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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
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    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. 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.
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