金融风险管理师(frm)2012考试真题

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

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

3、andardnormalrandomvariable.Toimplementthissimulation,yougenerateapathofthestockpricebystartingatt=0,generatingasamplefore,updatingthestockpriceaccordingtothemodel,incrementingtby1andrepeatingthisprocessuntiltheendofthehorizonisreached.Whichofthefollowingstrategiesforgeneratingasampleforewillimple

4、mentthissimulationproperly?Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.Generateasampleforebyusingtheinverseofthestanda

5、rdnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.UseCholeskydecompositiontocorrelate

6、thissamplewiththesamplefromtheprevioustimeinterval.Continuingwiththepreviousquestion,youhaveimplementedthesimulationprocessdiscussedaboveusingatimeintervalAt=0.001,andyouareanalyzingthefollowingstockpricepathgeneratedbyyourimplementation.tSt—1eAS030.000.09300.03130.030.84930.21230.230.96170.2333

7、0.470.24600.06430.530.47690.12530.650.71410.18Giventhissample,whichofthefollowingsimulationstepsmostlikelycontainsanerror.CalculationtoupdatethestockpriceGenerationofrandomsamplevalueforeCalculationofthechangeinstockpr