[其它考试]金融风险管理师frm2012考试真题

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1、QuestionbankMonteCarloMethodsLetNbeannx1vectorofindependentdrawsfromastandardnormaldistribution,andletVbeacovariancematrixofmarkettime-seriesdata.Then,ifLisadiagonalmatrixoftheeigenvaluesofV,EisamatrixoftheeigenvectorsofV,andCCistheCholeskyfactorizati

2、onofV,whichofthefollowingwouldgenerateanormallydistributedrandomvectorwithmeanzeroandcovariancematrixVtobeusedinaMonteCarlosimulation?NC'CNNCELECannotbedeterminedfromdatagivenConsiderastockthatpaysnodividends,hasavolatilityof25%paandanexpectedreturnof

3、13%pa.ThecurrentstockpriceisS0=$30.ThisimpliesthemodelSt+1=St(1+0.13At+0.25yAte),whereeisastandardnormalrandomvariable.Toimplementthissimulation,yougenerateapathofthestockpricebystartingatt=0,generatingasamplefore,updatingthestockpriceaccordingtothemo

4、del,incrementingtby1andrepeatingthisprocessuntiltheendofthehorizonisreached.Whichofthefollowingstrategiesforgeneratingasampleforewillimplementthissimulationproperly?Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasample

5、valuedrawnfromauniformdistributionbetween0and1.Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistri

6、butionbetween0and1.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.UseCholeskydecompositiontocorrelatethissamplewiththesamp

7、lefromtheprevioustimeinterval.Continuingwiththepreviousquestion,youhaveimplementedthesimulationprocessdiscussedaboveusingatimeintervalAt=0.001,andyouareanalyzingthefollowingstockpricepathgeneratedbyyourimplementation.tSt—1eAS030.000.09300.03130.030.8

8、4930.21230.230.96170.23330.470.24600.06430.530.47690.12530.650.71410.18Giventhissample,whichofthefollowingsimulationstepsmostlikelycontainsanerror.CalculationtoupdatethestockpriceGenerationofrandomsamplevalueforeCalculationofthechangeinstockpr