Abstract
In this study, we analyzed the risk faced by the reverse mortgage provider in the case of the lump-sum solution, which is increasingly becoming one of the most popular types of reverse mortgages. The risk faced by the mortgage provider was estimated by means of a value at risk (VaR) procedure that involves a Monte Carlo simulation method and an ARMA-EGARCH assumption for modeling house price returns in the United Kingdom from 1952 to 2019. The results showed that the reverse mortgage provider faced higher risk and consequently needed to allocate more funds to meet its regulatory capital requirements in the case of relatively young borrowers, especially when they reached their life expectancy and had high roll-up rates. The risk was even higher in the case of the female population. Furthermore, care must be taken when the rental yield rate is higher than the risk-free rate, as is currently the case, as the value of the no-negative-equity guarantee (NNEG) is relatively high and results in higher value at risk (VaR) and expected shortfall (ES) values. These results have important implications in terms of policy decision making when determining the countercyclical buffer for reverse mortgages in Basel III, as well as from a managerial perspective when determining the economic capital needed to support the risk taken by the lender.
Highlights
Reverse mortgages are granted by banks to elderly people who want to supplement their incomes, with the borrower’s home as collateral
We must take into account that our method considers three different sources of risk: house price risk, longevity risk, and the risk associated with the number of survivors in the theoretical portfolio of reverse mortgages owned by the financial institution
To compute this risk-neutral expectation, it is important to note that according to [1], the risk-neutral mean return of the underlying asset of the European put that must be used for option valuation purposes is r–g–ht /2, where r is the risk-free rate, g is the rental yield, and ht is the time-varying variance estimated from the ARMA-EGARCH model
Summary
Reverse mortgages are granted by banks to elderly people who want to supplement their incomes, with the borrower’s home as collateral. The borrower receives an amount of money, in the form of either a lump sum or periodic payments, and when he/she dies or moves out of the house, the amount of the home sale is used to repay the loan (plus interest). In a majority of cases, a no-negative-equity guarantee (NNEG) is incorporated into the loan. This is done so that at the time of death or abandonment of his/her home, the borrower is only responsible for the sale price of his/her home, which represents a potential loss for the mortgage provider. From a risk management perspective, reverse mortgages are complex products because they involve several types of risks—longevity risk, house price risk, interest rate risk, and rental yield risk
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