Optimal Mortgage Refinancing : A Closed Form Solution

We derive the first closed-form optimal refinancing rule for mortgages: Refinance when the current mortgage interest rate falls below the original mortgage interest rate by at least (1/ψ)[φ W(-exp(-φ))], where W(.) is the principal branch of the Lambert W-function, ψ=((√(2(ρ λ)))/σ), φ=1 ψ(ρ λ)((κ/M)/((1-τ))), ρ is the real discount rate (e.g. ρ= 0.05), λ is the expected real rate of exogenous mortgage repayment, including the effects of moving, principal repayment, and inflation (e.g. λ= 0.15), σ is the annual standard deviation of the mortgage rate (e.g. σ=0.0109), κ/M is the ratio of the refinancing cost and the remaining value of the mortgage (e.g. κ/M= $4,500/$250,000), and τ is the marginal tax rate (e.g. τ= 0.28). This expression is derived by solving a tractable class of stylized mortgage refinancing problems. Our quantitative results closely match those reported by other researchers using numerical methods