台灣施行逆向房貸之利潤與年金分析

Abstract

本研究以台灣近年試辦逆向房貸制度為背景，主要以承作逆向房貸者之角度就逆向房貸面臨之長壽風險、利率風險以及房屋價格風險，分別以Lee-Carter Model、CIR Model及ARMA-GARCH Model 三種動態隨機模型進行蒙地卡羅模擬並對未來各個隨機變數進行預測．將未來特定時點預測的三種隨機變數，加入本研究設計的逆向房貸模型之中，試算承作逆向房貸者之利潤金額的分配與每期給付年金金額之分配。再者，分別探討利率、平均餘命年數及房屋價格，進行單一變數對逆向房貸承作者之利潤和年金影響。最後再以利率連動房屋價格，更為貼近實際狀況之情境下，研究利率與房價兩種有相關性之風險因子變動時，將如何影響逆向房貸承作者之利潤水準以及給付的年金水準，並且觀察風險因子相互聯動影響時，是否增加利潤及年金的變動敏感程度。

The study mainly discusses about implementing the reverse mortgage system in Taiwan recently as the background, and researches on the perspective of the reverse mortgage companies who will encounter several risks, such as the longevity risk, the interest rate risk and the house price risk. Therefore, by respectively applying Lee-Carter model, CIR model and ARMA-GARCH model, three dynamic random variables are able to easily predict in the future period time while the Monte Carlo simulation method are primarily used in this research. Furthermore, three predicted random variables in the specific point of time in the future are able be added to our reverse mortgage model which is designed to calculating the profits of the companies and the amount of the reverse mortgage annuity with the amount allocated for each payment. Moreover, discussing the degree of changes of the interest rates, the average number of years of life expectancy and the house prices, individually affect the profit and annuity payment of reverse mortgage. Finally, using the house prices linked to the interest rates, which seems closer to the actual state of the situation, to discuss the changes of the profit levels of the reverse mortgage and the commitment level annuity payments. During the house prices correlated the interest rate risk factor, we can observe whether both of the sensitivity of profits and annuities increase when the mutual interaction of the two risk factors in the study.