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Pricing Mortgage-Backed Securities-First Hitting Time Approach

Author

Listed:
  • Jing-Tang Tsay

    () (National Taipei University of Business)

  • Che-Chun Lin

    () (National Tsing Hua University)

  • Jerry T. Yang

    () (National United University)

Abstract

This paper develops a pricing model and derives a closed-form formula for valuing mortgage-backed securities (MBSs) that embed a barrier option feature while the optimal prepayment or refinancing choices of borrowers are endogenously determined. Given that ¡§real estate investors¡¨ tend to prepay a loan relentlessly, an MBS with a high concentration of investor borrowers implies a lower MBS value. We specify the prepayment behavior of borrowers by using the first hitting time as a proxy for the trigger point of prepayment when house prices or interest rates hit a pre-determined barrier. Our results show that the MBS value is positively related to loan to value and house price volatility while negatively related to the proportion of real estate investors and interest rate volatility. We also find evidence which shows that the MBS value may increase due to the effects of the ¡§longevity¡¨ of mortgages, which outweigh the effects of default or prepayment as house price volatility increases. This model provides a faster pricing tool of MBSs than Monte Carlo simulation while retaining higher model accuracy and consistency than the hazard model approach.

Suggested Citation

  • Jing-Tang Tsay & Che-Chun Lin & Jerry T. Yang, 2018. "Pricing Mortgage-Backed Securities-First Hitting Time Approach," International Real Estate Review, Asian Real Estate Society, vol. 21(4), pages 419-446.
  • Handle: RePEc:ire:issued:v:21:n:04:2018:p:419-446
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    References listed on IDEAS

    as
    1. Hans U. Gerber & Hlias S. W. Shiu, 1996. "Martingale Approach To Pricing Perpetual American Options On Two Stocks," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 303-322, July.
    2. Tyler Yang & Che-Chun Lin & Man Cho, 2011. "Collateral Risk in Residential Mortgage Defaults," The Journal of Real Estate Finance and Economics, Springer, vol. 42(2), pages 115-142, February.
    3. Fabrice Barthélémy & Jean-Luc Prigent, 2009. "Optimal Time to Sell in Real Estate Portfolio Management," The Journal of Real Estate Finance and Economics, Springer, vol. 38(1), pages 59-87, January.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    6. Gerber, Hans U. & Shiu, Elias S.W., 1994. "Martingale Approach to Pricing Perpetual American Options," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(02), pages 195-220, November.
    7. Dunn, Kenneth B & McConnell, John J, 1981. "Valuation of GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 36(3), pages 599-616, June.
    8. Sheldon Lin, X., 1998. "Double barrier hitting time distributions with applications to exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 45-58, October.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Mortgage-Backed Security; First Hitting Time; Prepayment; Default;

    JEL classification:

    • L85 - Industrial Organization - - Industry Studies: Services - - - Real Estate Services

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