Securitisation of Crossover Risk in Reverse Mortgages

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. With consideration of housing price risk, interest rate risk and longevity risk, we provide a three-dimensional lattice method that simultaneously captures the evolution of housing prices and short-term interest rates to calculate the fair valuation of reverse mortgages numerically. For a reverse mortgage insurer, the premium structure of reverse mortgage insurance is determined by setting the present value of the total expected claim losses equal to the present value of the premium charges. However, when the actual loss is higher than the expected loss, the insurer will incur an unexpected loss. To offset the potential loss, we also design two types of crossover bonds to transfer the unexpected loss to bond investors. Therefore, through the crossover bonds, reverse mortgage insurers can partially transfer crossover risk onto bond holders.