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臺大管理論叢
第
26
卷第
2
期
159
Structural Analysis of Reverse Mortgages
1. Introduction and Study Purpose
The purpose of this study is to analyze the structure of reverse mortgages. In accordance
with the HECM (Home Equity Conversion Mortgage) program, this study decomposes the
collateralized property value into six components: loan amount, rental income, remaining
value (on loan termination), reverse mortgage insurance benefits (i.e., reverse mortgage
insurance costs) and expenses (premiums), and lender profits. This allows financial
institutions to understand the profitability and risks associated with reverse mortgages.
Previous studies have examined reverse mortgage insurance, including pricing under
the HECM program (c.f. Chen et al., 2010; Huang et al., 2011; Lee et al., 2012; Li et al.,
2010; Szymanoski, 1994) and the assessment of HECM risk (e.g., Boehm and Ehrhardt,
1994; Tse, 1995). However, none of these previous studies considered the profitability and
risks to the issuer of reverse mortgages, or the equity value remaining to the borrower. This
study fills this gap in the literature.
2. Design, Methodology and Approach
2.1 RM Contract
This study considers a lump-sum payment reverse mortgage. At the terminal date, the
outstanding loan balance is payable by selling the property. If the proceeds exceed the loan
balance, the remaining value belongs to any heirs of the borrower; otherwise the lender
recovers only the sale value of the property. Suppose that lenders can buy external insurance
to cover any contingent loss. Furthermore, the insurance premiums are assumed to be paid
by the borrower and include both upfront and annual payments. The loan balance accrues as
follows:
, t = 1,2,...
where
BAL
(0) denotes the loan amount;
r
is the risk-free interest rate;
π
r
represents the loan
interest spread;
π
0
represents the upfront premium charge rate;
π
m
is the annual premium rate;
and
H
(0) is the initial value of the property.
Yung-Tsung Lee
, Assistant Professor, Department of Banking and Finance, National Chiayi University
Yu-Hao Lo
, Financial Assistant, Gigastone Corporation