QuestionbankMonteCarloMethodsLetNbeannx1vectorofindependentdrawsfromastandardnormaldistribution,andletVbeacovariancematrixofmarkettime-seriesdata.Then,ifLisadiagonalmatrixoftheeigenvaluesofV,EisamatrixoftheeigenvectorsofV,andCCistheCholeskyfactorizationofV,whichofthefollowingwouldgenerateanormallydistributedrandomvectorwithmeanzeroandcovariancematrixVtobeusedinaMonteCarlosimulationNC'CNNCELECannotbedeterminedfromdatagivenConsiderastockthatpaysnodividends,hasavolatilityof25%paandanexpectedreturnof13%pa.ThecurrentstockpriceisS0=$30.ThisimpliesthemodelSt+1=St(1+At+e),whereeisastandardnormalrandomvariable.Toimplementthissimulation,yougenerateapathofthestockpricebystartingatt=0,generatingasamplefore,updatingthestockpriceaccordingtothemodel,incrementingtby1andrepeatingthisprocessuntiltheendofthehorizonisreached.WhichofthefollowingstrategiesforgeneratingasampleforewillimplementthissimulationproperlyGenerateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.Generateasampleforebysamplingfromanormaldistributionwithmeanandstandarddeviation.Generateasampleforebyusingtheinverseofthestandardnormalcumulativedistributionofasamplevaluedrawnfromauniformdistributionbetween0and1.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.Generateasampleforebysamplingfromanormaldistributionwithmeanandstandarddeviation.UseCholeskydecompositiontocorrelatethissamplewiththesamplefromtheprevioustimeinterval.Continuingwiththepreviousquestion,youhaveimplementedthesimulationprocessdiscussedaboveusingatimeintervalAt=,andyouareanalyzingthefollowingstockpricepathgeneratedbyyourimplementation.tSt—1eAS012345Giventhissample,whichofthefollowingsimulationstepsmostlikelycontainsanerror.CalculationtoupdatethestockpriceGenerationofrandomsamplevalueforeCalculationofthechangeinstockpriceduringeachperiodNoneoftheaboveInthegeometricBrownianmotionprocessforavariableS,I.Sisnormallydistributed.II.dln(S)isnormallydistributed.III.dS/Sisnormallydistributed.IV.Sislognormallydistributed.a.Ionlyb.II,III,andIVc.IVonlyd.IIIandIVConsiderthatastockpriceSthatfollowsageometricBrownianmotiondS=aSdt+bSdz,withbstrictlypositive.Whichofthefollowingstatementsisfalsea.Ifthedriftaispositive,thepriceoneyearfromnowwillbeabovetoday’sprice.b.Theinstantaneousrateofreturnonthestockfollowsanormaldistribution.c.ThestockpriceSfollowsalognormaldistribution.d.Thismodeldoesnotimposemeanreversion.TheVasicekmodeldefinesarisk-neutralprocessforrwhichisdr=a(b-r)dt+σdz,wherea,b,andσareconstant,andrrepresentstherateofinterest.Fromthisequationwecanconcludethatthemodelisaa.MonteCarlo-typemodelb.Single-factorterm-structuremodelc.Two-factorterm-structuremodeld.DecisiontreemodelTheterma(b-r)inthepreviousquestionrepresentswhichterma.Gammab.Stochasticc.Reversiond.VegaWhichgroupofterm-structuremodelsdotheHo-Lee,Hull-White,andHeath,Jarrow,andMortonmodelsbelongtoa.No-arbitragemodelsb.Two-factormodelsc.Lognormalmodelsd.DeterministicmodelsAplausiblestochasticprocessfortheshort-termrateisoftenconsideredtobeonewheretherateispulledbacktosomelong-runaveragelevel.Whichoneofthefollowingterm-structuremodelsdoesnotincludethischaracteristica.TheVasicekmodelb.TheHo-Leemodelc.TheHull-Whitemodeld.TheCox-Ingersoll-RossmodelWhichofthefollowingstatementsaboutMonteCarlosimulation...
