Reverse mortgages with long-term care cost coverage: The role of health state granularity in valuing prepayment options

The growing elderly population has intensified interest in financial products such as reverse mortgages (RM) with long-term care (LTC) cost coverage, which provide funding solutions for senior homeowners facing income shortfalls and rising care costs. This study advances existing research on reverse mortgage contracts with long-term care cost coverage (RM_LTC) by systematically examining how the granularity of health state information influences contract valuation, particularly in the presence of prepayment options and market risks. We develop a numerical framework to determine the fair annuity rate of RM_LTC contracts. The framework jointly captures stochastic house prices, interest rates, and multi-state health transition matrices calibrated with real-world disability data. Our results show that finer health state granularity improves the precision of prepayment decisions, increasing the value of embedded options while lowering fair annuities. Conversely, relying on less detailed health information leads to an underestimation of option value and results in higher annuities offered to homeowners. By clarifying these mechanisms, the study underscores the pivotal role of health state granularity in valuing RM_LTC contracts and provides insights into the design of home-equity-based financing for long-term care.