金融风险管理师FRM2012考试真题.doc.docx

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1、QuestionbankMonteCarloMethodsLetNbeannx1vectorofindependentdrawsfromastandardnormaldistribution,andletVbeacovariancematrixofmarkettime-seriesdata.Then,ifLisadiagonalmatrixoftheeigenvaluesofV,EisamatrixoftheeigenvectorsofV,andCCistheCholeskyfactorizationofV,whichofthefollowingwouldgenerateanormal

2、lydistributedrandomvectorwithmeanzeroandcovariancematrixVtobeusedinaMonteCarlosimulation?NC'CNNCELECannotbedeterminedfromdatagivenConsiderastockthatpaysnodividends,hasavolatilityof25%paandanexpectedreturnof13%pa.ThecurrentstockpriceisS0=$30.ThisimpliesthemodelSt+1=St(1+0.13At+0.25yAte),whereeisa

3、standardnormalrandomvariable.Toimplementthissimulation,yougenerateapathofthestockpricebystartingatt=0,generatingasamplefore,updatingthestockpriceaccordingtothemodel,incrementingtby1andrepeatingthisprocessuntiltheendofthehorizonisreached.Whichofthefollowingstrategiesforgeneratingasampleforewillim

4、plementthissimulationproperly?Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.Generateasampleforebyusingtheinverseofthest

5、andardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.UseCholeskydecompositiontocorr

6、elatethissamplewiththesamplefromtheprevioustimeinterval.Continuingwiththepreviousquestion,youhaveimplementedthesimulationprocessdiscussedaboveusingatimeintervalAt=0.001,andyouareanalyzingthefollowingstockpricepathgeneratedbyyourimplementation.tSt—1eAS030.000.09300.03130.030.84930.21230.230.9617

7、0.23330.470.24600.06430.530.47690.12530.650.71410.18Giventhissample,whichofthefollowingsimulationstepsmostlikelycontainsanerror.CalculationtoupdatethestockpriceGenerationofrandomsamplevalueforeCalculationofthechangeinstockpr