Valuation of Reverse Mortgages with Default Risk Models

Reverse mortgages are designed to offer additional sources of financing incomes to senior homeowners. In the United States, home equity conversion mortgages (HECMs) are nonrecourse reverse mortgage loans insured by the Federal Housing Administration (FHA). Based on a fairly recent stream of the reverse mortgage literature, the relatively high loan-to-value ratio has jeopardized the financial soundness of such contracts. In the wake of the 2008 financial crisis, rising property taxes and homeowner insurance defaults impaired HECM solvency; hence, policy changes were implemented to help prevent borrower default. In this paper, we propose a pricing solution which, as we demonstrate in the paper, effectively improves program solvency by fairly matching the benefits and liabilities of HECM participants. The methodology allows for customization of fair mortgage loan payments and premiums and improves program accessibility based on borrowers’ individual credit and default risk. Our proposed pricing solution and the corresponding newly designed rating system provide HECM policymakers with a better payment arrangement and offer important policy implications for the current HECM program. Rather than borrower property taxes and insurance delinquency, we demonstrate that the mispricing of HECM mortgage insurance premiums and the corresponding loan payments could be the primary reasons for program insolvency.