Optimal Mortgage Refinancing: A Closed‐Form Solution

We derive the first closed‐form optimal refinancing rule: refinance when the current mortgage interest rate falls below the original rate by at least1 ψ [ φ + W − exp − φ ] .In this formula W (.) is (the principal branch of) the Lambert W ‐function,ψ =2 ρ + λσ ,φ = 1 + ψ ρ + λκ / M ( 1 − τ ) ,where 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.