逆向抵押貸款的隨機規劃模型及其在台灣的應用

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\r\npricing 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\r\nAbstract .............................................. v\r\n摘要 ................................................. vi\r\nContents ............................................ vii\r\nList of Tables ....................................... ix\r\nList of Figures ....................................... x\r\n\r\nChapter 1 Introduction ................................ 1\r\n1.1 Motivation of Research ............................ 1\r\n1.2 Purpose and Structure of Research ................. 2\r\nChapter 2 Literature Review ........................... 3\r\n2.1 Reverse Mortgage Overview ......................... 3\r\n2.2 The Potential of RM in Taiwan ..................... 7\r\nChapter 3 Research Models ............................ 11\r\n3.1 Mortality Models ................................. 11\r\n3.2 Interest Rate Models ............................. 13\r\n3.3 House Price Models ............................... 14\r\n3.4 The Pricing Model ................................ 15\r\n3.5 The Mortgage Insurance Premium (MIP) ............. 15\r\nChapter 4 Empirical Analysis ......................... 17\r\n4.1 Mortality Results ................................ 17\r\n4.2 Interest Rates ................................... 18\r\n4.3 House Prices ..................................... 20\r\n4.4 The NRP and the Pricing .......................... 22\r\n4.5 The MIP Results .................................. 25\r\nChapter 5 Sensitivity Analysis ....................... 27\r\n5.1 The Effects of Interest Rates .................... 27\r\n5.2 The Effects of House Prices ...................... 32\r\n5.3 Modifying the MIP Function ....................... 36\r\nChapter 6 Discussion ................................. 40\r\n6.1 The Trial Project of RM in Taipei ................ 40\r\n6.2 A Possible Fair Price ............................ 42\r\n6.3 Weaknesses and Improvements ...................... 42\r\nChapter 7 Conclusion ................................. 45\r\nReferences ........................................... 47