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A Closed Form Formula for Valuing Mortgages


  • Collin-Dufresne, P
  • Harding, John P


We develop a closed form formula for the value of a fixed-rate residential mortgage that includes the provision that the borrower can prepay at any time with no penalty. The value of the mortgage equals the expectation, under the risk neutral probability measure, of the future cash flows. We model future cash flows by estimating an empirical model of prepayment behavior. A second change of measure leads to a closed form expression for the expectation. The closed form values explain most of the time series variation in MBS prices. The closed form formula significantly shortens the time to calculate mortgage values and durations and can be a useful tool for portfolio management and hedging. Copyright 1999 by Kluwer Academic Publishers

Suggested Citation

  • Collin-Dufresne, P & Harding, John P, 1999. "A Closed Form Formula for Valuing Mortgages," The Journal of Real Estate Finance and Economics, Springer, vol. 19(2), pages 133-146, September.
  • Handle: RePEc:kap:jrefec:v:19:y:1999:i:2:p:133-46

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    Cited by:

    1. Tsai, Ming-Shann & Liao, Szu-Lang & Chiang, Shu-Ling, 2009. "Analyzing yield, duration and convexity of mortgage loans under prepayment and default risks," Journal of Housing Economics, Elsevier, vol. 18(2), pages 92-103, June.
    2. Nicholas Sharp & David Newton & Peter Duck, 2008. "An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options," The Journal of Real Estate Finance and Economics, Springer, vol. 36(3), pages 307-342, April.
    3. Xudong An & John Clapp & Yongheng Deng, 2010. "Omitted Mobility Characteristics and Property Market Dynamics: Application to Mortgage Termination," The Journal of Real Estate Finance and Economics, Springer, vol. 41(3), pages 245-271, October.
    4. Szu-Lang Liao & Ming-Shann Tsai & Shu-Ling Chiang, 2008. "Closed-Form Mortgage Valuation Using Reduced-Form Model," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 36(2), pages 313-347, June.
    5. Chiang, Shu Ling & Yang, Tyler T. & Tsai, Ming Shann, 2016. "Assessing mortgage servicing rights using a reduced-form model: Considering the effects of interest rate risks, prepayment and default risks, and random state variables," Journal of Housing Economics, Elsevier, vol. 32(C), pages 29-46.
    6. Charlier, E. & van Bussel, A., 2001. "Prepayment Behavior of Dutch Mortgagors : An Empirical Analysis," Discussion Paper 2001-64, Tilburg University, Center for Economic Research.
    7. Niels Rom-Poulsen, 2007. "Semi-analytical MBS Pricing," The Journal of Real Estate Finance and Economics, Springer, vol. 34(4), pages 463-498, May.
    8. Jean-David Fermanian, 2013. "A Top-Down Approach for Asset-Backed Securities: A Consistent Way of Managing Prepayment, Default and Interest Rate Risks," The Journal of Real Estate Finance and Economics, Springer, vol. 46(3), pages 480-515, April.

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