# Optimal Mortgage Reﬁnancing: A Closed Form Solution

 Title: Optimal Mortgage Reﬁnancing: A Closed Form Solution Author: Agarwal, Sumit; Driscoll, John D.; Laibson, David I. Note: Order does not necessarily reflect citation order of authors. Citation: Agarwal, Sumit, John D. Driscoll, and David I. Laibson. Forthcoming. Optimal mortgage refinancing: a closed form solution. Journal of Money, Credit, and Banking. Full Text & Related Files: Optimal Mortgage Refinancing 092012.pdf (357.0Kb; PDF) 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. Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9918811

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Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University