Investment guarantees

358 Pages·2003·3.17 MB·English

by  Mary Hardy

Investment
Guarantees
Modeling and Risk Management for
Equity-Linked Life Insurance
MARY HARDY
John Wiley & Sons, Inc.

Investment
Guarantees
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Investment
Guarantees
Modeling and Risk Management for
Equity-Linked Life Insurance
MARY HARDY
John Wiley & Sons, Inc.
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Hardy,Mary,1958-
Investmentguarantees:modelingandriskmanagementforequity-linkedlifeinsurance/
MaryHardy.
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Includesbibliographicalreferencesandindex.
ISBN0-471-39290-1(cloth:alk.paper)
1.Insurance,Life-mathematicalmodels.2.Riskmanagement–Mathematicalmodels.
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HG8781.H3132003
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Acknowledgments
T
his work has been supported by the National Science and Engineering
Research Council of Canada, and by the Actuarial Education and
Research Fund. I would also like to thank the members of the Department
of Statistics at the London School of Economics and Political Science for
their hospitality while the book was being completed, especially Anthony
Atkinson,AngelosDassios,MartinKnott,andRagnarNorberg.
IwouldliketothankTaylorandFrancis,publishersoftheScandinavian
ActuarialJournal,forpermissiontoreproducematerialfromBayesianRisk
ManagementforEquity-LinkedInsuranceinChapter5.
I learned a great deal from my fellow members of the magnificent
CanadianInstituteofActuariesTaskForceonSegregatedFunds.Inpartic-
ular,IwouldliketothankGeoffreyHancock,whohasprovidedinvaluable
advice and assistance during the preparation of this book. Also, thanks to
Martin Le Roux, David Gilliland, and the two Chairs, Simon Curtis and
MurrayTaylor,whohadalottoputupwith,notleastfromme.
Ihavebeenveryluckytoworkwithsomewonderfulcolleaguesandstu-
dentsovertheyears,manyofwhomhavecontributeddirectlyorindirectly
to this book. In particular, thanks to Andrew Cairns, Julia Wirch, David
Wilkie,JudithChan,KarenChau,GeoffThiessen,YuanTao,So-YuenKim,
AnpingWang,BoyangLiu,HarryPanjer,andSheauwenYang.Thanksalso
to Glen Harris, who introduced me to regime-switching models. It is a
special privilege to work with Ken Seng Tan at the University of Waterloo
andwithHowardWatersatHeriot-WattUniversity.
Mybrother,PeterHardy,workedwithmetopreparetheRSLNsoftware
(HardyandHardy2002),whichisausefulcomplementtothiswork.Itwas
goodfunworkingwithhim.
Mostly I would like to express my deepest gratitude to my husband,
Phelim Boyle, for his unstinting encouragement, support, and patience;
culinary contributions; and unwavering readiness to share with me his
encyclopedicknowledgeoffinance.
M.H.
v

Contents
Introduction xi
CHAPTER 1
Investment Guarantees 1
Introduction 1
MajorBenefitTypes 4
ContractTypes 5
Equity-LinkedInsuranceandOptions 7
ProvisionforEquity-LinkedLiabilities 11
PricingandCapitalRequirements 14
CHAPTER 2
Modeling Long-Term Stock Returns 15
Introduction 15
DeterministicorStochastic? 15
EconomicalTheoryorStatisticalMethod? 17
TheData 18
TheLognormalModel 24
AutoregressiveModels 27
ARCH(1) 28
Regime-SwitchingLognormalModel(RSLN) 30
TheEmpiricalModel 36
TheStableDistributionFamily 37
GeneralStochasticVolatilityModels 38
TheWilkieModel 39
VectorAutoregression 45
CHAPTER 3
Maximum Likelihood Estimation for Stock Return Models 47
Introduction 47
PropertiesofMaximumLikelihoodEstimators 49
SomeLimitationsofMaximumLikelihoodEstimation 52
vii