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The Pricing of Default-Free Mortgages

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  • Stephen A. Buser
  • Patric H. Hendershott

Abstract

In this paperwe examine the household's option to prepay or call a standard fixed-rate mortgage. Results based on simulation indicate that the value of this option is sensitive to the expected path of interest rates, the variation around that path, risk aversion and refinancing costs. Unfortunately, efforts to estimate the interest rate process (by us and by previous authors) have met with only limited success, and uncertainty exists regarding the degree of risk aversion and the magnitude of refinancing costs.Thus we conclude that the application of contingent-claims methodology to options on bonds is conceptually more difficult and operationally less reliable than is the analogous application to options on stocks.Despite these reservations concerning the use of our model as a technique for absolute valuation, preliminary findings on the effects of changes in mortgage contract design on the value of the prepayment option are encouraging. For example, our estimate of the relative values of the call options on 30- and 15-year mortgages and on level-payment and graduated-payment mortgages appear to be reasonably robust with respect to specifications of the interestrate process and the other parameters.These findings suggest that our model may be of considerable use within the context of relative or comparative valuation.

Suggested Citation

  • Stephen A. Buser & Patric H. Hendershott, 1984. "The Pricing of Default-Free Mortgages," NBER Working Papers 1408, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:1408
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    References listed on IDEAS

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    Cited by:

    1. Andrew H. Chen & David C. Ling, 1989. "Optimal Mortgage Refinancing with Stochastic Interest Rates," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 17(3), pages 278-299, September.
    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. Deng, Yongheng & Quigley, John M. & Van Order, Robert & Mac, Freddie, 1996. "Mortgage default and low downpayment loans: The costs of public subsidy," Regional Science and Urban Economics, Elsevier, vol. 26(3-4), pages 263-285, June.
    4. Patric H. Hendershott, 1986. "Mortgage Pricing: What Have We Learned So Far?," NBER Working Papers 1959, National Bureau of Economic Research, Inc.
    5. Stephen A. Buser & Patric H. Hendershott & Anthony B. Sanders, 1988. "On the Determinants of the Value of Call Options on Default-Free Bonds," NBER Working Papers 2529, National Bureau of Economic Research, Inc.
    6. Donald F. Cunningham & Patric H. Hendershott, 1984. "Pricing FHA Mortgage Default Insurance," NBER Working Papers 1382, National Bureau of Economic Research, Inc.
    7. Archer, Wayne R. & Ling, David C. & McGill, Gary A., 1996. "The effect of income and collateral constraints on residential mortgage terminations," Regional Science and Urban Economics, Elsevier, vol. 26(3-4), pages 235-261, June.
    8. Nai Jia Lee, 2003. "Expected Return of Housing and Mortgage Termination," International Real Estate Review, Global Social Science Institute, vol. 6(1), pages 75-101.
    9. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    10. Isil Erol & Kanak Patel, 2007. "Pricing the Default Option of Inflation-Indexed Mortgages Using Explicit Finite Difference Method," International Real Estate Review, Global Social Science Institute, vol. 10(1), pages 48-92.
    11. Archer, Wayne R. & Ling, David C. & McGill, Gary A., 1997. "Demographic versus Option-Driven Mortgage Terminations," Journal of Housing Economics, Elsevier, vol. 6(2), pages 137-163, June.
    12. Almas Naseem & R. Reesor, 2015. "Risk and reward of home equity borrowing for investment in Canada, a stochastic analysis," Computational Management Science, Springer, vol. 12(1), pages 45-79, January.
    13. Dejun Xie, 2009. "A Steady State Solution to a Mortgage Pricing Problem," Papers 0909.5389, arXiv.org.
    14. 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.
    15. Deng, Yongheng & Gu, Quanlin & He, Jia, 2021. "Reinforcement learning and mortgage partial prepayment behavior," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    16. Stephen A. Buser & Patric H. Hendershott & Anthony B. Sanders, 1984. "Pricing Rate Caps on Default-Free Adjustable-Rate Mortgages," NBER Working Papers 1525, National Bureau of Economic Research, Inc.
    17. Harding, John P., 2000. "Mortgage Valuation with Optimal Intertemporal Refinancing Strategies," Journal of Housing Economics, Elsevier, vol. 9(4), pages 233-266, December.
    18. Sven Balder & Wolf Christoph Gramatke & Antje Mahayni & Gordon Müller-Seitz & Jörg Sydow, 2014. "Bewertung von Kündigungsrechten in der privaten Wohnungsbaufinanzierung — Über den separaten Ausweis von Margen- und Kursschäden," Schmalenbach Journal of Business Research, Springer, vol. 66(1), pages 3-36, February.

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