Structured Life Insurance and Investment Products for Retail Investors [Elektronische Ressource] / Judith-Christiane Schneider. Gutachter: Joachim Prinz. Betreuer: Antje Mahayni

Description

STRUCTURED LIFE INSURANCE ANDINVESTMENT PRODUCTS FOR RETAILINVESTORSVON DER MERCATOR SCHOOL OF MANAGEMENT¨ ¨ ¨- FAKULTAT FUR BETRIEBSWIRTSCHAFTSLEHRE- DER UNIVERSITATDUISBURG-ESSENZUR ERLANGUNG DES AKADEMISCHEN GRADESEINES DOKTORS DER WIRTSCHAFTSWISSENSCHAFTEN (DR. RER. OEC.)GENEHMIGTE DISSERTATIONVONJUDITH CHRISTIANE SCHNEIDERAUS BONNREFERENT: PROF. DR. ANTJE MAHAYNIKORREFERENT: PROF. DR. JOACHIM PRINZ¨ ¨TAG DER MUNDLICHEN PRUFUNG: 15.03.2011AcknowledgementsForemost, I thank my supervisor Prof. Dr. Antje Mahayni who was not only a men-tor/leader for my academic studies giving me various assistance, suggestions and ad-vice, but Prof. Dr. Antje Mahayni also creates a fantastic atmosphere in her departmentwhich supports effective, efficient and delightful researching. Without this my PhDcould not have run so smoothly. Moreover, I had the honor to be a co-author and toprofit from Prof. Dr. Antje Mahaynis creative ideas, excellence and experience. I haveto express my deepest gratitude!Likewise, I thank another co-author Prof. Dr. Nicole Branger. Besides having suchan excellent co-author in her, I also had the opportunity to gain from her knowledgeduring the Summer School 2008 in Naurod and our various other meetings during thedoctoral seminars. Her enthusiasm and passion in research are exceptional. Thank you!Moreover, amongst the people who gave me valuable supports and comments, I liketo thank in particular Prof. Dr. Annette Kohler¨ , Prof. Dr.

Informations

• Publié par: universitat_duisburg-essen
• Publié le: 01 janvier 2011
• Nombre de lectures: 63
• Poids de l'ouvrage: 1 Mo

Extrait

STRUCTUREDLIFEINSURANCEAND
INVESTMENTPRODUCTSFORRETAIL
INVESTORS

VONDERMERCATORSCHOOLOFMANAGEMENT
-FAKULTA¨TFU¨RBETRIEBSWIRTSCHAFTSLEHRE-DERUNIVERSITA¨T
DUISBURG-ESSEN
ZURERLANGUNGDESAKADEMISCHENGRADES
EINESDOKTORSDERWIRTSCHAFTSWISSENSCHAFTEN(DR.RER.OEC.)
GENEHMIGTEDISSERTATION
NOVJUDITHCHRISTIANESCHNEIDER
AUSBONN

REFERENT:PROF.DR.ANTJEMAHAYNI
KORREFERENT:PROF.DR.JOACHIMPRINZ
TAGDERMU¨NDLICHENPRU¨FUNG:15.03.2011

wledgementsAckno

Ftor/leaderoremost,IforthankmymyacademicsupervisorstudiesProf.givingDr.meAntjevariousMahayniassistance,whowasnotsuggestionsonlyaandmen-ad-
vice,whichbutsupportsProf.Dref.fectiAntjeve,efMahaynificientalsoandcreatesdelightfulafantasticresearching.atmosphereWithoutinherthismydepartmentPhD
couldnothaverunsosmoothly.Moreover,Ihadthehonortobeaco-authorandto
profitfromProf.Dr.AntjeMahayniscreativeideas,excellenceandexperience.Ihave
toexpressmydeepestgratitude!

aneLikexcellentwise,Ithankco-authorinanotherher,Ico-authoralsohadProf.theDr.opportunityNicoletoBrangergain.fromBesidesherhaknovingwledgesuch
duringdoctoraltheseminars.SummerHerSchoolenthusiasm2008inandNaurodpassionandinourvresearchariousareeotherxceptionalmeetings.Thankduringyou!the

tothankMoreoinver,particularamongstProf.theDr.peopleAnnettewhogKa¨veohlerme,vProf.aluableDr.JoachimsupportsPriandnz,Prof.comments,Dr.IKlauslike
neckiSandmannand-themycolleaguesDiplomaandsupervisorfriends-,fromProf.theDr.UniJensvSersity¨udekum,ofBonnDr.andMichaeltheLogisticSucha-
Dr.SvDepartmentenBalderof,theUniSusanneversityBrand,ofDuisbSarahurBrand,g-Essen.DanielSpecialSteuten,thanksgoDanieltomySchwake,colleaguesTim
whoPetershavandealsoDanielbecomeZielingfriends.fromtheDepartmentofInsuranceandRiskManagement

supportLastbutduringnotmyleast,Ieducationwishtoandtfarhankbemyyond.fYamilyou,areinallparticulardeartomymyheart!mother,fortheir

v

Contents

1IntroductionandMotivation.......................................

PartIStructuredLifeInsuranceProducts

2StructuredLifeInsuranceProducts:ASurvey.......................
2.1Introduction...................................................
2.1.1Fromclassicallifeinsurancetostructuredlifeinsuranceproducts
2.1.2Characteristicsofstructuredlifeinsuranceproducts............
2.2Classificationoftherelevantliterature.............................
2.2.1Modelchoice............................................
2.2.2Riskmanagement........................................
2.2.3Additionalridersandtheirpricingandriskmanagement........
2.3Interactionbetweeninsurancecompanyandinsured.................
2.4Conclusion...................................................

3OptimalDesignofInsuranceContractswithGuarantees..............
3.1Introduction...................................................
3.2Productdesign................................................
3.3Financialmarketandinvestmentstrategies.........................
3.3.1Completefinancialmarketmodel...........................
3.3.2Investmentstrategies......................................
3.3.3Pricingoftheembeddedoptions............................
3.3.4Analysisandillustrationoffairinsurancepayoffs..............
3.4Optimalinsurancecontractandbenchmarkutility...................
3.4.1Utilityloss..............................................
3.4.2Comparisonoftheutilitylosses.............................
3.5Conclusion...................................................

4VariableAnnuitiesandtheOptiontoseekrisk:Whyshouldyou
diversify?........................................................
4.1Introduction...................................................
4.2Contractspecification,modelsetupandpricing.....................
4.3Optimalchoiceofinvestmentstrategyunderbackgroundrisk.........

1

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313134383839414345474851

53535762

vii

viii

Contentsviii4.3.1Comparisonofputprices..................................64
4.3.2Backgroundrisk,generalizedconstantmixstrategiesand
optimality...............................................66
4.3.3Borrowingconstraints.....................................70
4.4NumericalIllustration..........................................71
4.4.1Comparisonofputprices..................................72
4.4.2Utilityloss..............................................74
4.4.3Realisticexample.........................................77
4.5Conclusion...................................................79
PartIIStructuredInvestmentProducts
5PricingandUpperPriceBoundsofRelaxCertificates.................83
5.1Introduction...................................................83
5.2Productspecification...........................................87
5.2.1Productspecification......................................87
5.2.2Attractiverelaxcertificates.................................88
5.3Risk-neutralpricingandupperpricebounds........................90
5.3.1Risk-neutralpricingofrelaxcertificates......................90
5.3.2Upperpriceboundsbasedoncouponbonds...................92
5.3.3Upperpriceboundsbasedonsmallerrelaxcertificates........94
5.4Numericalexamples............................................97
5.4.1Risk-neutralmeasure......................................97
5.4.2Pricesofrelaxcertificates..................................98
5.5Marketcomparison............................................107
5.5.1Contractspecifications....................................107
5.5.2Survivalprobabilitiesandpricebounds......................107
5.6Conclusion...................................................110
6Sub-optimalinvestmentstrategiesandmispricedputoptionsunder
borrowingconstraints.............................................113
6.1Introduction...................................................113
6.2Optimalportfolioselectionwithterminalwealthguaranteeand
borrowingconstraints...........................................115
6.2.1CRRAUtility............................................117
6.2.2HARAUtility............................................121
6.3Utilityloss....................................................125
6.3.1Utilitylosscausedbytheguaranteeandborrowingconstraints...127
6.3.2UtilitylosscausedbyCPPI................................128
6.3.3Mispricedputoptionsvs.suboptimalinvestmentstrategies......129
6.4Conclusion...................................................130
7ConclusionandFutureResearch...................................133

Contents

ix

AAppendix........................................................137
A.1AppendixChapter4............................................137
A.1.1ProofofTheorem4.1.....................................137
A.1.2ProofofProposition4.2...................................138
A.1.3ProofofProposition4.3...................................139
A.1.4ProofofProposition4.4...................................140
A.2AppendixChapter5............................................141
A.2.1FirstHittingTime-One-DimensionalCase...................141
A.2.2FirstHittingTime–TwoDimensionalCase..................143
A.3AppendixChapter6............................................146
A.3.1ProofofProposition6.1...................................146

Bibliography.........................................................147
References........................................................147

ablesTofList

2.12.22.32.42.5

3.13.2

4.14.24.3

5.15.2

6.16.2

Productfeatures...............................................12
Modelchoice.................................................17
Problemsinriskmanagement....................................19
Riskmanagement..............................................22
Additionalriders...............................................26

Investmentstrategies...........................................39
Lossratesandoptimalinvestmentfractions........................51

Benchmarkmodelandcontractparameters.........................61
IncomeandPensionParameters..................................78
TheTablegivesthelossratesofthelow,mediumandhigh
GMAB-investorforvaryingriskaversionlevelsγinbasispoints.The
parametersaresetasstatedinTable4.1and6.1.....................79

Summaryoftradedproductspecificationsandinterestrates...........108
Priceboundsfortradedcertificates...............................109

Benchmarksetupandstrategyparameters..........................121
Riskaversionvs.impliedriskaversion............................126

xi

ListesFigurof

3.13.23.33.43.54.14.24.34.4

5.15.25.35.45.56.1

Payoffofguaranteeschemes....................................36
Fairparticipationratesαforπ=1...............................44
Fairparticipationratesαforbuyandholdandconstantmixstrategies..45
Lossrateforconstantmixstrategy................................49
Lossratesforbuy-and-holdandCPPI.............................50
Fairversusfeasibleinvestmentfractions..........................62
Fair(solidline)andfeasible(dashedline)putpricesaspercentageof
theworstcasepriceforvaryinglevelsofriskaversionγ.Inbothplots,
thetimetomaturityisT=10.Theotherparametersaregivenasin
Table4.1.....................................................72
Fair(solidline)andfeasible(dashedline)putpricesaspercentage
oftheworstcasepriceforvaryingmeanofthebackgroundrisk.The
timetomaturityisT=10andtheriskaversionissettoγ=2.The
otherparametersaregivenasinTable4.1..........................74
ri