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Optimal Mortgage Refinancing: A Closed Form Solution.

Sumit Agarwal1, John C Driscoll2, David I Laibson3

  • 1Departments of Finance and Real Estate at the National University of Singapore ( ushakri@yahoo.com ).

Journal of Money, Credit, and Banking
|April 7, 2015
PubMed
Summary
This summary is machine-generated.

Homeowners should refinance their mortgage when the current interest rate drops significantly below their original rate. This study provides a precise, closed-form optimal refinancing rule for financial decision-making.

Keywords:
Mortgageoption valuerefinance

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Area of Science:

  • Financial Mathematics
  • Mortgage Market Analysis
  • Economic Modeling

Background:

  • Mortgage refinancing decisions are complex, involving various financial and economic factors.
  • Existing models often rely on numerical methods, lacking a simple, closed-form solution.

Purpose of the Study:

  • To derive the first closed-form optimal rule for mortgage refinancing.
  • To provide a precise threshold for when refinancing becomes financially optimal.

Main Methods:

  • Developed a tractable class of mortgage refinancing problems.
  • Solved the problem analytically to derive a closed-form solution using the Lambert W-function.
  • Incorporated factors like discount rate, repayment rate, rate volatility, refinancing costs, and tax rates.

Main Results:

  • Derived a closed-form optimal refinancing rule: refinance when the current mortgage rate is sufficiently lower than the original rate.
  • The threshold depends on the real discount rate (ρ), expected repayment rate (λ), rate standard deviation (σ), refinancing cost ratio (κ/M), and marginal tax rate (τ).
  • Quantitative results align closely with those from numerical methods.

Conclusions:

  • The study offers a novel, analytically derived rule for optimal mortgage refinancing.
  • This closed-form solution simplifies decision-making for homeowners and financial advisors.
  • The findings validate the accuracy of analytical approaches in mortgage market analysis.