Hostname: page-component-7c8c6479df-24hb2 Total loading time: 0 Render date: 2024-03-28T16:44:14.476Z Has data issue: false hasContentIssue false

NATURAL HEDGES WITH IMMUNIZATION STRATEGIES OF MORTALITY AND INTEREST RATES

Published online by Cambridge University Press:  03 January 2020

Tzuling Lin
Affiliation:
Department of Finance National Chung Cheng UniversityMinhsiung, 62102Taiwan E-Mail: tzuling@ccu.edu.tw
Cary Chi-liang Tsai*
Affiliation:
Department of Statistics and Actuarial Science Simon Fraser UniversityBurnaby BC V5A1S6, Canada E-Mail: cltsai@sfu.ca
*

Abstract

In this paper, we first derive closed-form formulas for mortality-interest durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel movement, respectively, in μ* (the force of mortality-interest), the addition of μ (the force of mortality) and δ (the force of interest). We then build several mortality-interest duration and convexity matching strategies to determine the weights of whole life insurance and deferred whole life annuity products in a portfolio and evaluate the value at risk and the hedge effectiveness of the weighted portfolio surplus at time zero. Numerical illustrations show that using the mortality-interest duration and convexity matching strategies with respect to an instantaneously proportional change in μ* can more effectively hedge the longevity risk and interest rate risk embedded in the deferred whole life annuity products than using the mortality-only duration and convexity matching strategies with respect to an instantaneously proportional shift or an instantaneously constant movement in μ only.

Type
Research Article
Copyright
© Astin Bulletin 2020 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cairns, A.J.G., Blake, D. and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73, 687718.CrossRefGoogle Scholar
Coughlan, G.D., Khalaf-Allah, M., Ye, Y., Kumar, S., Cairns, A.J.G., Blake, D. and Dowd, K. (2011) Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness. North American Actuarial Journal, 15, 150176.CrossRefGoogle Scholar
Courtois, C. and Denuit, M. (2007) On immunizations and s-convex extremal distributions. Annals of Actuarial Science, 2, 6790.CrossRefGoogle Scholar
Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A theory of the term structure of interest rates. Econometrica, 53, 385407.CrossRefGoogle Scholar
Cox, S.H. and Lin, Y. (2007) Natural hedging of life and annuity mortality risks. North American Actuarial Journal, 11(3), 115.CrossRefGoogle Scholar
Einav, L., Finkelstein, A. and Schrimpf, P. (2010) Optimal mandates and the welfare cost of asymmetric information: Evidence from the U.K. annuity market. Econometrica, 78, 10311092.Google ScholarPubMed
Finkelstein, A. and Poterba, J.M. (2002) Selection effects in the United Kingdom individual annuities market. Economic Journal, 112(476), 2850.CrossRefGoogle Scholar
Fisher, L. and Weil, R.L. (1971) Coping with the risk of interest-rate fluctuations: Returns to bondholders from naive and optimal strategies. Journal of Business, 44, 408431.CrossRefGoogle Scholar
Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659671.Google Scholar
Levantesi, S. and Menzietti, M. (2018) Natural hedging in long-term care insurance. ASTIN Bulletin, 48, 233274.CrossRefGoogle Scholar
Li, J.S.H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177200.CrossRefGoogle Scholar
Li, J.S.H. and Luo, A. (2012) Key q-duration: A framework for hedging longevity risk. ASTIN Bulletin, 42, 413452.Google Scholar
Lin, T. and Tsai, C.C.L. (2013) On the mortality/longevity risk hedging with mortality immunization. Insurance: Mathematics and Economics, 53(3), 580596.Google Scholar
Lin, T. and Tsai, C.C.L. (2014) Applications of mortality durations and convexities in natural hedges. North American Actuarial Journal, 18(3), 417442.CrossRefGoogle Scholar
Luciano, E., Regis, L. and Vigna, E. (2017) Single- and cross-generation natural hedging of longevity and financial risk. Journal of Risk and Insurance, 84, 961986.CrossRefGoogle Scholar
MacMinn, R. and Brockett, P. (2017) On the failure (success) of the markets for longevity risk transfer. Journal of Risk and Insurance, 84, 299317.CrossRefGoogle Scholar
Mitchell, O.S., Poterba, J.M., Warshawsky, M.J. and Brown, J.R. (1999) New evidence on the money’s worth of individual annuities. American Economic Review, 89, 12991318.CrossRefGoogle Scholar
Redington, F.M. (1952) Review of the principles of life-office valuations. Journal of the Institute of Actuaries, 78, 286315.CrossRefGoogle Scholar
Shiu, E.S.W. (1987) On the Fisher-Weil immunization theorem, Insurance: Mathematics and Economics, 6, 259266.Google Scholar
Shiu, E.S.W. (1990) On Redington’s theory of immunization. Insurance: Mathematics and Economics, 9, 171175.Google Scholar
Tsai, C.C.L. and Chung, S.L. (2013) Actuarial applications of the linear hazard transform in mortality immunization. Insurance: Mathematics and Economics, 53, 4863.Google Scholar
Tsai, C.C.L. and Yang, S. (2015) A linear regression approach to modeling mortality rates of different forms. North American Actuarial Journal, 19, 123.CrossRefGoogle Scholar
Warshawsky, M.J. (1988) Private annuity markets in the United States: 1919–1984. Journal of Risk and Insurance, 55, 518528.CrossRefGoogle Scholar
Wang, J.L., Huang, H.C., Yang, S.S. and Tsai, J.T. (2010) An optimal product mix for hedging longevity risk in life insurance companies: The immunization theory approach. Journal of Risk and Insurance, 77, 473497.CrossRefGoogle Scholar
Wong, A., Sherris, M. and Stevens, R. (2017) Natural hedging strategies for life insurers: Impact of product design and risk measure. Journal of Risk and Insurance, 84, 153175.CrossRefGoogle Scholar
Zelenko, I. (2014) Longevity risk and the stability of retirement systems: The Chilean longevity bond case. Journal of Alternative Investments, 17(1), 3554.CrossRefGoogle Scholar