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An Option-Theoretic Prepayment Model For Mortgages And Mortgage-Backed Securities

Author

Listed:
  • ANDREW KALOTAY

    (Andrew Kalotay Associates, Inc, 61 Broadway, Suite 1400, New York, NY 10006, USA)

  • DEANE YANG

    (Polytechnic University, Brooklyn, New York 11201, USA)

  • FRANK J. FABOZZI

    (School of Management, Yale University, New Haven, CT 06520, USA)

Abstract

We introduce a new approach for modeling the prepayments of a mortgage pool and show how it can be used to value mortgage pools and agency mortgage-backed securities. We describe the full spectrum of refinancing behavior using a notion of refinancing efficiency. Our approach has two distinguishing features: (1) our primary focus is on understanding the market value of a mortgage, in contrast with standard models that strive (often unsuccessfully) to predict future cash flows, and (2) we use two separate yield curves, one for modeling mortgage cash flows and the other for MBS cash flows.

Suggested Citation

  • Andrew Kalotay & Deane Yang & Frank J. Fabozzi, 2004. "An Option-Theoretic Prepayment Model For Mortgages And Mortgage-Backed Securities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(08), pages 949-978.
  • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:08:n:s0219024904002785
    DOI: 10.1142/S0219024904002785
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    References listed on IDEAS

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    8. Stanton, Richard, 1995. "Rational Prepayment and the Valuation Mortgage-Backed Securities," Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 677-708.
    9. Klaus Sandmann & Dieter Sondermann, 1997. "A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 119-125, April.
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    Cited by:

    1. Bilgi Yilmaz & A. Sevtap Selcuk-Kestel, 2019. "Computation of Hedging Coefficients for Mortgage Default and Prepayment Options: Malliavin Calculus Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 59(4), pages 673-697, November.
    2. Matteo Bissiri & Riccardo Cogo, 2017. "Behavioral Value Adjustments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-37, December.
    3. 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.
    4. Christopoulos, Andreas D. & Jarrow, Robert A., 2018. "CMBS market efficiency: The crisis and the recovery," Journal of Financial Stability, Elsevier, vol. 36(C), pages 159-186.
    5. G. Rigatos & P. Siano, 2018. "Stabilization of Mortgage Price Dynamics Using a Boundary PDE Feedback Control Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(1), pages 37-56, March.
    6. Xiaoxia Wu & Dejun Xie & David A. Edwards, 2019. "An Optimal Mortgage Refinancing Strategy with Stochastic Interest Rate," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1353-1375, April.
    7. Yerkin Kitapbayev & Scott Robertson, 2020. "Mortgage Contracts and Underwater Default," Papers 2005.03554, arXiv.org, revised May 2022.
    8. Sumit Agarwal & John C. Driscoll & David I. Laibson, 2013. "Optimal Mortgage Refinancing: A Closed‐Form Solution," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(4), pages 591-622, June.
    9. Yusuf VARLI & Gökhan ÖVENÇ, 2019. "Dynamic Analysis of Defaults and Prepayments in the Turkish Mortgage Market," Sosyoekonomi Journal, Sosyoekonomi Society, issue 27(39).
    10. Eickholt, Mathias & Entrop, Oliver & Wilkens, Marco, 2014. "Individual investors and suboptimal early exercises in the fixed-income market," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe 14, University of Passau, Faculty of Business and Economics.
    11. Zhe Cheng & Scott Robertson, 2017. "Endogenous current coupons," Finance and Stochastics, Springer, vol. 21(4), pages 1027-1071, October.
    12. Scott Robertson & Zhe Cheng, 2015. "Endogenous Current Coupons," Papers 1510.02010, arXiv.org.
    13. Emanuele Casamassima & Lech A. Grzelak & Frank A. Mulder & Cornelis W. Oosterlee, 2021. "Pricing and Hedging Prepayment Risk in a Mortgage Portfolio," Papers 2109.14977, arXiv.org, revised Oct 2021.
    14. 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.
    15. 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.
    16. Agarwal, Sumit & Driscoll, John D. & Laibson, David I., 2012. "Optimal Mortgage Reï¬ nancing: A Closed Form Solution," Scholarly Articles 9918811, Harvard University Department of Economics.
    17. Giulia De Rossi & Tiziano Vargiolu, 2010. "Optimal prepayment and default rules for mortgage-backed securities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 23-47, May.
    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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