Abstract

http://ssrn.com/abstract=1010702
 
 

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Optimal Mortgage Refinancing: A Closed Form Solution


Sumit Agarwal


National University of Singapore

John C. Driscoll


Federal Reserve Board - Division of Monetary Affairs

David Laibson


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

July 2, 2012

Journal of Money, Credit, and Banking, Forthcoming

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.

Number of Pages in PDF File: 46

Keywords: Mortgage, refinance, option value, normative economics

JEL Classification: G11, G21

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Date posted: August 31, 2007 ; Last revised: May 7, 2013

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: http://ssrn.com/abstract=1010702 or http://dx.doi.org/10.2139/ssrn.1010702

Contact Information

Sumit Agarwal (Contact Author)
National University of Singapore ( email )
15 Kent Ridge Drive
Singapore, 117592
Singapore
8118 9025 (Phone)
HOME PAGE: http://www.ushakrisna.com
John C. Driscoll
Federal Reserve Board - Division of Monetary Affairs ( email )
20th and C Streets, NW
Washington, DC 20551
United States
David I. Laibson
Harvard University - Department of Economics ( email )
Littauer Center
Room M-14
Cambridge, MA 02138
United States
617-496-3402 (Phone)
617-495-8570 (Fax)
National Bureau of Economic Research (NBER)
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
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