Added Jun 11, 2013
3 min
Optimal Mortgage Refinancing: A Closed Form Solution
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 =√2 (ρ + λ)σ ,
φ = 1 + ψ (ρ + λ) κ/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.
JEL Classification
G11, G21
Suggested Citation
Partners
Driscoll, J., and D. Laibson
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