金融风险管理师FRM2012考试真题-豆柴文库

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Questionbank
MonteCarloMethods
LetNbeannx1vectorofindependentdrawsfromastandardnormaldistribution,andletVbeacovariancematrixofmarkettime-seriesdata.Then,ifLisadiagonalmatrixoftheeigenvaluesofV,EisamatrixoftheeigenvectorsofV,andCCistheCholeskyfactorizationofV,whichofthefollowingwouldgenerateanormallydistributedrandomvectorwithmeanzeroandcovariancematrixVtobeusedinaMonteCarlosimulation?
TOC\o"1-3"\h\zNC'CN
NC
ELE
Cannotbedeterminedfromdatagiven

Considerastockthatpaysnodividends,hasavolatilityof25%paandanexpectedreturnof13%pa.ThecurrentstockpriceisS0=$30.ThisimpliesthemodelSt+1=St(1+0.13At+0.25yAte),whereeisastandardnormalrandomvariable.Toimplementthissimulation,yougenerateapathofthestockpricebystartingatt=0,generatingasamplefore,updatingthestockpriceaccordingtothemodel,incrementingtby1andrepeatingthisprocessuntiltheendofthehorizonisreached.Whichofthefollowingstrategiesforgeneratingasampleforewillimplementthissimulationproperly?
Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.
Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.
Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.
Generateasampleforebysamplingfromanormaldistributionwithmean0.13andstandarddeviation0.25.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.
Continuingwiththepreviousquestion,youhaveimplementedthesimulationprocessdiscussedaboveusingatimeintervalAt=0.001,andyouareanalyzingthefollowingstockpricepathgeneratedbyyourimplementation.
tSt—1eAS030.000.09300.03130.030.84930.21230.230.96170.23330.470.24600.06430.530.47690.12530.650.71410.18
Giventhissample,whichofthefollowingsimulationstepsmostlikelycontainsanerror.
Calculationtoupdatethestockprice
Generationofrandomsamplevaluef