Analyzing an elder’s desire for a reverse mortgage using an economic model that considers house bequest motivation, random death time and stochastic house price

Abstract

In recent decades, the aging of the population and the lengthening of life expectancy have caused seniors to need more retirement income over a longer time period. Because the reverse mortgage (RM) can fulfill this requirement, it has become increasingly popular among elderly homeowners. Based on the assumption that seniors seek maximum utility, this article presents a theoretical economic model that derives a decision rule for participating in the RM program. The model takes account of the influences of bequest motivation, random death times and stochastic house prices. A critical value for the intensity of house bequest motivation is also derived from our formula for the decision rule. We then use this value to show how the elder's desire to participate in the RM program is influenced by three sets of factors: the elder's personal characteristics and circumstances, the content of the RM contract, and the current economic situation. Elders' desire to participate in the RM program is found to be negatively correlated with the fixed cost of applying for an RM, the RM contract rate, and the cash income from the elder's retirement plan; on the contrary, the desire to participate is positively correlated with the RM principle limit factors, the elder's age at the time of joining the RM program, the elder's time preference, the elder's initial cash wealth, the elder's initial house price, the current interest rate, and the volatility of the house return. These analyses should help RM policy executors and providers understand the RM borrower's decision-making process and how the factors mentioned above influence an elder's desire to apply for an RM.