Optimal Mortgage Refinancing: A Closed Form Solution
National University of Singapore
John C. Driscoll
Federal Reserve Board - Division of Monetary Affairs
Harvard University - Department of Economics; National Bureau of Economic Research (NBER)
July 2, 2012
Journal of Money, Credit, and Banking, Forthcoming
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.
Number of Pages in PDF File: 46
Keywords: Mortgage, refinance, option value, normative economics
JEL Classification: G11, G21
Date posted: August 31, 2007 ; Last revised: May 7, 2013
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