IDEAS home Printed from https://ideas.repec.org/a/bpj/apjrin/v12y2018i1p30n4.html
   My bibliography  Save this article

A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks

Author

Listed:
  • Kogure Atsuyuki

    (Faculty of Policy Management, Keio UniversityTokyo, Japan)

  • Fushimi Takahiro

    (Department of Management Science and Engineering, School of Engineering, Stanford University, California, USA)

Abstract

Mortality-linked securities such as longevity bonds or longevity swaps usually depend on not only mortality risk but also interest rate risk. However, in the existing pricing methodologies, it is often the case that only the mortality risk is modeled to change in a stochastic manner and the interest rate is kept fixed at a pre-specified level. In order to develop large and liquid longevity markets, it is essential to incorporate the interest rate risk into pricing mortality-linked securities. In this paper we tackle the issue by considering the pricing of longevity derivatives under stochastic interest rates following the CIR model. As for the mortality modeling, we use a two-factor extension of the Lee-Carter model by noting the recent studies which point out the inconsistencies of the original Lee-Carter model with observed mortality rates due to its single factor structure. To address the issue of parameter uncertainty, we propose using a Bayesian methodology both to estimate the models and to price longevity derivatives in line with (Kogure, A., and Y. Kurachi. 2010. “A Bayesian Approach to Pricing Longevity Risk Based on Risk Neutral Predictive Distributions.” Insurance: Mathematics and Economics 46:162–172) and (Kogure, A., J. Li, and S. Y. Kamiya. 2014. “A Bayesian Multivariate Risk-neutral Method for Pricing Reverse Mortgages.” North American Actuarial Journal 18:242–257). We investigate the actual effects of the incorporation of the interest rate risk by applying our methodology to price a longevity cap with Japanese data. The results show significant differences according to whether the CIR model is used or the interest rate is kept fixed.

Suggested Citation

  • Kogure Atsuyuki & Fushimi Takahiro, 2018. "A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 12(1), pages 1-30, January.
    • Handle: RePEc:bpj:apjrin:v:12:y:2018:i:1:p:30:n:4
    DOI: 10.1515/apjri-2017-0017
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/apjri-2017-0017
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/apjri-2017-0017?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. 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.
    2. Shen, Yang & Siu, Tak Kuen, 2013. "Longevity bond pricing under stochastic interest rate and mortality with regime-switching," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 114-123.
    3. 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.
    4. José Tapia granados, 2008. "Macroeconomic fluctuations and mortality in postwar Japan," Demography, Springer;Population Association of America (PAA), vol. 45(2), pages 323-343, May.
    5. 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.
    6. Stutzer, Michael, 1996. "A Simple Nonparametric Approach to Derivative Security Valuation," Journal of Finance, American Finance Association, vol. 51(5), pages 1633-1652, December.
    7. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    8. 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.
    9. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
    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. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    2. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    3. Yang, Bowen & Li, Jackie & Balasooriya, Uditha, 2015. "Using bootstrapping to incorporate model error for risk-neutral pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 16-27.
    4. 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.
    5. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 485564, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    6. Chen, Hua & MacMinn, Richard & Sun, Tao, 2015. "Multi-population mortality models: A factor copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 135-146.
    7. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    8. Jackie Li & Atsuyuki Kogure, 2021. "Bayesian Mixture Modelling for Mortality Projection," Risks, MDPI, vol. 9(4), pages 1-12, April.
    9. Li, Hong & De Waegenaere, Anja & Melenberg, Bertrand, 2015. "The choice of sample size for mortality forecasting: A Bayesian learning approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 153-168.
    10. Karim Barigou & Stéphane Loisel & Yahia Salhi, 2020. "Parsimonious Predictive Mortality Modeling by Regularization and Cross-Validation with and without Covid-Type Effect," Risks, MDPI, vol. 9(1), pages 1-18, December.
    11. Geng Niu & Bertrand Melenberg, 2014. "Trends in Mortality Decrease and Economic Growth," Demography, Springer;Population Association of America (PAA), vol. 51(5), pages 1755-1773, October.
    12. Leung, Melvern & Li, Youwei & Pantelous, Athanasios A. & Vigne, Samuel A., 2021. "Bayesian Value-at-Risk backtesting: The case of annuity pricing," European Journal of Operational Research, Elsevier, vol. 293(2), pages 786-801.
    13. 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.
    14. Alonso, Pablo J., 2015. "Hierarchical Lee-Carter model estimation through data cloning applied to demographically linked countries," DES - Working Papers. Statistics and Econometrics. WS ws1510, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Li, Hong & Tan, Ken Seng & Tuljapurkar, Shripad & Zhu, Wenjun, 2021. "Gompertz law revisited: Forecasting mortality with a multi-factor exponential model," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 268-281.
    16. Moshe A. Milevsky & Thomas S. Salisbury & Alexander Chigodaev, 2018. "The implied longevity curve: How long does the market think you are going to live?," Papers 1811.09932, arXiv.org.
    17. Christiansen, Marcus C. & Niemeyer, Andreas & Teigiszerová, Lucia, 2015. "Modeling and forecasting duration-dependent mortality rates," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 65-81.
    18. David Blake & Andrew Cairns & Guy Coughlan & Kevin Dowd & Richard MacMinn, 2013. "The New Life Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 501-558, September.
    19. Raimond Maurer & Olivia S. Mitchell & Ralph Rogalla & Vasily Kartashov, 2013. "Lifecycle Portfolio Choice With Systematic Longevity Risk and Variable Investment—Linked Deferred Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 649-676, September.
    20. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2015. "A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing," Papers 1508.00322, arXiv.org.

    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:bpj:apjrin:v:12:y:2018:i:1:p:30:n:4. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.