住房反向抵押贷款的定价研究
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摘要
本文在采集数据的基础上研究了2004年以来南京市平均房价与南京市地区生产总值、城镇居民人均可支配收入和南京市平均地价之间的关系;给出了根据房价、地区生产总值、城镇居民人均可支配收入和地价等历史数据预测未来房价的数据处理方法;并在此基础上建立了住房反向抵押贷款的定价模型,根据贷款结束后借款人或其继承人是否可以将房屋抵押权赎回分为两类,一种是不可赎回产品,一种是可赎回产品。针对不可赎回产品,根据精算学原理进行定价;对于可赎回产品,根据期权定价原理进行定价,并分别给出了定价表达式;最后给出一个实例,模拟江宁区一位老人办理住房反向抵押贷款,详细介绍了定价过程,给出定价结果,并对两种产品的定价结果进行比较。比较发现,可赎回产品对应的年金额略少于不可赎回产品,这正是借款人为取得“可赎回”的权利而付出的期权费。
This article investigates the cointegration relation among Price of House, Gross Domestic Product, Disposal Personal Income and Price of the Ground. We propose a data processing method to forecast the future house value. Consequently, we build two pricing models for the house reverse mortgage. One uses the actuarial theory for irredeemable mortgage that the borrower can not redeem the house when the mortgage ends; the another uses the option pricing theory for redeemable mortgage that the borrower can redeem the house after paying off the principal and interest. In the end, an empirical application is discussed. We compare the two different pricing results of two pricing models which show the annuity of the redeemable mortgage is less than irredeemable mortgage and the margin between the two pricing results is option charge.
This article investigates the cointegration relation among Price of House, Gross Domestic Product, Disposal Personal Income and Price of the Ground. We propose a data processing method to forecast the future house value. Consequently, we build two pricing models for the house reverse mortgage. One uses the actuarial theory for irredeemable mortgage that the borrower can not redeem the house when the mortgage ends; the another uses the option pricing theory for redeemable mortgage that the borrower can redeem the house after paying off the principal and interest. In the end, an empirical application is discussed. We compare the two different pricing results of two pricing models which show the annuity of the redeemable mortgage is less than irredeemable mortgage and the margin between the two pricing results is option charge.
引文
1.Akgun A,P.Vanini,The Pricing of Index-Linked Mortgages:Technical Documentation,Working Paper,Zurich Cantonal Bank,Switzerland,2006.
2.阿曼(Ammann,M.,瑞士)著,杨玉明译。信用风险评估-方法、模型、应用.第二版.-北京:清华大学出版社,2004.10.
3.布里斯(Briys,E.)等著,史树中等译。期权、期货和特种衍生证券.北京:机械工业出版社,2002.3.
4.包林海,住房逆抵押贷款研究。北京,中国人民大学,2005.
5.T.P.Boehm,M.C.Ehrhardt,Reverse Mortgage and Interest Rate Risk,Journal of the American Real Estate and Urban Economics Association,1994.V22,2:387-408.
6.A.Caplin,W.Goetzmann et al.,Home Equity Insurance:A Pilot Project,
7.常玲,反向抵押贷款在我国的应用研究,辽宁大学硕士论文,2006.
8.D.Cossin.H.Piroote,高级信用风险分析,机械工业出版社,2005.
9.K.Cuthbertson.D.Nitzsche,金融工程,中国人民大学出版社,2004.
10.慈向阳,宣国良.房价上涨的因素及风险研究.价格理论与实践,2005年第3期,23-24
11.丁珊,房地产价格波动与宏观经济指标关系的实证研究.中国物价,2007年7月,48-51.
12.段岩燕,曹振良.调控房地产价格的关键-土地和金融.当代经济,2005年第2期,57-59
13.Elizalde,A.Credit Risk Models Ⅱ:Structural Models,preprint,September 2003.
14.Fons,J.S.Using Default Rates to Model the Term Structure of Credit Risk,Financial Analysts Journal.1994.
15.范子文,以房养老.中国金融出版社,2006年.
16.Geske,R.The Valuation of Corporate Liabilities as Compound Options,Journal of Financial and Quantitative Analysis,1977,541-552.
17.Giesecke,K.Credit Risk Modeling and Valuation:An Introduction Credit Risk:Models and Management.Vol.2,Riskbooks.London.2004.
18.杲新利,张建坤,反向抵押贷款风险研究,基建优化,2007年8月,第28卷第四期,47-49.
19.古扎拉蒂(美)著,费剑平,孙春霞等译.计量经济学基础.第4版.北京:中国人民大学出版社,2004.
20.华伟,房地产金融学,复旦大学出版社,2004.
21.J.C.Hull,期货期权入门,中国人民大学出版社,
22.Jarrow,R.A.,Lando,A.& Turnbull,S.A Markov model of the term structure of credit risk spreads.Review of Financial Studies,1997,10(2),481-523
23.Jarrow,R.A.& Turnbull,S.Pricing Derivatives on Financial Securities Subject to Credit Risk.Journal of Finance,1998,50,53-86.
24.经朝明,谈有花,中国房地产价格与通货膨胀的关系--基于计量模型的实证分析,中国物价,2006.02,p55-57.
25.蒋立红,李庆花.影响房价的区位因素分析.城市开发,2005年4月,79-81
26.姜礼尚,期权定价的数学模型和方法,高等教育出版社,2003.
27.Johannes,M.& Poison.MCMC Methods for Financial Econometrics.Working Paper.Columbia University,2002.
28.Jones,E.P.,Scott,P.M.& Rosenfeld,E.Contingent Claim Analysis of Corporate Capital Structures:An Empirical Investigation,Journal of Finance,1984,Vol.39,No.3,611-625.
29.P.Jorion,风险价值VAR,中信出版社,2005.
30.P.Jorion,金融风险管理师手册,中国人民大学出版社,2004.
31.Kau,J.B.& Keenan D.C.An Overview of the Option-Theoretic Pricing of Mortgages.Journal of Housing Research,1995,6(2),217-244.
32.Kau,J.B.& Keenan D.C.Reduced-Form Mortgage Valuation.Federal National Mortgage Association(Fannie Mae)August 25,2004.
33.Kim,I.J.,Ramaswamy,K.& Sundaresan,S.M.Valuation of Corporate Fixed-Income Securities,Financial Management,Autumn1993,117-131.
34.KMV Corporation.Modeling Default Risk.Sao Francisco,1993a.
35.KMV Corporation.Modeling Default Risk.Sao Francisco,1993a.
36.KMV Corporation.Portfolio Management of Default Risk,Sao Francisco,1993b.
37.Lando & David.On Cox Processes and Credit Risky Securities,Review of Derivatives Research,1998,2,99-120.
38.郎咸平,整合,东方出版社,2006.
39.Longstaff,F.A.& Schwartz,E.S.A Simple Approach to Valuing Risky Fixed and Floating Rate Debt,Journal of Finance,1995,50(3),789-819.
40.刘光耀,国外反向抵押贷款经验及对我国的借鉴,南开大学硕士论文,2005.
41.李咏涛,汪开诚,提问万科,辽宁教育出版社,2005.
42.刘洪玉,沈悦.房地产价格变化规律的经济学分析.建筑经济,2004年9月,43-47.
43.卢金北,刘立秋.基于交易的房地产定价模型研究.沈阳理工大学学报,2005年9月,第24卷第3期,87-90.
44.陆家骝,现代金融经济学.大连:东北财经大学出版社,2004.1.
45.Madan,D.& Unal,H.Pricing the Risks of Default.Review of Derivatives Research 2,1998,121-160.
46.Margrabe,W.The Value of an Option to Exchange One Asset for Another,Journal of Finance,1978,33,March,177-87.
47.B.J.McGill,C.Todd McCormick IV,Home Equity Protection Contracts and Method For Trading Them,United States,Patent Application Publication US 2006/0080228A1 2006.
48.Merton,R.C.On the Pricing of Corporate Debt:The Risk Structure of Interest Rates.Journal of Finance,1974,29,449-470.
49.默顿(美)著,郭多祚等译.连续时间金融.修订本.北京:中国人民大学出版社,2005.
50.马思新,李昂.基于Hedonic模型的北京住宅价格影响因素分析.土木工程学报,2003年第9期,59-64.
51.B.J.Nalebuff,A.Caplin,Home Equity Insurance Financial Product,United States,Patent Application Publication US 2003/0110122 A1 2003.
52.M.Neukirchen,H.Lange,House Price Risk-Some Risk Management Strategies,Universitas 21 Global,Working Paper,No.013,2005.
53.彭新育,吴甫成.土地价格和享乐评价方法.经济地理,第18卷第3期,14-19.
54.任纪军,房地产投资基金,经济管理出版社,2006.
55.沈悦,刘洪玉.房地产价格与宏观经济指标关系的研究.价格理论与实践,2002年第8期,20-22.
56.R.J.Shiller,A.N.Weiss,Moral Hazard in Home Equity Conversion,ARRUEA-ASSA session,January 1998.
57.R.J.Shiller,A.N.Weiss,Home Equity Insurance,Journal of Real Estate Finance and Economics,19:1,1999,21-47.
58.R.J.Shiller,金融新秩序,中国人民大学出版社,2004.
59.R.J.Shiller,宏观市场,上海财经大学出版社,2002.
60.史树中,金融经济学十讲,上海人民出版社,2004.
61.时筠仑,雷星晖,苏涛永.房价波动与影响因素分析.价格理论与实践,2005年第4期.
62.J.Stampfli,V.Goodman,金融数学,机械工业出版社,2004.
63.J.Syz,P.Vanini,M.Salvi,Property Derivatives and Index-Linked Mortgages,Zurich.
64.唐勇,刘峰涛.金融市场波动测量方法新进展.华南农业大学学报,2005年第1期,48-53.
65.屠佳华,张洁.什么推动了房价的上涨:来自上海房地产市场的证据.世界经济,2005年第5期,28-37.
66.王立宾.住房特征价格指数编制方法与实证分析.数量经济技术经济研究,1999年第7期,37-40.
67.王振龙,时间序列分析,中国统计出版社,
68.温海珍,城市住宅的特征价格:理论与实证研究.北京:经济科学出版社,2005.4
69.吴红华,房地产价格影响因素分析.温州大学学报,2001年第3期,22-25
70.奚俊芳,反向抵押贷款定价模型研究,华东师范大学硕士论文,2007.
71.叶中行,林建忠,数理金融-资产定价与金融决策理论,科学出版社,2000.
72.殷国新,周为吉,朱传保.关于房地产价格随机波动与评估、抵押风险的研究.产业研究,2003年第3期,31-33.
73.张东航,基准地价与土地权利-以住宅用地为例.中国土地科学,1993年9月,第11卷第2期,24-29.
74.张红,李文诞.北京商品住宅价格变动实证分析.中国房地产金融,2001年第3期,3-7.
75.张晶,我国寿险公司推展反向抵押贷款之研究,浙江大学硕士论文,2005.
76.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
77.C-S.Zhou,A jump-diffusion approach to modeling credit risk and valuing defaultable securities Federal Reserve Board,working paper,1997.
78.Zhou,C.The Term Structure of Credit Spreads with Jump Risk,Journal of Banking and Finance,2001,25,2015-40.
79.中国指数研究院,中国房地产指数系统理论与研究,经济管理出版社,2005.
80.邹小凡,张晶,寿险公司提供反向抵押贷款的精算问题研究,技术经济与管理研究,2006年第二期,45-46.
2.阿曼(Ammann,M.,瑞士)著,杨玉明译。信用风险评估-方法、模型、应用.第二版.-北京:清华大学出版社,2004.10.
3.布里斯(Briys,E.)等著,史树中等译。期权、期货和特种衍生证券.北京:机械工业出版社,2002.3.
4.包林海,住房逆抵押贷款研究。北京,中国人民大学,2005.
5.T.P.Boehm,M.C.Ehrhardt,Reverse Mortgage and Interest Rate Risk,Journal of the American Real Estate and Urban Economics Association,1994.V22,2:387-408.
6.A.Caplin,W.Goetzmann et al.,Home Equity Insurance:A Pilot Project,
7.常玲,反向抵押贷款在我国的应用研究,辽宁大学硕士论文,2006.
8.D.Cossin.H.Piroote,高级信用风险分析,机械工业出版社,2005.
9.K.Cuthbertson.D.Nitzsche,金融工程,中国人民大学出版社,2004.
10.慈向阳,宣国良.房价上涨的因素及风险研究.价格理论与实践,2005年第3期,23-24
11.丁珊,房地产价格波动与宏观经济指标关系的实证研究.中国物价,2007年7月,48-51.
12.段岩燕,曹振良.调控房地产价格的关键-土地和金融.当代经济,2005年第2期,57-59
13.Elizalde,A.Credit Risk Models Ⅱ:Structural Models,preprint,September 2003.
14.Fons,J.S.Using Default Rates to Model the Term Structure of Credit Risk,Financial Analysts Journal.1994.
15.范子文,以房养老.中国金融出版社,2006年.
16.Geske,R.The Valuation of Corporate Liabilities as Compound Options,Journal of Financial and Quantitative Analysis,1977,541-552.
17.Giesecke,K.Credit Risk Modeling and Valuation:An Introduction Credit Risk:Models and Management.Vol.2,Riskbooks.London.2004.
18.杲新利,张建坤,反向抵押贷款风险研究,基建优化,2007年8月,第28卷第四期,47-49.
19.古扎拉蒂(美)著,费剑平,孙春霞等译.计量经济学基础.第4版.北京:中国人民大学出版社,2004.
20.华伟,房地产金融学,复旦大学出版社,2004.
21.J.C.Hull,期货期权入门,中国人民大学出版社,
22.Jarrow,R.A.,Lando,A.& Turnbull,S.A Markov model of the term structure of credit risk spreads.Review of Financial Studies,1997,10(2),481-523
23.Jarrow,R.A.& Turnbull,S.Pricing Derivatives on Financial Securities Subject to Credit Risk.Journal of Finance,1998,50,53-86.
24.经朝明,谈有花,中国房地产价格与通货膨胀的关系--基于计量模型的实证分析,中国物价,2006.02,p55-57.
25.蒋立红,李庆花.影响房价的区位因素分析.城市开发,2005年4月,79-81
26.姜礼尚,期权定价的数学模型和方法,高等教育出版社,2003.
27.Johannes,M.& Poison.MCMC Methods for Financial Econometrics.Working Paper.Columbia University,2002.
28.Jones,E.P.,Scott,P.M.& Rosenfeld,E.Contingent Claim Analysis of Corporate Capital Structures:An Empirical Investigation,Journal of Finance,1984,Vol.39,No.3,611-625.
29.P.Jorion,风险价值VAR,中信出版社,2005.
30.P.Jorion,金融风险管理师手册,中国人民大学出版社,2004.
31.Kau,J.B.& Keenan D.C.An Overview of the Option-Theoretic Pricing of Mortgages.Journal of Housing Research,1995,6(2),217-244.
32.Kau,J.B.& Keenan D.C.Reduced-Form Mortgage Valuation.Federal National Mortgage Association(Fannie Mae)August 25,2004.
33.Kim,I.J.,Ramaswamy,K.& Sundaresan,S.M.Valuation of Corporate Fixed-Income Securities,Financial Management,Autumn1993,117-131.
34.KMV Corporation.Modeling Default Risk.Sao Francisco,1993a.
35.KMV Corporation.Modeling Default Risk.Sao Francisco,1993a.
36.KMV Corporation.Portfolio Management of Default Risk,Sao Francisco,1993b.
37.Lando & David.On Cox Processes and Credit Risky Securities,Review of Derivatives Research,1998,2,99-120.
38.郎咸平,整合,东方出版社,2006.
39.Longstaff,F.A.& Schwartz,E.S.A Simple Approach to Valuing Risky Fixed and Floating Rate Debt,Journal of Finance,1995,50(3),789-819.
40.刘光耀,国外反向抵押贷款经验及对我国的借鉴,南开大学硕士论文,2005.
41.李咏涛,汪开诚,提问万科,辽宁教育出版社,2005.
42.刘洪玉,沈悦.房地产价格变化规律的经济学分析.建筑经济,2004年9月,43-47.
43.卢金北,刘立秋.基于交易的房地产定价模型研究.沈阳理工大学学报,2005年9月,第24卷第3期,87-90.
44.陆家骝,现代金融经济学.大连:东北财经大学出版社,2004.1.
45.Madan,D.& Unal,H.Pricing the Risks of Default.Review of Derivatives Research 2,1998,121-160.
46.Margrabe,W.The Value of an Option to Exchange One Asset for Another,Journal of Finance,1978,33,March,177-87.
47.B.J.McGill,C.Todd McCormick IV,Home Equity Protection Contracts and Method For Trading Them,United States,Patent Application Publication US 2006/0080228A1 2006.
48.Merton,R.C.On the Pricing of Corporate Debt:The Risk Structure of Interest Rates.Journal of Finance,1974,29,449-470.
49.默顿(美)著,郭多祚等译.连续时间金融.修订本.北京:中国人民大学出版社,2005.
50.马思新,李昂.基于Hedonic模型的北京住宅价格影响因素分析.土木工程学报,2003年第9期,59-64.
51.B.J.Nalebuff,A.Caplin,Home Equity Insurance Financial Product,United States,Patent Application Publication US 2003/0110122 A1 2003.
52.M.Neukirchen,H.Lange,House Price Risk-Some Risk Management Strategies,Universitas 21 Global,Working Paper,No.013,2005.
53.彭新育,吴甫成.土地价格和享乐评价方法.经济地理,第18卷第3期,14-19.
54.任纪军,房地产投资基金,经济管理出版社,2006.
55.沈悦,刘洪玉.房地产价格与宏观经济指标关系的研究.价格理论与实践,2002年第8期,20-22.
56.R.J.Shiller,A.N.Weiss,Moral Hazard in Home Equity Conversion,ARRUEA-ASSA session,January 1998.
57.R.J.Shiller,A.N.Weiss,Home Equity Insurance,Journal of Real Estate Finance and Economics,19:1,1999,21-47.
58.R.J.Shiller,金融新秩序,中国人民大学出版社,2004.
59.R.J.Shiller,宏观市场,上海财经大学出版社,2002.
60.史树中,金融经济学十讲,上海人民出版社,2004.
61.时筠仑,雷星晖,苏涛永.房价波动与影响因素分析.价格理论与实践,2005年第4期.
62.J.Stampfli,V.Goodman,金融数学,机械工业出版社,2004.
63.J.Syz,P.Vanini,M.Salvi,Property Derivatives and Index-Linked Mortgages,Zurich.
64.唐勇,刘峰涛.金融市场波动测量方法新进展.华南农业大学学报,2005年第1期,48-53.
65.屠佳华,张洁.什么推动了房价的上涨:来自上海房地产市场的证据.世界经济,2005年第5期,28-37.
66.王立宾.住房特征价格指数编制方法与实证分析.数量经济技术经济研究,1999年第7期,37-40.
67.王振龙,时间序列分析,中国统计出版社,
68.温海珍,城市住宅的特征价格:理论与实证研究.北京:经济科学出版社,2005.4
69.吴红华,房地产价格影响因素分析.温州大学学报,2001年第3期,22-25
70.奚俊芳,反向抵押贷款定价模型研究,华东师范大学硕士论文,2007.
71.叶中行,林建忠,数理金融-资产定价与金融决策理论,科学出版社,2000.
72.殷国新,周为吉,朱传保.关于房地产价格随机波动与评估、抵押风险的研究.产业研究,2003年第3期,31-33.
73.张东航,基准地价与土地权利-以住宅用地为例.中国土地科学,1993年9月,第11卷第2期,24-29.
74.张红,李文诞.北京商品住宅价格变动实证分析.中国房地产金融,2001年第3期,3-7.
75.张晶,我国寿险公司推展反向抵押贷款之研究,浙江大学硕士论文,2005.
76.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
77.C-S.Zhou,A jump-diffusion approach to modeling credit risk and valuing defaultable securities Federal Reserve Board,working paper,1997.
78.Zhou,C.The Term Structure of Credit Spreads with Jump Risk,Journal of Banking and Finance,2001,25,2015-40.
79.中国指数研究院,中国房地产指数系统理论与研究,经济管理出版社,2005.
80.邹小凡,张晶,寿险公司提供反向抵押贷款的精算问题研究,技术经济与管理研究,2006年第二期,45-46.