Optimal Mortgage Refinancing: A Closed Form Solution

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Optimal Mortgage Refinancing: A Closed Form Solution

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Title: Optimal Mortgage Refinancing: A Closed Form Solution
Author: Agarwal, Sumit; Driscoll, John D.; Laibson, David I.

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Citation: Agarwal, Sumit, John D. Driscoll, and David I. Laibson. Forthcoming. Optimal mortgage refinancing: a closed form solution. Journal of Money, Credit, and Banking.
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Abstract: We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least \(\frac{1}{ψ}\)[φ + W (− exp (−φ))].
In this formula W(.) is the Lambert W-function,
ψ = \(\frac{2 (ρ + λ)}{σ}\),
φ = 1 + ψ (ρ + λ)\(\frac{κ/M}{(1 − τ )}\), 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.
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Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9918811
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