We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least ψ1[φ + W (− exp (−φ))].
In this formula W(.) is the Lambert W-function,
ψ = σ2(ρ+λ),
φ = 1 + ψ (ρ + λ)(1−τ)κ/M, ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods.Economic