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Multivariate Risk-Neutral Pricing of Reverse Mortgages under the Bayesian Framework

Author

Listed:
  • Jackie Li

    (Department of Actuarial Studies and Business Analytics, Macquarie University, Macquarie Park, NSW 2109, Australia)

  • Atsuyuki Kogure

    (Faculty of Business Administration, Tokyo Keizai University, Tokyo 185-8502, Japan)

  • Jia Liu

    (Department of Actuarial Studies and Business Analytics, Macquarie University, Macquarie Park, NSW 2109, Australia)

Abstract

In this paper, we suggest a Bayesian multivariate approach for pricing a reverse mortgage, allowing for house price risk, interest rate risk and longevity risk. We adopt the principle of maximum entropy in risk-neutralisation of these three risk components simultaneously. Our numerical results based on Australian data suggest that a reverse mortgage would be financially sustainable under the current financial environment and the model settings and assumptions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:11-:d:200525
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    References listed on IDEAS

    as
    1. Li, Johnny Siu-Hang, 2010. "Pricing longevity risk with the parametric bootstrap: A maximum entropy approach," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 176-186, October.
    2. Kogure Atsuyuki & Kitsukawa Kenji & Kurachi Yoshiyuki, 2009. "A Bayesian Comparison of Models for Changing Mortalities toward Evaluating Longevity Risk in Japan," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(2), pages 1-22, April.
    3. Marjorie Rosenberg & Virginia Young, 1999. "A Bayesian Approach to Understanding Time Series Data," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 130-143.
    4. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    5. Liang Wang & Emiliano Valdez & John Piggott, 2008. "Securitization of Longevity Risk in Reverse Mortgages," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(4), pages 345-371.
    6. Atsuyuki Kogure & Jackie Li & Shinichi Kamiya, 2014. "A Bayesian Multivariate Risk-Neutral Method for Pricing Reverse Mortgages," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 242-257.
    7. Kogure, Atsuyuki & Kurachi, Yoshiyuki, 2010. "A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 162-172, February.
    8. 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.
    9. Lee, Yung-Tsung & Wang, Chou-Wen & Huang, Hong-Chih, 2012. "On the valuation of reverse mortgages with regular tenure payments," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 430-441.
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    Cited by:

    1. Dixon Domfeh & Arpita Chatterjee & Matthew Dixon, 2022. "A Unified Bayesian Framework for Pricing Catastrophe Bond Derivatives," Papers 2205.04520, arXiv.org.
    2. Tsai, Pei-Hsuan & Wang, Ying-Wei & Chang, Wen-Chang, 2023. "Hybrid MADM-based study of key risk factors in house-for-pension reverse mortgage lending in Taiwan's banking industry," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).
    3. 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.
    4. Kyung Jin Choi & Byungkwon Lim & Jaehwan Park, 2020. "Evaluation of the Reverse Mortgage Option in Korea: A Long Straddle Perspective," IJFS, MDPI, vol. 8(3), pages 1-14, September.
    5. Jackie Li & Atsuyuki Kogure, 2021. "Bayesian Mixture Modelling for Mortality Projection," Risks, MDPI, vol. 9(4), pages 1-12, April.

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