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A Bayesian Pricing of Longevity Derivatives with Interest Rate Risks

Kogure Atsuyuki () and Fushimi Takahiro
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Kogure Atsuyuki: Faculty of Policy Management, Keio UniversityTokyo, Japan
Fushimi Takahiro: Department of Management Science and Engineering, School of Engineering, Stanford University, California, USA

Asia-Pacific Journal of Risk and Insurance, 2018, vol. 12, issue 1, 30

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 (search for similar items in EconPapers)
Date: 2018
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