The Valuation of Reverse Mortgage Insurance Contract

[[abstract]]本論文依據美國反向房屋抵押貸款Home Equity Conversion Mortgage (HECM) 商品的評價模式，運用歐式選擇權架構來評價美國反向房屋抵押貸款保險契約，有關房屋抵押貸款評價的文獻一般都是假設房價變動服從幾何布朗尼運動，此假設下，對於實際房價資料並沒有提供一個最佳的模型(Kuo 1996)。因此，本論文根據美國聯邦住屋委員會(Federal Housing Financial Board)所公布之房價資料，區分新屋與舊屋，首先建立一個符合實際房價變動過程之模型，而不是假設房價變動過程服從幾何布朗尼運動，然後利用保險精算收支平衡原理，運用歐式選擇權架構，修正HECM商品的評價模式，透過精算方式計算反向房屋抵押貸款保險費。實證分析下，根據實際房價資料配適房價變動過程，顯示房價變動過程服從MA(1)過程，並非服從幾何布朗尼運動。在歐式賣權評價模式下，實際房價變動過程為MA過程下的保險費用低於房價過程服從幾何布朗尼運動，這隱含如果反向房屋抵押貸款保險費假設房價服服從幾何布朗尼運動所精算出的保險費將會高估，導致評價錯誤；另外數值分析的結果顯示，借款人的生存機率( )、房屋價格 、房屋價格波動度 以及房價MA過程所估計出的 係數，皆對於反向房屋抵押貸款保險保費皆產生影響，研究中發現，除了房屋價格與保險費用為反向關係，其餘參數與保險費用為正向關係。[[abstract]]This dissertation analyzed the reverse mortgages in United States (U S ) after building reverse mortgage insurance pricing model using the framework of European put options The previous literature on mortgage valuation typically assumes that housing prices follow a geometric Brownian motion but the assumption of the change of housing price which evolve according to GBM has not provided a good fit for actual housing price data (Kuo 1996) Hence this dissertation based on published U S housing prices data from Federal Housing Financial Board to set up a more realistic housing price model rather than assumed that housing prices follow a geometric Brownian motion For empirical analysis the housing price follow MA(1) process and then apply the empirically estimated housing price model through the framework of European put options to build reverse mortgage insurance pricing model According to pricing premium model used it to calculate the fair reverse mortgage insurance premium to charge This dissertation show that the stochastic model with realistic housing price model that follow MA (1) type process is fitter than stochastic model with GBM in modeling the reverse mortgage insurance contract when pricing insurance premium It is true that the estimated coefficient of MA (1) type process has positive effects on the reverse mortgage insurance premium That implied that insurance premium is overestimated and using stochastic model with GBM to evaluate the reverse mortgage insurance contract could cause significant mispricing In numerical analysis the reverse mortgage insurance pricing model with undetermined parameters: the findings are that all of the parameters of the survival probability ( ); the housing price ; the volatility of housing price ; the estimated coefficient are important factors in determining the value of the reverse mortgage insurance premium The housing price has negative effects on relationship reverse mortgage insurance premium The other parameters have positive effects on relationship reverse mortgage insurance premiu