Valuation models

Reverse mortgages

The balance accrues at a fixed rate or the 1-year rate plus a margin and insurance until death, move-out or refinancing (Gompertz-Makeham mortality plus decrements); the lender gets the lesser of the balance and the house value net of sale costs on rate and house price paths. Price, the no-negative-equity guarantee cost, crossover probability, expected life and effective duration.

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Methodology

Conventions

  • The balance accrues at the rate plus the insurance premium until the borrower dies, moves out or repays.
  • Termination: Gompertz-Makeham mortality for the borrower's age plus move-out and refinance rates.
  • The lender gets the lesser of the balance and the house value less sale costs (no negative equity), on rate and house price paths.

References

  • Chen, Cox and Wang (2010)

Formulas

Mortality
μ(x) = A + B cˣ
Repayment
min(B_t, (1 − k) H_t)