評價連生年金型式之反向抵押貸款: 關聯結構法

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姓名

李家宏(Chia-hung Li) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

評價連生年金型式之反向抵押貸款: 關聯結構法
(Pricing Joint-live Reverse Mortgage Using Copula Approach)

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摘要(中)

隨著低死亡率及低生育率的影響且伴隨著人口老化的問題，在台灣退休準備金不足已是個嚴重且急迫的議題，加上台灣老年人口的高自有住宅率，反向抵押房屋貸款可視為除了國民年金、企業退休金、個人儲蓄等傳統退休金來源之外，另一項新的退休金來源。本篇研究主要去建立一個考慮配偶間死亡率相關的連生反向抵押房屋貸款評價模型，文中使用Lee-Carter模型配適真實死亡率資料，利用關聯結構(Copula)計算各年齡配偶間的聯合存活機率，再經由自我回歸整合移動平均(ARIMA)模型配適信義房價指數，接下來利用蒙地卡羅模擬、Wang轉換和條件Esscher轉換去評價無追索權的連生反向抵押房屋貸款的價值，本研究發現若忽略死亡率具相關性會導致商品價值被低估。

摘要(英)

Because of low mortality rates and decreased fertility, as well as the subsequent increased aging problem, insufficient pensions have become a serious issue in Taiwan. Besides, the high home ownership rate for elders in Taiwan is the other reason that regard reverse mortgage as a new resource option for retirement except for tradition resources, such as public and private pensions, commercial annuities, individual savings and investments. The purpose of this paper is build a modeling and pricing framework, which consider the correlation between spouses’ mortality, to assess a suitable value of reverse mortgage. We propose Lee-Carter model to fit the actually mortality data, use copula approach to measure the joint survival probability at each age and model the house price index via ARIMA process. We employ the conditional Esscher transform to price the non-recourse provision of joint-live reverse mortgages by using Monte Carlo simulation with Antithetic variance reduction.

關鍵字(中)

★ 自我回歸整合移動平均過程
★ 關聯結構
★ Lee-Carter模型
★ 條件Esscher轉換
★ 反向抵押房屋貸款
★ 蒙地卡羅模擬

關鍵字(英)

★ Lee-Carter model
★ ARIMA process
★ Copula
★ Conditional Esscher transform
★ Monte Carlo simulation
★ Reverse mortgage

論文目次

摘要 ............................................................................................................... I
Abstract ......................................................................................................... II
Acknowledgement ....................................................................................... III
Contents ......................................................................................................... V
List of Tables ................................................................................................ VI
List of Figures ............................................................................................. VII
1. Introduction ................................................................................................ 1
1.1 Background ......................................................................................... 1
1.2 Mortality Literature ............................................................................. 3
1.3 Purpose of this Study ........................................................................... 4
2. Reverse mortgage ....................................................................................... 4
2.1 HECM Program .................................................................................. 4
2.2 HECM pricing Formula ....................................................................... 6
2.3 Risk for Reverse Mortgage .................................................................. 7
3. Modeling the Longevity Risk ..................................................................... 8
3.1 Lee-Carter Model ................................................................................ 8
3.2 Fitting the Lee-Carter model ............................................................. 10
3.3 Mortality Projections ......................................................................... 11
4. Joint-live Mortality................................................................................... 13
4.1 Independent Joint-live Mortality........................................................ 13
4.2 Correlated Joint-live Mortality .......................................................... 15
4.3 Coupla Function ................................................................................ 16
4.4 Probability Comparison ..................................................................... 18
5. Modeling the House Price Depreciation Risk .......................................... 20
5.1 Modeling Dynamics Process ............................................................. 20
5.2 Fitting ARIMA Process ..................................................................... 22
6. Pricing Framework for Reverse Mortgage ............................................. 26
6.1 Pricing Formula for HECM Program ................................................. 26
6.2 Conditional Esscher Transform ......................................................... 28
7. Numerical Analysis ................................................................................... 32
8. Conclusion ................................................................................................ 35
Appendix A: .................................................................................................. 36
Appendix B: .................................................................................................. 39
References ..................................................................................................... 43

參考文獻

[1]. Booth, H., Maindonald, J. & Smith, L. (2001). Age-time interactions in mortality projection: applying Lee-Carter to Australia. Working Papers in Degraphy,85.
[2]. Brouhns, N., Denuit, M. & Vermunt, J.K. (2002). A Poisson log-bilinear regression approach to the construction of projected life-tables. Insurance: Mathematics and Economics, 31,373-393.
[3]. Buhlmann, H., Delbaen, F., Embrechts, P. & Shiryaev, A. (1996). No-arbitrage, change of measure and conditional Esscher transforms. CWI quarterly, 9(4), 291-317.
[4]. Case, K. & Shiller, R. (1989). The Efficiency of the Market for Single-Family Homes. American Economic Review, 79(1), 125-137.
[5]. Cairns, A., Blake, D., Dowd, K., Coughlan, G., Epstein, D. & Campus, J, (2007). A quantitative comparison of stochastic mortality models using data from England & Wales and the United States. Pensions Institute Discussion Paper PI-0701.
[6]. Cairns, A., Blake, D., Dowd, K., Coughlan, G., Epstein, D., & Campus, J. (2008a). Mortality density forecasts: An analysis of six stochastic mortality models. Pensions Institute Discussion Paper PI-0801.
[7]. Chen, H., Cox, S., & Wang, 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(2), 371-384.
[8]. Chen, L. & Lee W. (1998). On the Dynamic Relations Among Housing Prices, Stock Prices and Interest Rate, Evidence in Taiwan–Simultaneous Equations Model and Vector Autoregression Model. Journal of Financial Studies , 5 (4), 51-71.
[9]. Cheng, Y. (2008). The Application of Reverse Mortgages in Aging Society. Journal of Risk Management , 10(3), 293-314.
[10]. Chia, N. & Tsui, A. (2004). Reverse mortgages as retirement financing instrument: an option for “Asset-rich and cash-poor” Singaporeans. Department of Economics National University of Singapore.
[11]. Cox, J., Ingersoll Jr, J., & Ross, S. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385-407.
[12]. Crawford, G.W. & Fratantoni, M.C. (2003). Assessing the Forecasting Performance of Regime-Switching, ARIMA and GARCH Models of House Prices. Real Estate Economics, 31(2),223-243.
[13]. Duan, J.C., (1995). The GARCH Option Pricing Model. Mathematical Finance ,5,13-32.
[14]. Duan, J.C. & Pliska S. (2004). Option Valuation with Co-Integrated Asset Prices. Journal of Economic Dynamics and Control, 28, 727-754.
[15]. Dowd, K., Cairns, A., Blake, D., Coughlan, G., Epstein, D., & Campus, J. (2008b). Evaluating the Goodness of Fit of Stochastic Mortality Models. Pensions Institute Discussion Paper PI-0802.
[16]. Esscher, F. (1932). On the Probability Function in the Collective Theory of Risk. Skandinavisk Aktuarietidskrift, 15, 175-195.
[17]. Gompertz, B.(1825). On the native of the function expressive of the law of human mortality and on the new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society London, 115, 513-585.
[18]. Gerber, H. & Shiu, E. (1994). Option pricing by Esscher transforms. Transactions of the Society of Actuaries, 46, 99-191.
[19]. Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting the time series of U.S. mortality. Journal of the American Statistical Association, 87, 659-671.
[20]. Lee, R.D. (2000). The Lee-Carter method of forecasting mortality, with various extensions applications. North American Actuarial Journal, 4(1), 80-93.
[21]. Luciano, E. Spreeuw, J. & Vigna, E., (2007). Modelling stochastic mortality for dependent lives. CeRP Working Paper.
[22]. Ma, S., Kim, G. and Lew, K. (2007). Estimating Reverse Mortgage Insurer’s Risk Using Stochastic Models. Conference of Asia-Pacific Risk and Insurance Association in Taipei.
[23]. Pitacco, E. (2004). Survival models in a dynamic context: a survey. Insurance: Mathematics and Economics, 35, 279-298.
[24]. Renshaw, A.E., & Haberman, S. 2003.Lee-Carter mortality forecasting with age specific Enhancement. Insurance: Mathematics and Economics, 33, 255-272.
[25]. Shemyakin A. & Youn, H. (1999). Statistical aspects of joint-life insurance pricing. Proceedings of American Statistical Association, 34-38.
[26]. Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris, 8, 229–231.
[27]. Trivedi, P.K. & Zimmer, D.M. (2007). Copula Modeling: An Introduction for Practitioners. Foundations and Trends in Econometrics, 1(1), 1-111.
[28]. Tsay, R. (2005). Analysis of Financial Time Series (2nd ed.). Hoboken, New Jersey, John Wiley & Sons, Inc.
[29]. Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of financial economics, 5(2), 177-188.
[30]. Wang, S. (2000). A Class of Distortion Operators for Pricing Financial and Insurance Risks. Journal of Risk and Insurance, 67(1), 15-36.
[31]. Zhou, Z. (1997). Forecasting Sales and Price for Existing Single-Family Homes: A VAR Model with Error Correction. Journal of Real Estate Research, 14, 155-167.

指導教授

楊曉文、鄒宗山
(Sharon S. Yang、Tsung-Shan Tsou)

審核日期

2010-7-22

推文