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Optimal Mortgage Refinancing: A Closed Form Solution

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  • Sumit Agarwal
  • John C Driscoll
  • David Laibson

Abstract

We derive the first closed-form optimal mortgage refinancing rule. The expression is derived by using the Lambert-W function to solve a tractable class of mortgage refinancing problems. We calibrate our solution and show that our quantitative results closely match those reported by researchers who use numerical methods.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 122247000000002021.

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Date of creation: 21 Mar 2008
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Handle: RePEc:cla:levarc:122247000000002021

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  1. Stanton, Richard, 1995. "Rational Prepayment and the Valuation Mortgage-Backed Securities," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 8(3), pages 677-708.
  2. Hurst, Erik & Stafford, Frank, 2004. "Home Is Where the Equity Is: Mortgage Refinancing and Household Consumption," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 36(6), pages 985-1014, December.
  3. Wayne R. Archer & David C. Ling, 1993. "Pricing Mortgage-Backed Securities: Integrating Optimal Call and Empirical Models of Prepayment," Real Estate Economics, American Real Estate and Urban Economics Association, American Real Estate and Urban Economics Association, vol. 21(4), pages 373-404.
  4. Xavier Gabaix & David Laibson, 2005. "Shrouded Attributes, Consumer Myopia, and Information Suppression in Competitive Markets," NBER Working Papers 11755, National Bureau of Economic Research, Inc.
  5. Schwartz, Eduardo S & Torous, Walter N, 1992. "Prepayment, Default, and the Valuation of Mortgage Pass-through Securities," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 65(2), pages 221-39, April.
  6. Patric H. Hendershott & Robert Van Order, 1987. "Pricing Mortgages: An Interpretation of the Models and Results," NBER Working Papers 2290, National Bureau of Economic Research, Inc.
  7. Olivier Vigneron, & Xavier Gabaix & Arvind Krishnamurthy, 2004. "Limits of Arbitrage: Theory and Evidence from the Mortgage-Backed Securities Market," Econometric Society 2004 North American Summer Meetings, Econometric Society 430, Econometric Society.
  8. Eduardo S. Schwartz & Walter N. Torous, 1993. "Mortgage Prepayment and Default Decisions: A Poisson Regression Approach," Real Estate Economics, American Real Estate and Urban Economics Association, American Real Estate and Urban Economics Association, vol. 21(4), pages 431-449.
  9. Green, Jerry & Shoven, John B, 1986. "The Effects of Interest Rates on Mortgage Prepayments," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 18(1), pages 41-59, February.
  10. Quigley, John M, 1987. "Interest Rate Variations, Mortgage Prepayments and Household Mobility," The Review of Economics and Statistics, MIT Press, vol. 69(4), pages 636-43, November.
  11. Campbell, John, 2006. "Household Finance," Scholarly Articles 3157877, Harvard University Department of Economics.
  12. Yongheng Deng & John M. Quigley & Robert Van Order, 2000. "Mortgage Terminations, Heterogeneity and the Exercise of Mortgage Options," Econometrica, Econometric Society, Econometric Society, vol. 68(2), pages 275-308, March.
  13. Yan Chang & Abdullah Yavas, 2009. "Do Borrowers Make Rational Choices on Points and Refinancing?," Real Estate Economics, American Real Estate and Urban Economics Association, American Real Estate and Urban Economics Association, vol. 37(4), pages 635-658.
  14. Bennett, Paul & Peach, Richard & Peristiani, Stavros, 2001. "Structural Change in the Mortgage Market and the Propensity to Refinance," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 33(4), pages 955-75, November.
  15. Paul Bennett & Richard Peach & Stavros Peristiani, 1998. "Implied mortgage refinancing thresholds," Staff Reports, Federal Reserve Bank of New York 49, Federal Reserve Bank of New York.
  16. Follain, James R & Scott, Louis O & Yang, T L Tyler, 1992. "Microfoundations of a Mortgage Prepayment Function," The Journal of Real Estate Finance and Economics, Springer, Springer, vol. 5(2), pages 197-217, June.
  17. Andrew H. Chen & David C. Ling, 1989. "Optimal Mortgage Refinancing with Stochastic Interest Rates," Real Estate Economics, American Real Estate and Urban Economics Association, American Real Estate and Urban Economics Association, vol. 17(3), pages 278-299.
  18. Li, Minqiang & Pearson, Neil D. & Poteshman, Allen M., 2004. "Conditional estimation of diffusion processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 74(1), pages 31-66, October.
  19. Dunn, Kenneth B & McConnell, John J, 1981. "Valuation of GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, American Finance Association, vol. 36(3), pages 599-616, June.
  20. Chris Downing & Richard Stanton & Nancy Wallace, 2005. "An Empirical Test of a Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter?," Real Estate Economics, American Real Estate and Urban Economics Association, American Real Estate and Urban Economics Association, vol. 33(4), pages 681-710, December.
  21. Caplin, Andrew & Freeman, Charles & Tracy, Joseph, 1997. "Collateral Damage: Refinancing Constraints and Regional Recessions," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 29(4), pages 496-516, November.
  22. John P. Harding, 1997. "Estimating Borrower Mobility from Observed Prepayments," Real Estate Economics, American Real Estate and Urban Economics Association, American Real Estate and Urban Economics Association, vol. 25(3), pages 347-371.
  23. Green, Richard K. & LaCour-Little, Michael, 1999. "Some Truths about Ostriches: Who Doesn't Prepay Their Mortgages and Why They Don't," Journal of Housing Economics, Elsevier, Elsevier, vol. 8(3), pages 233-248, September.
  24. Giliberto, S Michael & Thibodeau, Thomas G, 1989. "Modeling Conventional Residential Mortgage Refinancings," The Journal of Real Estate Finance and Economics, Springer, Springer, vol. 2(4), pages 285-99, December.
  25. Kenneth B. Dunn & Chester S. Spatt, 2005. "The Effect of Refinancing Costs and Market Imperfections on the Optimal Call Strategy and the Pricing of Debt Contracts," Real Estate Economics, American Real Estate and Urban Economics Association, American Real Estate and Urban Economics Association, vol. 33(4), pages 595-617, December.
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Citations

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Cited by:
  1. Sumit Agarwal & Richard J. Rosen & Vincent Yao, 2013. "Why do borrowers make mortgage refinancing mistakes?," Working Paper Series, Federal Reserve Bank of Chicago WP-2013-02, Federal Reserve Bank of Chicago.
  2. Benjamin J. Keys & Devin G. Pope & Jaren C. Pope, 2014. "Failure to Refinance," NBER Working Papers 20401, National Bureau of Economic Research, Inc.
  3. Khandani, Amir E. & Lo, Andrew W. & Merton, Robert C., 2013. "Systemic risk and the refinancing ratchet effect," Journal of Financial Economics, Elsevier, Elsevier, vol. 108(1), pages 29-45.
  4. Toshio Kimura & Naoki Makimoto, 2008. "Optimal Mortgage Refinancing with Regime Switches," Asia-Pacific Financial Markets, Springer, Springer, vol. 15(1), pages 47-65, March.
  5. Guiso, Luigi & Sodini, Paolo, 2012. "Household Finance: An Emerging Field," CEPR Discussion Papers, C.E.P.R. Discussion Papers 8934, C.E.P.R. Discussion Papers.
  6. Aytek Malkhozov & Philippe Mueller & Andrea Vedolin & Gyuri Venter, 2013. "Mortgage Hedging in Fixed Income Markets," FMG Discussion Papers, Financial Markets Group dp722, Financial Markets Group.
  7. Barry Bosworth & Rosanna Smart, 2009. "The Wealth of Older Americans and the Sub-Prime Debacle The Wealth of Older Americans and the Sub-Prime Debacle," Working Papers, Center for Retirement Research at Boston College, Center for Retirement Research wp2009-21, Center for Retirement Research, revised Nov 2009.
  8. Werner Hürlimann, 2012. "Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations," Decisions in Economics and Finance, Springer, Springer, vol. 35(2), pages 171-202, November.

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