Optimal Mortgage Refinancing: A Closed Form Solution

46 Pages Posted: 31 Aug 2007 Last revised: 7 May 2013

Sumit Agarwal

Georgetown University - Department of Finance

John C. Driscoll

Federal Reserve Board

David Laibson

Harvard University - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: July 2, 2012

Abstract

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.

Keywords: Mortgage, refinance, option value, normative economics

JEL Classification: G11, G21

Suggested Citation

Agarwal, Sumit and Driscoll, John C. and Laibson, David, Optimal Mortgage Refinancing: A Closed Form Solution (July 2, 2012). Journal of Money, Credit, and Banking, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1010702 or http://dx.doi.org/10.2139/ssrn.1010702

Sumit Agarwal (Contact Author)

Georgetown University - Department of Finance ( email )

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John C. Driscoll

Federal Reserve Board ( email )

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HOME PAGE: http://www.federalreserve.gov/econresdata/john-c-driscoll.htm

David I. Laibson

Harvard University - Department of Economics ( email )

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617-495-8570 (Fax)

National Bureau of Economic Research (NBER) ( email )

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