TY - JOUR

T1 - Delta-hedging longevity risk under the M7–M5 model

T2 - The impact of cohort effect uncertainty and population basis risk

AU - Zhou, Kenneth Q.

AU - Li, Johnny Siu Hang

N1 - Funding Information:
This work is supported by research grants from the Natural Sciences and Engineering Research Council of Canada (Discovery Grant RGPIN-356050-2013 ) and the Society of Actuaries Center of Actuarial Excellence Program .

PY - 2019/1

Y1 - 2019/1

N2 - In a recent project commissioned by the Institute and Faculty of Actuaries and the Life and Longevity Markets Association, a two-population mortality model called the M7–M5 model is developed and recommended as an industry standard for the assessment of population basis risk. In this paper, we contribute a delta hedging strategy for use with the M7–M5 model, taking into account of not only period effect uncertainty but also cohort effect uncertainty and population basis risk. To enhance practicality, the hedging strategy is formulated in both static and dynamic settings, and its effectiveness can be evaluated in terms of either variance or 1-year ahead Value-at-Risk (the latter is highly relevant to solvency capital requirements). Three real data illustrations are constructed to demonstrate (1) the impact of population basis risk and cohort effect uncertainty on hedge effectiveness, (2) the benefit of dynamically adjusting a delta longevity hedge, and (3) the relationship between risk premium and hedge effectiveness.

AB - In a recent project commissioned by the Institute and Faculty of Actuaries and the Life and Longevity Markets Association, a two-population mortality model called the M7–M5 model is developed and recommended as an industry standard for the assessment of population basis risk. In this paper, we contribute a delta hedging strategy for use with the M7–M5 model, taking into account of not only period effect uncertainty but also cohort effect uncertainty and population basis risk. To enhance practicality, the hedging strategy is formulated in both static and dynamic settings, and its effectiveness can be evaluated in terms of either variance or 1-year ahead Value-at-Risk (the latter is highly relevant to solvency capital requirements). Three real data illustrations are constructed to demonstrate (1) the impact of population basis risk and cohort effect uncertainty on hedge effectiveness, (2) the benefit of dynamically adjusting a delta longevity hedge, and (3) the relationship between risk premium and hedge effectiveness.

KW - Cohort effect

KW - Delta hedging

KW - Population basis risk

KW - The M7–M5 model

KW - Value-at-risk

UR - http://www.scopus.com/inward/record.url?scp=85056612164&partnerID=8YFLogxK

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U2 - 10.1016/j.insmatheco.2018.10.003

DO - 10.1016/j.insmatheco.2018.10.003

M3 - Article

AN - SCOPUS:85056612164

VL - 84

SP - 1

EP - 21

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

ER -