔刘柳,业银行信贷合约行为理论[M],上海：上海财经大学出版社, 2001：
[15]李静,商业银行住房抵押贷款风险管理研究,西南财经大学硕士论文,2008,11：
[16]李鹏雁,王雅林,基于层次分析法的住房抵押贷款风险评价,哈尔滨工业大学学报,2006(11)；
[17]李鹏雁,住房抵押贷款风险规避研究[D],哈尔滨,哈尔滨工业大学,2006；
[18]林建华,方翊,冯敬海,随机利率下提前还贷的优劣分析,运筹与管理,2003(4),6-9；
[19]林海.股利政策与上市公司收益的实证研究[EB/OL],华财会网(WWW. e521.com),2002-04-15；
[20]刘春红,上海市个人住房抵押贷款违约因素实证分析,《上海金融》,2000(1)；
[21]刘疆,游江,个人住房抵押贷款提前还款行为分析[J].西南金融,2006,(10)；
[22]刘畅,徐承龙,谢志华,提前还款及隐含期权的研究,应用数学与计算数学学报,2006(12)；
[23]刘川巍.不对称信息条件下商业银行信贷风险的博弈分析[J],上海财经大学学报,2004(5)：31-36；
[24]罗力力,我国个人住房抵押贷款风险控制问题研究,经济管理,2009；
[25]马宇,韩存,申亮,美国次级债危机影响为何如此之大—基于风险分担视角的解释[J],经济学家,2008(3)92-98；
[26]买建国,住房抵押贷款被动违约风险控制方略,货币银行,2005(9)；
[27]牛凤瑞,2007房地产蓝皮书,中国房地产发展报告N0.4[M],北京,社会科学文献出版社.
[28]卜壮志,徐成贤,浮动利率房贷提前还款的损失度量,金融论坛,2008.2；
[29]孙冰,刘洪玉,个人住房抵押贷款提前还款风险因素实证研究,同济大学学报,自然科学版,2007(1)35；
[30]施方,俞自由,黄保佳,住房抵押贷款的比例提前偿付模型,数理统计与管理,2003(3),36-40；
[31]施锡铨,张淼,我国住房抵押贷款提前还款的博弈分析,财经研究,2002 (10),35-42；
[32]尚耀华,国外个人住房抵押贷款违约问题的研究概述,环球经济,2006,1；
[33]石晓军.试析我国信用风险产生的原因[J],财经科学(增刊),2003,(5)
[34]田启伟,肖凯,住房抵押贷款理性违约的博弈分析,郑州航空工业管理学院学报,(管理科学版),2004(6)；
[35]王福林,个人住房抵押贷款违约风险影响因素实证研究,浙江大学博士论文,2004；
[36]吴冲锋、王海成,吴文锋,金融工程研究[M],上海,上海交通大学出版社,2000；
[37]王重润,赵冬暖,王浩润.信息非对称对住房抵押市场的影响[J],中国房地产金融,2003,(11)；
[38]王建红,陈松,郑志明.住房抵押贷款的理性违约及其风险的规避[J],重庆建筑大学学报,2002,(5)：80-85；
[39]吴晨,蒋晓枫,黄卫国.个人住房抵押贷款风险的博弈分析[J],中国纺织大学学报.1999(6)：9-12；
[40]肖任凤,杨明,银行对抗住房抵押贷款提前还贷的合同设计,应用数学,2005(18增),167-170；
[41]谢赤,一个动态化的利率期限结构模型群[J],预测,2000,19(3)：49-52：
[42]杨健青,马万智,如何规避和降低房地产抵押贷款风险,中国房地信息,2000(2)；
[43]杨德才.我国个人住房贷款发展的制约因素与对策,中国房地产,2000,(7)
[44]袁贵秋,姜礼尚,罗俊,固定支付利率的抵押贷款定价理论,系统工程理论与实践,2004；
[45]姚捷,我国住房抵押贷款借款人提前还款行为分析,商业研究,2005(23),120；
[46]张尧庭,金融市场的统计分析[M]南宁,广西师范大学出版社,1998,175-230；
[47]张红,娜,房抵押贷款理性违约风险及其规避[J],庆建筑大学学报(增刊),2001：84-8；
[48]张劲,滑翔,我国目前住房个人按揭贷款风险分析及对策[J],西南金融,2003(1)：58-9；
[49]郑作标.浅谈个人住房贷款风险防范[J]海南金融,2003,(7)：50-51；
[50]Brent W Ambrose, Ricardo J but timer J r. Embedded options in the mortgage contract [J],Journal of Real Estate Finance and Economics,2000,21 (2):95-111;
[51]Cox J, Ingersoll J, Ross R, A Re-examination of traditional hypotheses about the term structure of interest rates [J]. Journal of Finance,1981,36:769-799;
[52]Cox J, Ingersoll J, Ross R.A theory of the term structure of interest rates [J]. Econometrica,1985,53 (2):302-363;
[53]Chan, K. C., G.A. Karolin, F. A. Long staff and A. B. Sanders. An Empirical Comparison of Alternative Models of the Short tern Interest Rate [J]. Journal of Finance,1992,47:1209-1227;
[54]Chen, R. and L. Scott. Maximum Likelihood Estimation of a Multifactor Equilibrium Model of the Term Structure of Interest Rates [J]. Journal of Fixed Income,1993,3 (3):14-32;
[55]Deng Y, Zhen D, Ling C. An early assessment of residential mortgage performance in China [J]. Forthcoming in Journal of Real Estate Finance and Economics,2005,31 (2);
[56]Deng, Y.H., J.M. Quigley, R. Van Order. Mortgage terminations [D],Center for Real Estate Finance and Urban Economics Working Paper 95-230, University of California at Berkeley,1995;
[57]Fabozzi F, Fabozzi T. Prepayment, Default, and the Valuation of Mortgage Pass-Through Securitization, Journal of Business,1992 (2) 221-239;
[58]Foster, Chester, Robert Van Oder, An Option-Based Model of Mortgage default, Housing Finance Review,1984,3,351-3721;
[59]Gau, A Taxonomic Model for The Risk-Rating of Residential Mortgages, Journal of Business,1978,51:687-7061;
[60]Hilliard Jimmy E, Kau J B, Kennan D C. Valuing prepayment and default in a fixed-rate mortgage, abivariate binomial options pricing technique [J].Real Estate Economics,1998,26 (3):431-468;
[62]Henderson Patrice H, Robert V an Order. Pricing mortgages:an interpretation of the models and results [J]. Journal of Financial Services Research,1987,1: 77-111;
[62]Jung, Allen F., Terms of Conventional Mortgage Loans on Existing Houses Journal of Finance,1962,432-443;
[63]James B Kau, and Donald C. Keenan. A n overview of the option theoretic pricing of mortgages [J] Journal of Housing Research, Fannie M ac,1995,6 (Issue2):217-244;
[64]Kau J B, Kennan D C. An overview of the option-theoretic pricing of mortgages [J]. Journal of Housing Research,1995,6 (2):217-244;
[65]Kenneth B. Rational Prepayment and Valuation of Mortgage Backed Securitization, Review of Finance Studies,1995 (3):673-685;
[66]Quercia, Roberto G. and Michael A. Stegman, Residential Mortgage Default:A Review of the Literature[J], Journal of Housing Research, 1992,3,341-379;
[67]Quigley John M, Robert Van Oder, Yong heng Deng, The Competing Risks for Mortgage Termination by Default and Prepayment in the Residential Housing Market, paper presented at the NBER Summer Institute, Mimeo11 9931;
[68]Robert F. Cotterman, Neighborhood effects in mortgage default risk March, Unicom Research Corporation,2000;
[69]Sunil G. M BS structuring:Concepts and techniques [J]. The Securitization Conduit,1998,1(3):77 82;
[70]Von Furstenberg, George M., Default Risk on FHA2Insured Home Mortgages as a Function of the Terms of Financing:A Quantitative Analysis [J]. Journal of Finance,1969,24,459-477;
[71]Vasicek O A. An equilibrium characterization of the Term Structure [J] Journal of Financial Economics,1977,5:177-88;