以下则是北美精算师考试SOA：真题系列Course8V（Part 4），烦请重视小编的辛勤劳作，我们很认真在制作。
　　15.(4points)Aone-stepbinomialtreeisusedtomodeltheimpactofanimportant
　　announcementonthestockpriceofCompanyXYZ.Thereisa50%chancethatthe
　　announcementwillbepositiveforthecompany.TheCompanydoesnotpaydividends.
　　Currentstockprice=$20
　　Stockpriceaftergoodnews=$30
　　Stockpriceafterbadnews=$15
　　Timeperiod=3months
　　Risk-freerate(continuouscompounding)=5%
　　(a)Calculatethepriceofa3-monthcalloptionontheCompanystockwithstrike
　　priceequalto$22.
　　(b)Thecallwriterdecidestodynamicallydelta-gammahedgetheoptionbasedona
　　standardlognormalmodel.Evaluatetheeffectivenessofthisapproachinthis
　　context.
　　COURSE8:Fall2005-7-GOTONEXTPAGE
　　Investment
　　AfternoonSession
 
　　16.(8points)YouareconsultingtoaP&Ccompanyregardingthefairvalueoftheir
　　insuranceliabilities.Youareexaminingasingleone-yearpolicywithanuncertainclaim
　　paymentpayableattheendoftheyear.Youranalysisdeterminesthefollowing:
　　?Theexpectedclaimpaymentis$2,000.
　　?Theexpectedannualreturnoftheassetportfoliobackingtheliabilityis7%.
　　?Theone-yearrisk-freerateis5%.
　　?Thecompany’staxrateis35%.
　　?Theratioofequitytoliabilitiesforsimilarproductsinthemarketplaceis20%.
　　?Thereturnonequityforsimilarproductsinthemarketplaceis15%.
　　(a)Calculatethefairvalueoftheliabilityatthebeginningofthepolicyyearusing
　　thecost-of-capitalapproach.
　　(b)CalculatetheMarketValueMarginthatwillproducethesamefairvaluewhen
　　discountingattherisk-freerate.
　　(c)Identifytheassumptionsunderlyingperfectmarketsthatmaynotholdinthereal
　　worldwithrespecttoinsurancerisks.
　　(d)ListtworeasonswhyU.S.Treasurysecuritiesmaynotbeappropriateastheriskfree
　　rateforfairvaluation.
　　COURSE8:Fall2005-8-GOTONEXTPAGE
　　Investment
　　AfternoonSession
 
　　17.(7points)YouhavebeenaskedtoapplytheExcessSpreadapproachto*uatethe
　　staticcreditedrateresetstrategyandthedynamicresetstrategy.
　　(a)DefineExcessSpreadandRequiredSpreadonAssets(RSA).
　　(b)ListtherisksassociatedwithanSPDApolicy.
　　(c)ListthestepswhenmeasuringinterestrateriskwiththeExcessSpreadapproach.
　　(d)CalculatetheExcessSpreadsofthefollowingtwostrategies:
　　?Thestaticcreditedrateresetstrategy:
　　RSA=80bp
　　Spreadonassetsis150bp,creditriskis5bp,andexpenseis15bp.
　　?Thedynamicresetstrategy:
　　RSA=70bp
　　Spreadonassetsis160bp,creditriskis10bp,andexpenseis20bp.
　　(e)AppraisetheuseofeachofthetwostrategiesforsettingtheSPDAcreditedrates.
　　COURSE8:Fall2005-9-GOTONEXTPAGE
　　Investment
　　AfternoonSession
 
　　18.(4points)Youareperforminganactuarialvaluationofadefinedbenefitpensionplan.
　　Yourresultsareshowingtheplantobeunder-funded,withafundingratioof70%.The
　　plansponsorwishestofindanassetportfoliousingthesurplusfrontierapproachthatwill
　　correcttheproblem.
　　Youaregiventhefollowing:
　　?Liabilitybeta=0.8
　　?Risk-freerate=4.0%
　　?Marketportfolioexcessreturnoverrisk-freerate=8%
　　?Alpha=0
　　(a)ExplaintheMinimumSurplusVariancePortfolio.
　　(b)Computetheminimumassetbetarequiredtogiveapositivesurplusreturn.
　　(c)Assesstheappropriatenessofthisstrategy.
　　COURSE8:Fall2005-10-GOTONEXTPAGE
　　Investment
　　AfternoonSession
 
　　19.(7points)Youworkforapubliclytradedcompanywithadefined-benefitpensionplan.
　　YourCFOreadrecentlythatshiftingpensionassetsfromstocksto100%bondsreduces
　　risk,andcreatesataxarbitrage,resultingingainstoshareholders.Youaregiventhe
　　following:
　　Currentpensionassets=$10,000,000
　　Currentpensionliabilities=$10,000,000
　　Currentpensionassetallocation:60%stocks,40%bonds
　　Corporatetaxrate=35%
　　Personaltaxrateonstocks=18%
　　Personaltaxrateonbonds=28%
　　Estimatedstockreturn=11%
　　Estimatedbondreturn=7%
　　(a)ComparetheTepperarbitrageandtheBlackarbitrage.
　　(b)Computethetheoreticalshareholdergainusingbothmethods.
　　(c)OutlinethechallengesandargumentsyourCFOmayfaceinmovingto100%
　　bonds.
　　COURSE8:Fall2005-11-STOP
　　Investment
　　AfternoonSession
 
　　20.(3points)AstheCFOofyourlifeinsurancecompany,youhavebeenaskedtoprovidea
　　singlemeasureofriskassociatedwithaportfolioofwholelifeinsuranceproducts.
　　Thecurrentvalueoftheportfoliois$61,125,856.Mostofth*ueoftheportfoliocan
　　beexplainedbyasetofmonthlyobservableindependentvariables.
　　The95%confidencelevelofVaRfortheportfoliovalueoveratwo-yeartimehorizonis
　　$30,170,914.
　　Critiquethisapproachasameasureofportfoliorisk.
　　**ENDOFEXAMINATION**
　　AFTERNOONSESSION
　　高顿网校之精品语录：人类的全部历史都告诫有智慧的人，不要笃信时运，而应坚信思想。 —— 爱献生