Pricing tenure payment reverse mortgages with optimal exercised prepayment options by accounting for house prices, interest rates, and mortality risk

Abstract

Prepayment options can be exercised to terminate reverse mortgages (RM hereafter) early and receive house prices, minus loan balances, at the expense of future annuity proceeds. Prior RM evaluation studies use probability or intensity models to calibrate option exercise policies with historical prepayment records and may not apply to countries without sufficient historical records. In addition, these models may fail to capture time-varying policies due to changing market conditions. Accordingly, insurers may run the risk of undervaluing option premiums and overestimating fair annuity rates. To find optimal exercise policies that maximize option premiums and establish the most conservative annuity rates, we propose a three-dimensional tree for modeling stochastic house prices, interest rates, and mortality risks. We analyze the gain and loss to exercise the option in each scenario to determine the optimal policy. Fair annuity rates are evaluated to ensure that expected insurer losses (i.e. loan balances exceeding house values) equal gains (i.e. insurance premiums plus house values exceeding loan balances). We find that such non-optimal exercise policies undervalue option premiums and overestimate fair annuity rates. Increasing upfront premiums, insurance premium rates, and early redemption charges reduce prepayment incentives and increase fair annuity rates. We also analyze influences from factors such as the policyholder's age and volatilities of house prices and interest rates.