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NATURAL HEDGES WITH IMMUNIZATION STRATEGIES OF MORTALITY AND INTEREST RATES

Published online by Cambridge University Press:  03 January 2020

Tzuling Lin  and
Cary Chi-liang Tsai
Tzuling Lin
Affiliation:
Department of Finance National Chung Cheng UniversityMinhsiung, 62102Taiwan E-Mail: [email protected]
Cary Chi-liang Tsai*
Affiliation:
Department of Statistics and Actuarial Science Simon Fraser UniversityBurnaby BC V5A1S6, Canada E-Mail: [email protected]
*
E-Mail: [email protected]
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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.

Keywords

Interest rate risklongevity riskdurationconvexitynatural hedge
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 1 , January 2020 , pp. 155 - 185
Copyright
© Astin Bulletin 2020 

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