IDEAS home Printed from https://ideas.repec.org/a/cup/anacsi/v6y2012i02p235-257_00.html
   My bibliography  Save this article

A Semi-Markov Multiple State Model for Reverse Mortgage Terminations

Author

Listed:
  • Ji, Min
  • Hardy, Mary
  • Li, Johnny Siu-Hang

Abstract

Reverse mortgages provide a mechanism for seniors to release the equity that has been built up in their home. At termination, the mortgagors are usually guaranteed to owe no more than the value of their property. The value of the reverse mortgage guarantee is heavily dependent on the maturity or termination date, which is uncertain. In this paper, we model reverse mortgage terminations using a semi-Markov multiple state model which incorporates three different modes of exit: death, entrance into a long-term care facility, and voluntary prepayment. We apply the proposed model specifically to develop the valuation formulas for roll-up mortgages in the UK and Home Equity Conversion Mortgages (HECMs) in the USA. We examine the significance of each mode of termination by valuing the contracts allowing progressively for each mode. On the basis of our model and assumptions, we find that both health related terminations and voluntary (non-health related) terminations significantly impact the contract value. In addition we analyze the premium structure for US reverse mortgage insurance, and demonstrate that premiums appear to be too high for some borrowers, and substantial cross-subsidies may result.

Suggested Citation

  • Ji, Min & Hardy, Mary & Li, Johnny Siu-Hang, 2012. "A Semi-Markov Multiple State Model for Reverse Mortgage Terminations," Annals of Actuarial Science, Cambridge University Press, vol. 6(2), pages 235-257, September.
  • Handle: RePEc:cup:anacsi:v:6:y:2012:i:02:p:235-257_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S1748499512000061/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shao, Adam W. & Hanewald, Katja & Sherris, Michael, 2015. "Reverse mortgage pricing and risk analysis allowing for idiosyncratic house price risk and longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 76-90.
    2. Emilia Lorenzo & Gabriella Piscopo & Marilena Sibillo & Roberto Tizzano, 2021. "Reverse mortgages through artificial intelligence: new opportunities for the actuaries," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 23-35, June.
    3. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    4. Carole Bernard & Adam Kolkiewicz & Junsen Tang, 2023. "Valuation of Reverse Mortgages with Default Risk Models," The Journal of Real Estate Finance and Economics, Springer, vol. 66(4), pages 806-839, May.
    5. Shu Ling Chiang & Ming Shann Tsai & Chien An Wang, 2021. "Determining an Optimal Principal Limit Factor for Reverse Mortgages under Economics-Based Models," The Journal of Real Estate Finance and Economics, Springer, vol. 63(4), pages 565-597, November.
    6. Fuino, Michel & Wagner, Joël, 2018. "Long-term care models and dependence probability tables by acuity level: New empirical evidence from Switzerland," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 51-70.
    7. Yung-Tsung Lee & Tianxiang Shi, 2022. "Valuation of Reverse Mortgages with Surrender: A Utility Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 65(4), pages 593-621, November.
    8. Manuel Ventura-Marco & Carlos Vidal-Meliá & Juan Manuel Pérez-Salamero González, 2022. "Life care annuities to help couples cope with the cost of long-term care," Documentos de Trabajo del ICAE 2022-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    9. Shi, Tianxiang & Lee, Yung-Tsung, 2021. "Prepayment risk in reverse mortgages: An intensity-governed surrender model," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 68-82.
    10. Kim, Joseph H.T. & Li, Johnny S.H., 2017. "Risk-neutral valuation of the non-recourse protection in reverse mortgages: A case study for Korea," Emerging Markets Review, Elsevier, vol. 30(C), pages 133-154.
    11. Jackie Li & Atsuyuki Kogure & Jia Liu, 2019. "Multivariate Risk-Neutral Pricing of Reverse Mortgages under the Bayesian Framework," Risks, MDPI, vol. 7(1), pages 1-12, January.
    12. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2017. "Insuring wind energy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 542-553.
    13. Shao, Adam W. & Chen, Hua & Sherris, Michael, 2019. "To borrow or insure? Long term care costs and the impact of housing," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 15-34.
    14. Ventura-Marco, Manuel & Vidal-Meliá, Carlos & Pérez-Salamero González, Juan Manuel, 2023. "Joint life care annuities to help retired couples to finance the cost of long-term care," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 122-139.

    More about this item

    Statistics

    Access and download statistics

    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:cup:anacsi:v:6:y:2012:i:02:p:235-257_00. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/aas .

    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.