160 / 372
反向房屋抵押貸款商品結構分析
160
2.2 House Price Process and the Mortality Model
Under the risk-neutral measure
Q
, the house price is constructed as follows:
where
δ
denotes the rental rate;
σ
H
represents the volatility of housing prices; and
W
Q
(
t
) is a
standard Brownian motion under measure
Q
.
This study uses the Lee-Carter model (Lee and Carter, 1992) to represent the mortality
of the borrower and assumes the death of the borrower to be the unique factor that causes
loan termination. Additionally, mortality and house price processes are assumed to be
independent.
2.3 Structure Analysis of Reverse Mortgages
Given a specific loan amount, the present value of rental income (
V
R
(0)), the remaining
value (
V
B
(0)), insurance premiums (
V
P
(0)) and the cost of RM insurance (
V
I
(0)) are
determined using the following equations: