NATURAL HEDGES WITH IMMUNIZATION STRATEGIES OF MORTALITY AND INTEREST RATES. Issue 1 (3rd January 2020)

• Record Type: Journal Article
• Authors: Lin, Tzuling; Tsai, Cary Chi-liang
• Is Part Of: ASTIN bulletin. Volume 50:Issue 1(2020)
• Page Start: 155
• Page End: 185
• Publication Date: 2020-01-03
• Subjects: Interest rate risk, -- longevity risk, -- duration, -- convexity, -- natural hedge; Insurance -- Mathematics -- Periodicals; Risk (Insurance) -- Mathematics -- Periodicals; 368.01
• DOI: 10.1017/asb.2019.38
• Languages: English
• ISSNs: 0515-0361

Abstract

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.