IDEAS home Printed from https://ideas.repec.org/a/kap/apfinm/v11y2004i2p185-214.html
   My bibliography  Save this article

Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

Author

Listed:
  • Toru Sugimura

Abstract

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported. Copyright Springer Science+Business Media, Inc. 2004

Suggested Citation

  • Toru Sugimura, 2004. "Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(2), pages 185-214, June.
    • Handle: RePEc:kap:apfinm:v:11:y:2004:i:2:p:185-214
    DOI: 10.1007/s10690-006-9009-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10690-006-9009-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10690-006-9009-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Downing, Chris & Stanton, Richard & Wallace, Nancy E., 2003. "An Empirical Test of a Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter?," Research Program in Finance, Working Paper Series qt2qb613r5, Research Program in Finance, Institute for Business and Economic Research, UC Berkeley.
    2. 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, vol. 21(4), pages 431-449, December.
    3. Chris Downing & Richard Stanton & Nancy Wallace, 2003. "An empirical test of a two-factor mortgage valuation model: how much do house prices matter?," Finance and Economics Discussion Series 2003-42, Board of Governors of the Federal Reserve System (U.S.).
    4. Kau, James B, et al, 1992. "A Generalized Valuation Model for Fixed-Rate Residential Mortgages," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 24(3), pages 279-299, August.
    5. repec:bla:jfinan:v:44:y:1989:i:2:p:375-92 is not listed on IDEAS
    6. Stanton, Richard, 1995. "Rational Prepayment and the Valuation Mortgage-Backed Securities," The Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 677-708.
    7. Kau, James B. & Keenan, Donald C. & Muller III, Walter J. & Epperson, James F., 1995. "The Valuation at Origination of Fixed-Rate Mortgages with Default and Prepayment," The Journal of Real Estate Finance and Economics, Springer, vol. 11(1), pages 5-36, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chang, Chia-Chien, 2014. "Valuation Of Mortgage Insurance Contracts With Counterparty Default Risk: Reduced-Form Approach," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 303-334, May.
    2. Cristina Viegas & Jos� Azevedo-Pereira, 2012. "Mortgage valuation: a quasi-closed-form solution," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 993-1001, May.
    3. Ahmad, Ferhana & Shehzad, Choudhry Tanveer, 2024. "The role of interest rate environment in mortgage pricing," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 225-245.
    4. Yongheng Deng & Peng Liu, 2009. "Mortgage Prepayment and Default Behavior with Embedded Forward Contract Risks in China’s Housing Market," The Journal of Real Estate Finance and Economics, Springer, vol. 38(3), pages 214-240, April.
    5. Khandani, Amir E. & Lo, Andrew W. & Merton, Robert C., 2013. "Systemic risk and the refinancing ratchet effect," Journal of Financial Economics, Elsevier, vol. 108(1), pages 29-45.
    6. Mikhail Chernov & Brett R. Dunn & Francis A. Longstaff, 2018. "Macroeconomic-Driven Prepayment Risk and the Valuation of Mortgage-Backed Securities," The Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 1132-1183.
    7. John Clapp & Yongheng Deng & Xudong An, 2005. "Unobserved heterogeneity in Models of Competing Mortgage Termination Risks," Working Paper 8585, USC Lusk Center for Real Estate.
    8. McCollum, Meagan N. & Lee, Hong & Pace, R. Kelley, 2015. "Deleveraging and mortgage curtailment," Journal of Banking & Finance, Elsevier, vol. 60(C), pages 60-75.
    9. Yongheng Deng & John M. Quigley, 2003. "Woodhead Behavior and the Pricing of Residential Mortgages," Working Paper 8616, USC Lusk Center for Real Estate.
    10. Fang, Lu & Munneke, Henry J., 2021. "A spatial analysis of borrowers’ mortgage termination decision – A nonparametric approach," Regional Science and Urban Economics, Elsevier, vol. 86(C).
    11. Michael LaCour-Little & Michael Marschoun & Clark L. Maxam, 2002. "Improving Parametric Mortgage Prepayment Models with Non-parametric Kernel Regression," Journal of Real Estate Research, American Real Estate Society, vol. 24(3), pages 299-328.
    12. Nicholas Sharp & Paul Johnson & David Newton & Peter Duck, 2009. "A New Prepayment Model (with Default): An Occupation-time Derivative Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 39(2), pages 118-145, August.
    13. Ming‐Chi Chen & Chia‐Chien Chang & Shih‐Kuei Lin & So‐De Shyu, 2010. "Estimation of Housing Price Jump Risks and Their Impact on the Valuation of Mortgage Insurance Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 399-422, June.
    14. Hidetoshi Nakagawa & Tomoaki Shouda, 2004. "Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 233-266, September.
    15. Ahmad, F. & Hambly, B.M. & Ledger, S., 2018. "A stochastic partial differential equation model for the pricing of mortgage-backed securities," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3778-3806.
    16. 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.
    17. 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.
    18. Scott Robertson & Zhe Cheng, 2015. "Endogenous Current Coupons," Papers 1510.02010, arXiv.org.
    19. Hartarska, Valentina & Gonzalez-Vega, Claudio, 2006. "Evidence on the effect of credit counseling on mortgage loan default by low-income households," Journal of Housing Economics, Elsevier, vol. 15(1), pages 63-79, March.
    20. Hawkins, Raymond J., 2011. "Lending sociodynamics and economic instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4355-4369.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:apfinm:v:11:y:2004:i:2:p:185-214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.