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 least 1[phi+Wexp phi].In this formula W(.) is (the principal branch of) the Lambert W-function, =2+sigma, phi=1++/M(1),where is the real discount rate, is the expected real rate of exogenous mortgage repayment, sigma is the standard deviation of the mortgage rate, /M is the ratio of the tax-adjusted refinancing cost and the remaining mortgage value, and 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.