新冠肺炎对最佳估计死亡率假设的影响

MILLIMANWHITE PAPER Impact of COVID-19 on bestestimate mortality assumptions Adjustmentof COVID-19mortality datapointsImpact on the calibration of mortality models Flora AuterAmal ElfassihiSalima El KhababiJan Thiemen PostemaEve-Elisabeth TitonRaymond van Es Following the COVID-19 pandemicwhichkilledmorethan7millionpeople worldwide, the mortality data relative to the years 2020 to 2022 isnotdirectlyusable for updating the calibration of stochasticmortalitymodels or Solvency II internal model calibrations for mortality andlongevity risks. In this paper,several approachesare presentedtoadjustCOVID-19mortalitydata points prior to the calibration of mortalitymodels.We thendiscuss their impact onmortality projections and shocks. Various national and statistical institutes haverecordedthe number of deaths attributable to COVID-19.Thesedeathscorrespond to the excess mortality caused by the pandemic, where excess mortality is the differencebetween the mortality that occurred and the expected mortality. These COVID-19 death dataarehighlydependent on how deaths are counted and correspond only to the direct effect of the pandemic on mortality.Thisdirect effect may be overestimated in some countries, especially those with intensive testing and highsensitisation and/or incentives for COVID-19 diagnoses, or underestimated in other countries, especially inAfrica.1Inaddition to theCOVID-19 direct effects, which are the deaths caused by the virus,there arealsoindirect effects such as thedecreasein the number of deathsdue toother viruses such as influenza,or thepostponement ofsomesurgical operations. Insurersand reinsurers have severaloptionsto update thecalibration of theirmortalityand longevitymodelsconsidering the COVID-19 experience.One option is to changethemodelcalibration process,e.g.,byintroducingaweighting mechanismthat allowsless weightto be placedon years withunusualmortalityexperience.For instance,the2022CMI(Continuous Mortality Investigation)Core Model considerssuch amechanism and putsa0% weight on the 2020and2021 mortality datayears, a 25% weighton the year2022,anda100% weight on all other yearsincluded in the calibration period.2 Dataadjustmentoptions canalsobeusedtodeterminea reference mortality levelwithout the short-term effectsof theCOVID-19 pandemic, andthis option will be explored in the rest of ourpaper.Note that the long-termeffects of COVID-19on the non-pandemic mortalityand,in particular,long COVID arealsonotconsideredin ourapproach.The most robust and reliable approachesto quantify theexcessmortality due to short-term risk factorssuch as COVID-19 arebased on estimating weekly excess mortality, unlikethose only based on official COVID-19 death counts.Theymakeit possible toexcludebothpositive and negative indirect effects of COVID-19, e.g.,thepostponements of surgical operationsor thedecrease in the number of seasonalinfluenzacases.This kind ofadjustmentis useful for different applications, such as avoiding double counting ininternalmodels where it istaken into account in the pandemic module (along with its consequences), or to avoid distortions on forecasts forinsured portfoliomortality since the models are not designed to capture such one-off/irregular effects. In thenext section, we present a methodology toadjustCOVID-19 mortality data points prior to the calibration ofmortality models. The data required and the modelling framework are describedfirst,and thenthe theory behindthe adjustment methodswill beexplained. The results for some countries for whichHuman Mortality Database(HMD)data are available are presented, followed by the results of a study of mortality rates in the Netherlands.Finally, we present alternative calibration strategies to model mortality considering the COVID-19 experience. Note that the models and projections do not take into account other effects on mortality, such as the evolution ofneurodegenerative diseases or the opioid crisis, which are not the focus of the work presented here.Theseeffects can be studied by modelling mortality by cause of death.3 Methodology DATA Thestudy is based on theuse of the following mortality databases: TheHuman Mortality Database:4The HMD is a joint initiative of the Department of Demography at theUniversity of California at Berkeley in the United States and the Max Planck Institute for DemographicResearch in Rostock in Germany.It was created in 2000 with the objective of bringing together detailedpopulation mortality dataandto serveas a reference for anyone interested in human longevity. It containsdatafor almost 40 countries or areasin the form of periodic tables by year, age and sex, and also in the formof cohort tables. TheShort-TermMortalityFluctuations(STMF)dataseries:5This dataresourcehas been created toprovide data for scientific analysis of all-cause mortality fluctuations by week within each calendar year. Thedecision to add this new resource to the HMD was triggered by the COVID-19 pandemic. An additionalmotivation f