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Option Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate Mortgages

Author

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  • Kau, James B
  • Keenan, Donald C
  • Muller, Walter J, III
  • Epperson, James F

Abstract

This article demonstrates how to value floating-rate securities, in particular adjustable-rate mortgages, in the presence of default. The problem is not a straightforward one since endogenous termination (default and prepayment) necessitates solution by backward procedures, but caps on the floating rate then create path dependencies. The solution is to introduce an artificial state variable, the past contract rate, in addition to the natural stochastic variables, the interest and the house price process. With this technique, a numerical investigation of the properties of defaultable adjustable-rate mortgages is provided. In all cases, a comparison is made with standard fixed-rate mortgages. Coauthors are Donald C. Keenan, Walter J. Muller III, and James F. Epperson. Copyright 1993 by University of Chicago Press.

Suggested Citation

  • Kau, James B & Keenan, Donald C & Muller, Walter J, III & Epperson, James F, 1993. "Option Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate Mortgages," The Journal of Business, University of Chicago Press, vol. 66(4), pages 595-618, October.
  • Handle: RePEc:ucp:jnlbus:v:66:y:1993:i:4:p:595-618
    DOI: 10.1086/296619
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    Cited by:

    1. Eddie Lam, 2002. "A Risk Management Model for MBS Issuers," International Real Estate Review, Asian Real Estate Society, vol. 5(1), pages 169-195.
    2. Clyde F. Martin & Nikola Kojucharov & Robert F. Martin & Lili Xu, 2009. "The subprime mortgage crisis: irrational exuberance or rational error?," Proceedings, Federal Reserve Bank of San Francisco, issue jan.
    3. Werner Hürlimann, 2012. "Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 171-202, November.
    4. McConnell, John J. & Saretto, Alessio, 2010. "Auction failures and the market for auction rate securities," Journal of Financial Economics, Elsevier, vol. 97(3), pages 451-469, September.
    5. Patel, Nimesh & Daglish, Toby, 2011. "Fixed come hell or high water? Selection and prepayment of fixed rate mortgages outside the US," Working Paper Series 4107, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    6. 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.
    7. Ming Shann Tsai & Shu Ling Chiang, 2016. "The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions," International Review of Finance, International Review of Finance Ltd., vol. 16(3), pages 421-444, September.
    8. 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.
    9. Agarwal, Sumit & Ambrose, Brent W. & Chomsisengphet, Souphala & Liu, Chunlin, 2006. "An empirical analysis of home equity loan and line performance," Journal of Financial Intermediation, Elsevier, vol. 15(4), pages 444-469, October.
    10. Lanot, Gauthier & Leece, David, 2010. "The Performance of UK Securitized Subprime Mortgage Debt: ‘Idiosyncratic’ Behaviour or Mortgage Design?," MPRA Paper 27137, University Library of Munich, Germany.
    11. 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.
    12. Posey, Lisa L. & Yavas, Abdullah, 2001. "Adjustable and Fixed Rate Mortgages as a Screening Mechanism for Default Risk," Journal of Urban Economics, Elsevier, vol. 49(1), pages 54-79, January.
    13. James Kau & Donald Keenan, 1999. "Catastrophic Default and Credit Risk for Lending Institutions," Journal of Financial Services Research, Springer;Western Finance Association, vol. 15(2), pages 87-102, March.
    14. Ray Sturm & Drew Winters, 2009. "Does time have value? An empirical examination of the put option embedded in refundable U.S. air fares," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 33(4), pages 376-392, October.
    15. repec:ire:issued:v:21:n:01:2018:p:1-40 is not listed on IDEAS
    16. Daglish, Toby, 2009. "What motivates a subprime borrower to default?," Journal of Banking & Finance, Elsevier, vol. 33(4), pages 681-693, April.
    17. 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.
    18. 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.
    19. Geetesh Bhardwaj & Rajdeep Sengupta, 2008. "Did prepayments sustain the subprime market?," Working Papers 2008-039, Federal Reserve Bank of St. Louis.
    20. Cristina Viegas & José Azevedo-Pereira, 2012. "Mortgage valuation: a quasi-closed-form solution," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 993-1001, May.
    21. Bhardwaj, Geetesh & Sengupta, Rajdeep, 2012. "Subprime mortgage design," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1503-1519.
    22. Stephen F. Thode, 2000. "CMOs, Duration Risk and a New Mortgage," Journal of Real Estate Research, American Real Estate Society, vol. 19(1), pages 73-103.

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