在Hull-White隨機利率及隨機死亡率下評價反向房屋抵押貸款

Abstract

RM(reverse mortgage)為退休的人解決退休後的收入以及醫療照護費用的問題，此商品將房屋權益轉換成收入，使得年長的屋主能確保退休後的生活水平。RM有著多樣化的給付方式，不論採用何種給付方式，年長的屋主僅需要在借款人死亡、售出或搬離房屋時，將房屋之所有權轉給貸款人，不需要償還借貸金額超出房價的部分。由於RM的價值會根據利率、房價、死亡率風險而改變，且因利率與房價有相關性，不易求得其聯合機率，因此難以對其進行評價與避險。在過去的文獻中，大多假設商品為利率與房價無相關性，而這會大幅影響商品評價的準確性。本研究旨在隨機死亡率及隨機利率設定下，給定RM商品之公平貸款保險費率找出每期最大可貸成數，或是給定後者找出前者。為了貼近實務，本研究探討以終身年金給付為給付方式之RM。

The Reverse Mortgages, abbreviated as RM, provide a way to funding for retirement income and health care costs. RM converts a retiree’s mortgage into cash income by collateralizing house to bank to ensure the living standard of retiree. A RM holder can receive cash inflow in many different patterns, like a lump sum payment, a finite annuity. And the holder is not required to repay the loan that exceeds the value of his/her house. Three main factors that influence the value of reverse mortgage, interest rate, house price and mortality risk are considered in this thesis. The correlation between interest rate and house price makes the joint probability of a tree pricing model hard to be implemented. Much literature overlook the correlation and may significantly misprice RMs. This thesis develops a tree model to numerically evaluate mortgage insurance fees or maximum cash inflow amounts to make a RM a fair contract under stochastic interest rate and stochastic house price. In order to approximate reality, we consider a RM with tenure payments.