The security mortgage valuation in a stochastic perspective

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. Increase in life expectancies and decrease in the real income at retirement continue to worry the those who are retired or close to retirement. Therefore, financial products that help to alleviate the “risk of living longer” continue to be attractive among the retirees. 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. We analyse the combined impact of these risks on the pricing and the risk profile of reverse mortgage loans in a stochastic interest-mortality-house pricing model. Our results show shows that pricing of reverse mortgages loans does not accurately assess the risks underwritten by reverse mortgages lenders and that failing to take into account mortality improvements substantially underestimates the longevity risk involved in reverse mortgage loans.