An analysis of pricing and risks of reverse mortgage loans and long-term care insurance

The thesis develops new pricing and risk analysis frameworks for reverse mortgage loans and long-term care insurance. These are two important products that are increasingly used by individuals to finance their health costs and retirement needs. The results provide insights into the design of affordable products and risk management for product providers. The developed pricing framework for reverse mortgage loans takes into account a wide range of risks, including idiosyncratic house price risk, longevity risk, occupancy risk, and interest rate risk. The pricing model is based on projections of future state variables, including house price, rental yields, GDP, and zero-coupon yield rates. Idiosyncratic house price risk has not been widely studied in the literature due to limited public access to detailed individual house price transactions data. The thesis employs a new data set on detailed property transactions in Sydney that allows for the quantification of the idiosyncratic component of house price risk. Individual house prices are found to have very different trends and volatility compared to the aggregate house price index. Failing to take into account idiosyncratic house price risk considerably underestimates the risks of reverse mortgage providers.Health transition rates are graduated using flexible and comprehensive Generalised Linear Models (GLMs) under a multi-state Markov model framework. GLMs are shown to be more accurate in capturing the sex- and age-specific patterns in the transition rates, compared to the widely used Robinson's method. Thiele's differential equation is used in the base case analysis for pricing and reserving of generic long-term care insurance policies. A simulation-based model is then developed to take into account typical product features, such as the elimination period and the maximum benefit period. The elimination period is shown to be effective in making long-term care insurance more affordable whereas the maximum benefit period is more effective in extreme loss control. Solvency capital requirements taking into account longevity risk and disability risk are derived for a wide range of long-term care insurance policies under Solvency II. It is found that rider benefit policies and life care annuities have considerable capital reductions compared to stand-alone policies