住房抵押贷款支持证券（MBSs）定价方法研究
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摘要
针对于目前市场缺少关注中国市场和借款人提前还款行为特点的MBSs定价方法的局面,本文提出了一种创新的,全面的MBS定价方法。这种方法考虑到了中国抵押贷款市场的特殊性,同时也考虑了这个资本市场未来的发展方向,并且结合了目前理论界的最新研究成果,适合于发行机构应用,直观、易行。
本文的定价方法,包括了三个大的部分。第一部分构建了适合中国国情的提前还款模型。文中认为国内的提前还款来源,主要来自于收入和支付能力的提高,文中也研究了再融资贷款对提前还款的影响,并建立了这两种因素的相关模型。然后根据两个模型考虑了单因素和双因素两种情况,计算出相应的单月提前还款率(SMM)。在两种模型的构建和关键量SMM的推导方面,本文综合了国外学者最新的关于考虑借款人异质性(heterogeneity)的提前还款模型方面的相关成果,在模型中考虑了异质性因素,如在再融资决策模型中,加入了交易成本因素,并假设其服从beta分布,通过概率的变换得到SMM。
定价方法中的第二个重要部分是对于利率期限结构的确定。本文主要采用了CIR双因子模型计算短期利率和长期收益率。并且采用卡尔曼滤波方法估计CIR双因子模型参数。同时也研究了房贷利率和相同期限国债收益率之间的关系。
定价方法的最后利用估计参数进行蒙特卡罗仿真研究。在不同路径上模拟未来利率,同时利用提前还款模型对每条路径上的SMM进行计算,得到未来各期的现金流在某时点的折现值,而后对多条路径上的价格求算术平均值作为MBS的理论价格。
This dissertation has proposed a innovative and compelete MBS pricing method. This method considers of the particularity of Chinese secured-loan markets and the developing direction of market at the same time. The method also combines the latest research results at present. This method is suited to SPV(special purpose vechile) to use practically and scientificly.
The pricing method includes three parts. In Part one the paper builds prepayment models describing the particularity of Chinese people.And the author concludes that the prepayment source mainly comes from the improvement of income.In this part also a model is included,which is based on refinancing prepayment. Then the author calculates the corresponding Single-monthly-mortality (SMM) of the single-factor model and dual-factor model. In this part the author also adds unobeservable heterogeneity variable into model, which is latest development of foreign scholar study. The transaction cost is put into the refinance model and supposed to obey beta-distribution. Finally this method gets SMM through the probability.
Part two includes the study of term-structure of interest rates.This paper has mainly adopted CIR two-factor model to calculate short-term interest rate and long-term earning ratio.This dissertation uses Kalman-filter to estimate parameters in CIR model.Finally this part studys the relationship betwen the housing loan rate and long-term interest rate.
Part three uses Monte-carlo method with estimated parameters to simulate a path of interest rate.And then utilizes prepayment model to calculate SMM to get discouted cash-flow.Finally the author gets the average and theoritical price.
本文的定价方法,包括了三个大的部分。第一部分构建了适合中国国情的提前还款模型。文中认为国内的提前还款来源,主要来自于收入和支付能力的提高,文中也研究了再融资贷款对提前还款的影响,并建立了这两种因素的相关模型。然后根据两个模型考虑了单因素和双因素两种情况,计算出相应的单月提前还款率(SMM)。在两种模型的构建和关键量SMM的推导方面,本文综合了国外学者最新的关于考虑借款人异质性(heterogeneity)的提前还款模型方面的相关成果,在模型中考虑了异质性因素,如在再融资决策模型中,加入了交易成本因素,并假设其服从beta分布,通过概率的变换得到SMM。
定价方法中的第二个重要部分是对于利率期限结构的确定。本文主要采用了CIR双因子模型计算短期利率和长期收益率。并且采用卡尔曼滤波方法估计CIR双因子模型参数。同时也研究了房贷利率和相同期限国债收益率之间的关系。
定价方法的最后利用估计参数进行蒙特卡罗仿真研究。在不同路径上模拟未来利率,同时利用提前还款模型对每条路径上的SMM进行计算,得到未来各期的现金流在某时点的折现值,而后对多条路径上的价格求算术平均值作为MBS的理论价格。
This dissertation has proposed a innovative and compelete MBS pricing method. This method considers of the particularity of Chinese secured-loan markets and the developing direction of market at the same time. The method also combines the latest research results at present. This method is suited to SPV(special purpose vechile) to use practically and scientificly.
The pricing method includes three parts. In Part one the paper builds prepayment models describing the particularity of Chinese people.And the author concludes that the prepayment source mainly comes from the improvement of income.In this part also a model is included,which is based on refinancing prepayment. Then the author calculates the corresponding Single-monthly-mortality (SMM) of the single-factor model and dual-factor model. In this part the author also adds unobeservable heterogeneity variable into model, which is latest development of foreign scholar study. The transaction cost is put into the refinance model and supposed to obey beta-distribution. Finally this method gets SMM through the probability.
Part two includes the study of term-structure of interest rates.This paper has mainly adopted CIR two-factor model to calculate short-term interest rate and long-term earning ratio.This dissertation uses Kalman-filter to estimate parameters in CIR model.Finally this part studys the relationship betwen the housing loan rate and long-term interest rate.
Part three uses Monte-carlo method with estimated parameters to simulate a path of interest rate.And then utilizes prepayment model to calculate SMM to get discouted cash-flow.Finally the author gets the average and theoritical price.
引文
[1] Andrew Kalotay,Deane Yang,and Frank J. Fabozzi, An Option-Theoretic Prepayment Model for Mortgages and Mortgage-Backed Securities, International Journal of Theoretical and Applied Finance, 2004,24(7);931~948
[2] Archer,Ling and Mcgill,The effect of income and collateral constraints on residential mortgage terminations,Regional Science and Urban Economics;253~261
[3] Austin Kelly,Racial and Ethnic Disparities In Mortgage Prepayment,Jounal of Housing Economics,1994,4;350~372
[4] Chris Downing, Richard Stanton and Nancy Wallace, An Empirical Test of a Two-Factor Mortgage Prepayment and Valuation Model: How Much Do House Prices Matter, Journal of Theoretical and Applied Finance, 2002,20(5);456~520
[5] Deng,Quigley and Frank J. Fabozzi and Andrew Kalotay,Ginnie Mae and the Secondary Mortgage Market:an Integral Part of the American Economic Engine, Government Report; 2001,126~162
[6] Gonzalo Cortazar,Eduardo S. Schwartz and Lorenzo Naranjo, Term Structure Estimation in Low-Frequency Transaction Markets: A Kalman Filter Approach with Incomplete Panel-Data,working paper,2003
[7] Gourieroux and Scaillet(1996),Unemployment Insurance and Mortages,Insurance Mathematics and Economics,20;173-195
[8] Huarong Tang and Yihong Xia, An International Examination of Affine Term Structure Models and the Expectations Hypothesis,2005,working paper
[9] Michael .W. Brandt Ping He,Simulated Likelihood Estimation of Affine Term Structure Models from Panel Data, Jounal of Financial Research, 2000,12;263~300
[10] Greg Welch, An Introduction to the Kalman Filter,2003
[11] James R. Follain and Jan Ondrich(1997), Ruthless Prepayment? Evidence from Multifamily Mortgages, JOURNAL OF URBAN ECONOMICS 41, 78~101
[12] Jin-Chuan Duan,Jean-Guy Simonato, Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter, Review of Quantitative Finance and Accounting, 1999,13;111~135
[13] Joe Mattey and Nancy Wallace(1998), Housing Prices and the (In)stability of Mortgage Prepayment Models:Evidence from California,working paper
[14] Nakagawa and Shouda,Valution of Mortgage-backed Securities Based on Unobservable Prepayment Costs,2004,Math.Econ.6,123~147
[15] Kau and Slawson.JR(2002),Frictions,Heterogeneity and Optimality In Mortgage Modeling,Journal of Real Estate Finance and Economics,24(2);239~260
[16] Qiang Dai and Kenneth J. Singleton,Specification Analysis of Affine
[17] Term Structure Models, 2000,The Jounal Of Finance ,6(5);1943~1982
[18] Richard Stanton, Unobservable Heterogeneity and Rational Learning:Pool Specic vs. Generic Mortgage-Backed Security Prices. Estate Finance and Economics,1995,4;214-250
[19] Richard Stanton, Rational Prepayment and the Valuation of Mortgage-Backed Securities,Review of Financial Studies 8;677~708
[20] Ren-Raw Chen Louis Scott ,Pricing Interest Rate Options in a Two-Factor Cox-
[21] Ingersoll-Ross Model of the Term Structure,woking paper
[22] Sa-Aadu and Megbolugbe(1995),Heterogeneous Borrowers,Mortgage Selection,and Mortgage Pricing,Journal of Housing Research,6(2);333~356
[23] Schwartz and Torous,Prepayment and Valution of Mortgage-backed Securities,The Jounal of Finance,1989,44(2);375~392
[24] Takeaki Kariya,Fumikai Ushiyama,and Stanley R. Pliska(2002),A 3-factor Valuation Model for Mortgage-Backed Securities (MBS),working paper
[25] Takeaki Kariya and Masaaki Kobayashi, Pricing Mortgage Mortgage-Backed Securities (MBS)—A Model Describing the Burnout Effect ,Asia-Pacific Financial Markets, 2000,7;189-204
[26] Van Order(2000),Mortgage Terminations,Heterogenerty and The Exercise of Mortgage Options,Econometrica,68(2);275~307
[27] V. Digalakis, J. R. Rohlicek, Member, IEEE, and M. Ostendorf, Member, ML Estimation of a Stochastic Linear System with the EM Algorithm and Its Application to Speech Recognition,1995, IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING, VOL.1;236~250
[28] Xavier Gabaix,Arvind Krishnamurthy and Olivier Vigneron(2004), Limits of Arbitrage: Theory and Evidence from the Mortgage-Backed Securities Market,Jounal of Estate Finance and Economics,25(2);240~301
[29] 陈柏东,住房抵押贷款支撑证券定价方法研究,中南财经政法大学学报,2005,149(2);40~49
[30] 陈钊,住房抵押贷款提前还款行为分析,上海金融,2001,1;25~28
[31] 陈昆贤,不动产抵押权证券之评价研究-选择权调整利差法之应用:[硕士毕业论文],朝阳科技大学财务金融所,2002
[32] 陈颖,屠梅曾,国外住房抵押贷款支持证券定价理论的方法研究,中国房地产金融,2004,9;44~49
[33] 戴建国,黄培清,住房抵押贷款定价研究进展,管理工程学报,2001,15(1);72~75
[34] 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);120~125
[35] 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);122~127
[36] 范龙振, 张国庆,仿射模型、广义仿射模型与上交所利率期限结构, 管理工程学报,2005,19(3);97~102
[37] 范龙振,上交所利率期限结构的三因子广义高斯仿射模型,管理工程学报,2005,19(1);81~87
[38] 范龙振,广义仿射模型在上交所债券市场的实证分析,系统工程学报,2004,19(6);639~642
[39] 龚懿,吕晖蓉,吕昊炜,我国个人住房贷款风险因素分析,西南农业大学学报(社会科学版),2004,2(2);27~30
[40] 樊相如,窦晓飞,浅析我国住房抵押贷款中的提前还款风险,黑龙江社会科学,2002,1;33~35
[41] 陈为涛,程英春,对我国住房抵押贷款期前清偿的研究,哈尔滨商业大学学报(社会科学版),2005,2;53~56
[42] 路磊,非平稳时间序列的状态空间建模与预测,北京大学中国经济研究中心学刊,1999,10(4);1~10
[43] 邱淑暖,董家熊,序列抵押担保债券之结构与风险,运筹研究集刊,2002,12;139~162
[44] 唐亚光, 王维利,随机利率下提前还贷的数学模型及实证分析,纺织高校基础科学学报,17(1);60~64
[45] 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,2002,28(10);35~45
[46] 施方,住房抵押贷款中提前偿付行为的研究,国际金融研究,2001,9;10~16
[47] 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,2003,23(2);36~41
[48] 王建红,提前还款对抵押贷款及其支持证券定价的影响,中国房地产金融,2002,9;10~14
[49] 吴光长,金融资产证券化与资本市场之关联性-以台湾市场为例:[博士毕业论文],2005
[50] 宋晓春,对我国住房按揭贷款“提前还贷”现象的思考,重庆邮电学院学报(社会科学版),2004,3;51-54
[51] 宋福铁,卡尔曼滤波法模拟和预测沪市国债期限结构,2004
[52] 谢赤,吴雄伟,基于 Vasicek 和 CIR 模型中的中国货币市场利率行为实证分析,2002,10(2);23~27
[53] 袁桂秋, 丁正中,固定支付利率抵押贷款定价的一般原理,高校应用数学学报 A 辑,2004,19(3);353-362
[54] 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,系统工程理论与实践,2003,9;49-57
[55] 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,系统工程学报,2004,19(2);136~139
[56] 张美华,住宅抵押债权证券化之探讨-国内浮动利率贷款之评价:[博士毕业论文]国立中山大学财务管理研究所,2002
[57] 邹运,赵峰,黄继伟,国内市场 MBS 定价考,上海申银万国证券研究所报告,2005;
[58] 朱延功,崔平远,吴瑶华,参数估计中的系统初始状态确定,飞行力学,1997,15(3);36~42
[2] Archer,Ling and Mcgill,The effect of income and collateral constraints on residential mortgage terminations,Regional Science and Urban Economics;253~261
[3] Austin Kelly,Racial and Ethnic Disparities In Mortgage Prepayment,Jounal of Housing Economics,1994,4;350~372
[4] Chris Downing, Richard Stanton and Nancy Wallace, An Empirical Test of a Two-Factor Mortgage Prepayment and Valuation Model: How Much Do House Prices Matter, Journal of Theoretical and Applied Finance, 2002,20(5);456~520
[5] Deng,Quigley and Frank J. Fabozzi and Andrew Kalotay,Ginnie Mae and the Secondary Mortgage Market:an Integral Part of the American Economic Engine, Government Report; 2001,126~162
[6] Gonzalo Cortazar,Eduardo S. Schwartz and Lorenzo Naranjo, Term Structure Estimation in Low-Frequency Transaction Markets: A Kalman Filter Approach with Incomplete Panel-Data,working paper,2003
[7] Gourieroux and Scaillet(1996),Unemployment Insurance and Mortages,Insurance Mathematics and Economics,20;173-195
[8] Huarong Tang and Yihong Xia, An International Examination of Affine Term Structure Models and the Expectations Hypothesis,2005,working paper
[9] Michael .W. Brandt Ping He,Simulated Likelihood Estimation of Affine Term Structure Models from Panel Data, Jounal of Financial Research, 2000,12;263~300
[10] Greg Welch, An Introduction to the Kalman Filter,2003
[11] James R. Follain and Jan Ondrich(1997), Ruthless Prepayment? Evidence from Multifamily Mortgages, JOURNAL OF URBAN ECONOMICS 41, 78~101
[12] Jin-Chuan Duan,Jean-Guy Simonato, Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter, Review of Quantitative Finance and Accounting, 1999,13;111~135
[13] Joe Mattey and Nancy Wallace(1998), Housing Prices and the (In)stability of Mortgage Prepayment Models:Evidence from California,working paper
[14] Nakagawa and Shouda,Valution of Mortgage-backed Securities Based on Unobservable Prepayment Costs,2004,Math.Econ.6,123~147
[15] Kau and Slawson.JR(2002),Frictions,Heterogeneity and Optimality In Mortgage Modeling,Journal of Real Estate Finance and Economics,24(2);239~260
[16] Qiang Dai and Kenneth J. Singleton,Specification Analysis of Affine
[17] Term Structure Models, 2000,The Jounal Of Finance ,6(5);1943~1982
[18] Richard Stanton, Unobservable Heterogeneity and Rational Learning:Pool Specic vs. Generic Mortgage-Backed Security Prices. Estate Finance and Economics,1995,4;214-250
[19] Richard Stanton, Rational Prepayment and the Valuation of Mortgage-Backed Securities,Review of Financial Studies 8;677~708
[20] Ren-Raw Chen Louis Scott ,Pricing Interest Rate Options in a Two-Factor Cox-
[21] Ingersoll-Ross Model of the Term Structure,woking paper
[22] Sa-Aadu and Megbolugbe(1995),Heterogeneous Borrowers,Mortgage Selection,and Mortgage Pricing,Journal of Housing Research,6(2);333~356
[23] Schwartz and Torous,Prepayment and Valution of Mortgage-backed Securities,The Jounal of Finance,1989,44(2);375~392
[24] Takeaki Kariya,Fumikai Ushiyama,and Stanley R. Pliska(2002),A 3-factor Valuation Model for Mortgage-Backed Securities (MBS),working paper
[25] Takeaki Kariya and Masaaki Kobayashi, Pricing Mortgage Mortgage-Backed Securities (MBS)—A Model Describing the Burnout Effect ,Asia-Pacific Financial Markets, 2000,7;189-204
[26] Van Order(2000),Mortgage Terminations,Heterogenerty and The Exercise of Mortgage Options,Econometrica,68(2);275~307
[27] V. Digalakis, J. R. Rohlicek, Member, IEEE, and M. Ostendorf, Member, ML Estimation of a Stochastic Linear System with the EM Algorithm and Its Application to Speech Recognition,1995, IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING, VOL.1;236~250
[28] Xavier Gabaix,Arvind Krishnamurthy and Olivier Vigneron(2004), Limits of Arbitrage: Theory and Evidence from the Mortgage-Backed Securities Market,Jounal of Estate Finance and Economics,25(2);240~301
[29] 陈柏东,住房抵押贷款支撑证券定价方法研究,中南财经政法大学学报,2005,149(2);40~49
[30] 陈钊,住房抵押贷款提前还款行为分析,上海金融,2001,1;25~28
[31] 陈昆贤,不动产抵押权证券之评价研究-选择权调整利差法之应用:[硕士毕业论文],朝阳科技大学财务金融所,2002
[32] 陈颖,屠梅曾,国外住房抵押贷款支持证券定价理论的方法研究,中国房地产金融,2004,9;44~49
[33] 戴建国,黄培清,住房抵押贷款定价研究进展,管理工程学报,2001,15(1);72~75
[34] 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);120~125
[35] 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);122~127
[36] 范龙振, 张国庆,仿射模型、广义仿射模型与上交所利率期限结构, 管理工程学报,2005,19(3);97~102
[37] 范龙振,上交所利率期限结构的三因子广义高斯仿射模型,管理工程学报,2005,19(1);81~87
[38] 范龙振,广义仿射模型在上交所债券市场的实证分析,系统工程学报,2004,19(6);639~642
[39] 龚懿,吕晖蓉,吕昊炜,我国个人住房贷款风险因素分析,西南农业大学学报(社会科学版),2004,2(2);27~30
[40] 樊相如,窦晓飞,浅析我国住房抵押贷款中的提前还款风险,黑龙江社会科学,2002,1;33~35
[41] 陈为涛,程英春,对我国住房抵押贷款期前清偿的研究,哈尔滨商业大学学报(社会科学版),2005,2;53~56
[42] 路磊,非平稳时间序列的状态空间建模与预测,北京大学中国经济研究中心学刊,1999,10(4);1~10
[43] 邱淑暖,董家熊,序列抵押担保债券之结构与风险,运筹研究集刊,2002,12;139~162
[44] 唐亚光, 王维利,随机利率下提前还贷的数学模型及实证分析,纺织高校基础科学学报,17(1);60~64
[45] 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,2002,28(10);35~45
[46] 施方,住房抵押贷款中提前偿付行为的研究,国际金融研究,2001,9;10~16
[47] 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,2003,23(2);36~41
[48] 王建红,提前还款对抵押贷款及其支持证券定价的影响,中国房地产金融,2002,9;10~14
[49] 吴光长,金融资产证券化与资本市场之关联性-以台湾市场为例:[博士毕业论文],2005
[50] 宋晓春,对我国住房按揭贷款“提前还贷”现象的思考,重庆邮电学院学报(社会科学版),2004,3;51-54
[51] 宋福铁,卡尔曼滤波法模拟和预测沪市国债期限结构,2004
[52] 谢赤,吴雄伟,基于 Vasicek 和 CIR 模型中的中国货币市场利率行为实证分析,2002,10(2);23~27
[53] 袁桂秋, 丁正中,固定支付利率抵押贷款定价的一般原理,高校应用数学学报 A 辑,2004,19(3);353-362
[54] 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,系统工程理论与实践,2003,9;49-57
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