Optimal Mortgage Refinancing: A Closed‐Form Solution
推导出首个闭式最优再融资规则：当当前抵押贷款利率低于原利率至少一个由Lambert W函数给出的阈值时再融资。该规则通过求解一类易处理的再融资问题得到，定量结果与数值方法高度吻合。
We derive the first closed‐form optimal refinancing rule: refinance when the current mortgage interest rate falls below the original rate by at least urn:x-wiley:00222879:jmcb12017:equation:jmcb12017-math-0001 In this formula W (.) is (the principal branch of) the Lambert W ‐function, urn:x-wiley:00222879:jmcb12017:equation:jmcb12017-math-0002 urn:x-wiley:00222879:jmcb12017:equation:jmcb12017-math-0003 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, 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.