Risk-neutral valuation of the non-recourse protection in reverse mortgages: A case study for Korea

- Risk-neutral valuation for the non-recourse protection in the Korean reverse mortgage market is performed.
- A multivariate DCC-GARCH model is used for the economic variables involved.
- Future mortalities are projected to capture macro longevity risks.
- Risk-neutralization is accomplished using the canonical valuation.
- The results reveal several limitations of the current fee structure and we suggest possible new fee schemes.

Reverse mortgages are increasingly seen as an alternative source of retirement income among Koreans. All reverse mortgage loans in Korea are sold with a non-recourse protection, limiting the borrowers' exposure to house price appreciation risk. This paper performs risk-neutral valuation for the non-recourse protection in the Korean reverse mortgage market. Specifically, we adopt a multivariate DCC-GARCH model that incorporates different forms of correlations between the economic variables. Risk-neutralization is accomplished using the minimum relative entropy method. Our valuation results reveal several limitations of the fee structure currently used by reverse mortgage providers. Recommendations to improve the fee structure are provided.