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Asia-Pacific Journal of Risk and Insurance

The Official Journal of the Asia-Pacific Risk and Insurance Association

Editor-in-Chief: Kwon, W. Jean

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A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks

Atsuyuki Kogure / Takahiro Fushimi
  • Department of Management Science and Engineering, School of Engineering, Stanford University, California, USA
  • Other articles by this author:
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Published Online: 2017-10-13 | DOI: https://doi.org/10.1515/apjri-2017-0017

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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.

Keywords: longevity derivatives; lee-carter methodology; interest rate risk; CIR model; Bayesian pricing; maximum entropy principle

References

  • Blake, D., Cairns A. J., and Dowd K. 2006a. “Living with Mortality: Longevity Bonds and Other Mortality-Linked Securities.” British Actuarial Journal 12:153–228.CrossrefGoogle Scholar

  • Blake, D., Cairns A. J., and Dowd K. 2006b. “A Two Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration.” Journal of Risk and Insurance 73:687–718.CrossrefGoogle Scholar

  • Booth, H., Mainldonald J., and Smith L. 2002. “Applying Lee-Carter under Conditions of Variable Mortality Decline.” Population Studies 56:325–336.CrossrefGoogle Scholar

  • Cox, J. C., Ingersoll J. E., and Ross S. A. 1985. “A Theory of the Term Structure of Interest Rate.” Econometrica 53:385–407.CrossrefGoogle Scholar

  • Feng, X., and Xie D. 2012. “Bayesian Estimation of CIR Model.” Journal of Data Science 10:271–280.Google Scholar

  • Granados, J. A. 2008. “Macroeconomic Fluctuations and Mortality in Postwar Japan.” Demography 45:323–343.CrossrefGoogle Scholar

  • Jaren, L., and Mamon R. 2009. “Valuation of Contingent Claims with Mortality and Interest Rate Risks.” Mathematical and Computing Modeling 49:1893–1904.CrossrefGoogle Scholar

  • Kim, J., and Li J. 2017. “Risk-Neutral Valuation of the Non-Recourse Protection in Reverse Mortgages: A Case Study for Korea.” Emerging Markets Review 30:133–154.Web of ScienceCrossrefGoogle Scholar

  • Kogure, A., Fushimi T., and Takamatsu Y. 2012. “A Bayesian Multi-Factor Lee-Carter Model Toward Evaluating Longevity Risk,” The 2012 Annual Conference of Asia-Pacific Risk and Insurance Association.Google Scholar

  • Kogure, A., and Kurachi Y. 2010. “A Bayesian Approach to Pricing Longevity Risk Based on Risk Neutral Predictive Distributions.” Insurance: Mathematics and Economics 46:162–172.Google Scholar

  • Kogure, A., Li J., and Kamiya S. Y. 2014. “A Bayesian Multivariate Risk-neutral Method for Pricing Reverse Mortgages.” North American Actuarial Journal 18:242–257.CrossrefGoogle Scholar

  • Lazer, D., and Denuit M. M. 2009. “A Multivariate Time Series Approach to Projected Life Tables.” Applied Stochastic Models in Business and Industry 25:806–823CrossrefWeb of ScienceGoogle Scholar

  • Lee, R. D., and Carter L. R. 1992. “Modeling and Forecasting U.S. Mortality.” Journal of the American Statistical Association 87:659–675.Web of ScienceGoogle Scholar

  • Petris, G., Petrone S., and Campagnoli P. 2009. Dynamic Linear Model with R. Newyork: Springer.Google Scholar

  • Pitacco, E., Denuit M., Haberman S., and Olivieri A. 2009. Modeling Longevity Dynamics for Pensions and Annuity Business. Oxford: Oxford University Press.Google Scholar

  • Renshaw, A. E., and Haberman S. 2003. “Lee-Carter Mortality Forecasting with Age Specific Enhancement.” Insurance: Mathematics and Economics 33:255–272.Google Scholar

  • Shen, Y., and Siu T. K. 2013. “Longevity Bond Pricing Under Stochastic Interest Rate and Mortality with Regime-Switching.” Insurance: Mathematics and Economics 52:114–123.Google Scholar

  • Stutzer, M. 1996. “A Simple Nonparametric Approach to Derivative Security Valuation.” The Journal of Finance 51:1633–1652.CrossrefGoogle Scholar

  • Vasicek, O. 1977. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics 5:177–188.CrossrefGoogle Scholar

  • Wang, S. 2000. “A Class of Distortion Operators for Pricing Financial and Insurance Risks.”Journal of Risk and Insurance 67:15–36.CrossrefGoogle Scholar

About the article

Published Online: 2017-10-13

Citation Information: Asia-Pacific Journal of Risk and Insurance, Volume 12, Issue 1, 20170017, ISSN (Online) 2153-3792, DOI: https://doi.org/10.1515/apjri-2017-0017.

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