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Reverse mortgage pricing and risk analysis allowing for idiosyncratic house price risk and longevity risk. (English) Zbl 1348.91179

Summary: Reverse mortgages provide an alternative source of funding for retirement income and health care costs. The two main risks that reverse mortgage providers face are house price risk and longevity risk. Recent real estate literature has shown that the idiosyncratic component of house price risk is large. We analyse the combined impact of house price risk and longevity risk on the pricing and risk profile of reverse mortgage loans in a stochastic multi-period model. The model incorporates a new hybrid hedonic-repeat-sales pricing model for houses with specific characteristics, as well as a stochastic mortality model for mortality improvements along the cohort direction (the Wills-Sherris model). Our results show that pricing based on an aggregate house price index does not accurately assess the risks underwritten by reverse mortgage lenders, and that failing to take into account cohort trends in mortality improvements substantially underestimates the longevity risk involved in reverse mortgage loans.

MSC:

91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography
91G20 Derivative securities (option pricing, hedging, etc.)
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