English

Abstract

The reverse mortgage market has been expanding rapidly in developed economies in recent years. Reverse mortgages provide an alternative source of funding for retirement income and health care costs. We often hear the phrase “house rich and cash poor” to refer the increasing number of elderly persons who hold a substantial proportion of their assets in home equity. Reverse mortgage contracts involve a range of risks from the insurer’s perspective. When the outstanding balance exceeds the housing value before the loan is settled, the insurer suffers an exposure to crossover risk induced by three risk factors: interest rates, house prices, and mortality rates. In this context, Covid-19 has occurred and the insurer is faced with this additional source of risk. We analyse the combined impact of these risks on the pricing and the risk profile of reverse mortgage loans. We consider a CIR process for the evolution of the interest rate, a Black & Scholes model for the dynamics of house prices and the Gompertz model for the trend in mortality Our results show that the decrease in the mortality curve due to Covid exposes the insurer to higher risks once the shock is reabsorbed. The risk is higher the higher the age of entry. Only a significant reduction of the shock adjustment coefficient will return the situation to normality.