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The Valuation and Analysis of Adjustable Rate Mortgages

Author

Listed:
  • James B. Kau

    (The University of Georgia, College of Business Administration, 314 Brooks Hall, Athens, Georgia 30602)

  • Donald C. Keenan

    (The University of Georgia)

  • Walter J. Muller

    (NCNB National Bank)

  • James F. Epperson

    (University of Alabama---Huntsville)

Abstract

Securities whose payoffs depend upon the actual path of the underlying state variables pose problems for standard backward-valuation techniques. In this paper, we show that there is a method of solving such problems that requires the addition of but a single auxiliary state variable. The technique is illustrated by examining an adjustable rate mortgage (ARM) with yearly and lifetime caps. The ARM amortizes and can be prepaid at any time. We also handle other prominent features of ARMs including points and teasers. This method of using a single auxiliary state variable to handle path dependencies is a general one, applicable to more complex models of the economic environment and to other financial contracts.

Suggested Citation

  • James B. Kau & Donald C. Keenan & Walter J. Muller & James F. Epperson, 1990. "The Valuation and Analysis of Adjustable Rate Mortgages," Management Science, INFORMS, vol. 36(12), pages 1417-1431, December.
  • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:12:p:1417-1431
    DOI: 10.1287/mnsc.36.12.1417
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    File URL: http://dx.doi.org/10.1287/mnsc.36.12.1417
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    Citations

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    Cited by:

    1. Dressler, Jonathan B. & Stokes, Jeffrey R., 2006. "Mortgage Termination at AgChoice Farm Credit," 2006 Agricultural and Rural Finance Markets in Transition, October 2-3, 2006, Washington, DC 133077, Regional Research Committee NC-1014: Agricultural and Rural Finance Markets in Transition.
    2. Isil Erol & Kanak Patel, 2007. "Pricing the Default Option of Inflation-Indexed Mortgages Using Explicit Finite Difference Method," International Real Estate Review, Asian Real Estate Society, vol. 10(1), pages 48-92.
    3. Moshe Milevsky, 2004. "A diffusive wander through human life," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 21-23.
    4. Yongheng Deng & Della Zheng & Changfeng Ling, 2005. "An Early Assessment of Residential Mortgage Performance in China," The Journal of Real Estate Finance and Economics, Springer, vol. 31(2), pages 117-136, September.
    5. Chow, Ying-Foon & Huang, Charles & Liu, Ming, 2000. "Valuation of adjustable rate mortgages with automatic stretching maturity," Journal of Banking & Finance, Elsevier, vol. 24(11), pages 1809-1829, November.
    6. Anthony Pennington‐Cross & Giang Ho, 2008. "Predatory Lending Laws and the Cost of Credit," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 36(2), pages 175-211, June.
    7. Sprecher, C. R. & Willman, Elliott, 1998. "The Margin Paradox in Adjustable-Rate Mortgages," Journal of Housing Economics, Elsevier, vol. 7(2), pages 180-190, June.
    8. Isil Erol & Kanak Patel, 2004. "Housing Policy and Mortgage Finance in Turkey During the Late 1990s Inflationary Period," International Real Estate Review, Asian Real Estate Society, vol. 7(1), pages 98-120.
    9. Sprecher, C. R. & Willman, Elliott, 2000. "The Role of the Initial Discount in the Pricing of Adjustable-Rate Mortgages," Journal of Housing Economics, Elsevier, vol. 9(1-2), pages 64-75, March.
    10. Raymond Chiang & Thomas F. Gosnell & Andrea J. Heuson, 1997. "Evaluating the Interest-Rate Risk of Adjustable-Rate Mortgage Loans," Journal of Real Estate Research, American Real Estate Society, vol. 13(1), pages 77-94.
    11. Eddie Lam, 2002. "A Risk Management Model for MBS Issuers," International Real Estate Review, Asian Real Estate Society, vol. 5(1), pages 169-195.
    12. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    13. 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.
    14. Naoki Kishimoto, 2004. "Pricing Path-Dependent Securities by the Extended Tree Method," Management Science, INFORMS, vol. 50(9), pages 1235-1248, September.

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