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| Title: | 逆向抵押貸款的隨機規劃模型及其在台灣的應用
A Stochastic Programming Model for Reverse Mortgage with an Application in Taiwan |
| Authors: | 曾郁婷
Tseng, Yu Ting |
| Contributors: | 劉明郎
Liu, Ming Long
曾郁婷
Tseng, Yu Ting |
| Keywords: | 逆向抵押貸款
逆向房地產抵押貸款
Lee-Carter 模型
CIR-SR 模型
幾何布朗運動
死亡率
利率
房價
reverse mortgage
home equity conversion mortgage
Lee-Carter model
CIR-SR model
mortality
interest rate
house price |
| Date: | 2014 |
| Issue Date: | 2015-06-01 11:04:30 (UTC+8) |
| Abstract: | 正如同許多國家正面臨人口老化所產生的種種問題，台灣社會不可避免也面臨相同困境。加上台灣政府退休金的短缺也是一個嚴酷的社會議題，為了使老年人口能夠避免上述之經濟問題，逆向抵押貸款的產品因而引進台灣。本論文主要目的是尋找且計算逆向抵押貸款在台灣應用時的公正定價。在定價模型中最重要的三個因素分別是死亡率、利率與房價。論文中分別使用Lee-Carter模型、CIR-SR 模型與幾何布朗運動來描述並預測死亡率、利率與房價。最後，我們設定不同的情境將美國逆向房地產抵押貸款(HECM)的定價模型應用在台灣的資料上，找出最可能適合台灣的最佳定價。
Many nations in the world are facing the problems caused by aging society. In Taiwan, one of the urgent issues is the shortage of pension fund. In order to prevent elderlies from economic impact, reverse mortgage (RM) programs had been brought into Taiwan. The aim of this thesis is to find a fair price for RM in Taiwan. The
pricing model involves three factors, which are, mortality, interest rates, and house prices. We use Lee-Carter model (1992), CIR-SR model (1985), and GBM model to forecast mortality, interest rates, and house prices respectively. Finally, we use the home equity conversion mortgage (HECM) program from the US as our basic model and apply statistics in Taiwan under different scenarios to find the best price that may be used in Taiwan.
謝辭 ................................................. iv
Abstract .............................................. v
摘要 ................................................. vi
Contents ............................................ vii
List of Tables ....................................... ix
List of Figures ....................................... x
Chapter 1 Introduction ................................ 1
1.1 Motivation of Research ............................ 1
1.2 Purpose and Structure of Research ................. 2
Chapter 2 Literature Review ........................... 3
2.1 Reverse Mortgage Overview ......................... 3
2.2 The Potential of RM in Taiwan ..................... 7
Chapter 3 Research Models ............................ 11
3.1 Mortality Models ................................. 11
3.2 Interest Rate Models ............................. 13
3.3 House Price Models ............................... 14
3.4 The Pricing Model ................................ 15
3.5 The Mortgage Insurance Premium (MIP) ............. 15
Chapter 4 Empirical Analysis ......................... 17
4.1 Mortality Results ................................ 17
4.2 Interest Rates ................................... 18
4.3 House Prices ..................................... 20
4.4 The NRP and the Pricing .......................... 22
4.5 The MIP Results .................................. 25
Chapter 5 Sensitivity Analysis ....................... 27
5.1 The Effects of Interest Rates .................... 27
5.2 The Effects of House Prices ...................... 32
5.3 Modifying the MIP Function ....................... 36
Chapter 6 Discussion ................................. 40
6.1 The Trial Project of RM in Taipei ................ 40
6.2 A Possible Fair Price ............................ 42
6.3 Weaknesses and Improvements ...................... 42
Chapter 7 Conclusion ................................. 45
References ........................................... 47 |
| Reference: | Capinski, M. and Zastawniak, T., 2011, Mathematics for finance: An introduction to financial engineering, 2nd ed., Springer-Verlag London.
Central Bank of the Republic of China (Taiwan), 2015, 五大銀行存放款利率歷史資料, available online at: http://www.cbc.gov.tw/mp1.html
Chan, K. C., Karolyi G. A., Longstaff, F. A., and Sanders, A. B., 1992, An empirical comparison of alternative models of the short-term interest rate, The Journal of Finance 47(3), 1209-1227.
Chen, H., Cox, S. H., and Wang, S. S., 2010, Is the home equity conversion mortgage in the United States sustainable? Evidence from pricing mortgage insurance
premiums and non-recourse provisions using the conditional Esscher transform, Insurance: Mathematics and Economics 46, 371-384.
Chen, Y. A. (陳昱安), 2009, 台灣反向房屋抵押貸款之可貸年金金額與存續期間之分析，國立政治大學風險管理與保險學系碩士論文。
Department of Social Welfare, Taipei City Government, 2015, 台北市公益型以房養老實驗方案, available online at: http://rmsc.ippi.org.tw/index.html
Hancock, R., 1998, Can housing wealth alleviate poverty among Britain’s older population? Fiscal Studies 19(3), 249-272.
Lee, R. D. and Carter, L. R., 1992, Modeling and forecasting U.S. mortality, Journal of the American Statistical Association 87(419), 659-671.
Li, J. S-H., Hardy, M. R. and Tan, K. S., 2010, On pricing and hedging the nonegative-equity guarantee in equity release mechanisms, Journal of Risk and
Insurance 77(2), 499-522.
Lien, C-H. (連春紅), Liao, S-L. (廖四郎), Lee, C-F. (李政峰), 2005, 估計與比較連續時間利率模型—台灣商業本票之實證分析，管理評論24(1)：29–53。
Mayer, C. J. and Simons, K. V., 1994, Reverse mortgages and the liquidity of housing wealth, Journal of American Real Estate Urban Economics Association 22(2), 235-255.
Ministry of Interior, 2005a, 老人居住安排與長期照顧選擇之探討, available online at: http://www.moi.gov.tw/stat/
Ministry of Interior, 2005b, 民國94 年老人狀況調查結果摘要分析, available online at: http://www.moi.gov.tw/stat/
Ministry of Interior, 2014, 簡易生命表及平均餘命查詢, available online at: http://sowf.moi.gov.tw/stat/Life/List.html
Ministry of Interior, 2015, 住宅價格—買賣契約平均單價, available online at: http://pip.moi.gov.tw/
Ong, R., 2008, Unlocking housing equity through reverse mortgages: The case of elderly homeowners in Australia, European Journal of Housing Policy 8(1), 61-79.
Phillips, W. A. and Gwin, S. B., 1992, Reverse mortgages, Transactions of Society of Actuaries 44, 289-323.
Wang, J. L., Hsieh, M-H., and Chiu, Y-F., 2011, Using reverse mortgages to hedge longevity and financial risks for life insurers: a generalized immunization approach, The Geneva Papers 36, 697-717.
Weng, H. M. (翁宏明) and Zeng, Y. X. (曾奕翔), 2010, Lee-Carter 估計模式與台灣地區死亡率推估之研究，大同技術學院學報18：53–70。
Zheng, Y. R. (鄭堯任) and Sun, Z. L. (孫彰良), 2010, 「以房養老」活躍老化，社區發展季刊132：106–122。 |
| Description: | 碩士
國立政治大學
應用數學研究所
101751013
103 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0101751013 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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