搜索
©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2005)1120051204,(,200052):,(),.,(EBSOP),;,,.:;;;:F840162:AAPricingModelofEquity2linkedLifeInsurancewithInvestmentReturnGuaranteesYANGGe,TIANPeng(AntaiSchoolofManagement,ShanghaiJiaotongUniversity,Shanghai200030,China)Abstract:Thispaperpresentsanewpricingmodelforequity2linkedlifeinsurancewithtwokindsofguarantees:deathbenefitguaranteesandinvestmentreturnguarantees.Somenumericalresultsaregiven.TheresultsshowthatsuchkindofcontractiscomposedwithaguaranteedinvestmentfundandaEuropeanbearspreadsoptionpackage(EBSOP)whosevaluecannotbeignored.Thepackageisout2of2moneyonlywhenthedeathbenefitguaranteeissmallerthaninvestreturnguarantee.Onsuchcondition,thecontractcanbetreatedasanearlyexercisablefundwithinterestrateguarantees.Keywords:equity2linkedlifeinsurance;pricingmodel;guaranteedreturn;optionpackages:2004211229:(1972-),,,,,,:,E2mail:gyang428@sjtu.edu.cn;(1958-),,,,(),,,.,.,.1999,.,.,,.,,.2003,,,.,,.,.,,,..BrennanSchwartz[1,2]BoyleSchwartz[3]Black2Scholes.,BacinelloOrtu[4]NielsenSandmann[5].2002,BacinelloPersson[6].©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[7],,.,,.,.,.,,,.1111,U0T.,().,().,.,,.,,.,.,,.,:,;(),.112:Stt;Gtt,Gt=G0ergt;Att,At=max[St,Gt];F;b(t)t,b(t)=max[At,F];V(xt)xt;c(x,t-,Kt)t,x,Kt(calloption);p(x,t-,Kt)t,x,Kt(putoption);rg;r.113.:,.,,:dS(t)=rS(t)dt+S(t)dWQ(t)(1)r,r,WQ.25200511,.©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=G0ergt,rg.t,At:At=max[St,Gt]:At=St+max[Gt-St,0](2)(2),tSt().,Gt.,=0,:V0(At)=V0(St)+p(S0,t,Gt)(3),V0(St)=EQ[e-rtSt]=S0,EQ[](equivalentmartingalemeasure).Black2Scholes[8]:p(St,t,Gt)=G0e-(r-rg)tN(-d2)-S0N(-d1)(4):d1=ln(S0PGt)+(r+2P2)tt,d2=d1-t.114,tbt.,,bt=max[At,F].,t,bt:bt=At+max[F-At,0]=At+max[F-max(St,Gt),0](5),tAtF.,,.,(5),().,FGt,,0.FGt,[9]:max[F-St,0]-max[Gt-St,0](bearspreads).,FGt,t.,At,,.,(Europeanbearspreadsoptionpackage,EBSOP).pbs(S,t-,Gt,F),t,x,GtF(EBSOP).,:pbs(S0,t,Gt,F)=p(S0,t,F)-p(S0,t,Gt)(6),.,.,..,.,.,:Tt=1tqxpbs(S0,t,Gt,F)tqxxt.,:U0=S0+p(S0,T,Gt)+Tt=1tqxpbs(S0,t,Gt,F)(7)3511©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(5),FGt,0.,.,.:U0=sup[0,T]E{e-rAt}(8)[7](6).[7].(8)[7],.,,,F,Gt..,[1].Gt=0,(7),:U0=S0+Tt=1tqxp(S0,t,F)(7a),[1].,[1].3,.30,:S0=100,G0=100,F=1000,rg=1175%.(19901993)(CL1),.T=10152025,r=210%215%310%,=20%40%,1.(EBSOP),.,7%25%.1=012=014r=2.0%r=2.5%r=3.0%r=2.0%r=2.5%r=3.0%T=10133.51(10.21)130.36(9.89)127.50(9.58)155.49(10.01)151.74(9.70)148.22(9.39)T=15146.01(18.22)140.85(17.33)136.28(16.50)171.15(17.87)164.96(17.01)159.30(16.20)T=20160.8(29.53)153.13(27.55)146.46(25.70)188.01(29.07)178.87(27.17)170.69(25.41)T=25179.69(45.55)168.60(41.57)159.16(37.96)208.31(45.12)195.43(41.35)184.12(37.93)4.,.(EBSOP),,.,,,.,,,.,BrennanSchwartz[1]GrosenJorgensen[7].(91)45200511©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.((c)(f))((a),(b)(d),(e)).1010041,010031,010012;010421,010061,010033,Kaplan2meier.,((c)(a),(f)(d)).Kaplan2meier(311)(211).:[1]KaplanEL,MeierP.Nonparametricestimationfromincompleteobservations[J].JournaloftheAmericanStatisticalAssociation,1958,(53):457-481.[2],.[M].:,1993.ZhengZu2kang,LiZi2liang.SurvivalAnalysis[M].Hangzhou:ZhejiangScienceandTechnologyPublishingHouse,1993.[3]BurkeMD,CsÊrgÈS,HorvthL.Acorrectiontoandimprovementofstrongapproximationofaomebiometricestimatesunderrandomcensorship[J].ProbabilityTheoryandRelatedFields,1988,(79):51-57.[4]QihuaWang,ZhongguoZheng.TheedgeworthexpansionsandsmoothedbootstrapapproximationforthestudentizedKaplan2Meierestimator[J].StatisticaSinica,1998,(8):571-587.[5]CaoR,JanssenP,LpezdeullibarriI,VeraverbekeN.PresmoothedKaplan2MeierandNelson2Aalenestimators[R].ReportsinStatisticsandOperationsResearch,UniversityofSantiagedeCompastela,2003.[6].[D].:,1999.WangWei.Thestudyofnon2parametricinferenceforcontaminateddistribution[D].Shanghai:FudanUniversity,1999.(54):[1]BrennanMJ,SchwartzES.Thepricingofequity2linkedlifeinsurancepolicieswithanassetvalueguarantee[J].JournalofFinancialEconomics,1976,3(3):195-213.[2]BrennanMJ,SchwartzES.Alternativeinvestmentstrategiesfortheissuersofequitylinkedlifeinsurancepolicieswithanassetvalueguarantee[J].JournalofBusiness,1979,52(1):63-93.[3]BoylePP,SchwartzES.Equilibriumpricesofguaranteesunderequity2linkedcontracts[J].JournalofRiskandInsurance,1977,44(4):639-660.[4]BacinelloAR,OrtuF.Pricingequity2linkedlifeinsurancewithendogenousminimumguarantees[J].Insurance:MathematicsandEconomics,1993,12(3):245-257.[5]NielsenJA,SandmannK.Equity2linkedlifeinsurance:amodelwithstochasticinterestrates[J].Insurance:MathematicsandEconomics,1995,16(3):225-253.[6]BacinelloAR,PerssonS-A.Designandpricingofequity2linkedlifeinsuranceunderstochasticinterestrates[J].JournalofRiskFinance,2002,3(2):6-21.[7]GrosenA,JorgensenPL.Valuationofearlyexercisableinterestrateguarantees[J].JournalofRiska