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Optimal Mortgage Refinancing: A Closed-Form Solution

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  • SUMIT AGARWAL
  • JOHN C. DRISCOLL
  • DAVID I. LAIBSON

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 1ψ[φ+W−exp−φ].In this formula W(.) is (the principal branch of) the Lambert W‐function, ψ=2ρ+λσ, φ=1+ψρ+λκ/M(1−τ),where 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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Suggested Citation

  • Sumit Agarwal & John C. Driscoll & David I. Laibson, 2013. "Optimal Mortgage Refinancing: A Closed-Form Solution," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(4), pages 591-622, June.
    • Handle: RePEc:mcb:jmoncb:v:45:y:2013:i:4:p:591-622
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    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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