chapter6金融工程

18SimpleImplementingofOptionOricingModels!WK1.IntheEWMAmodelandtheGARCH(1,1)model,theweightsassignedtoobserva-tionsdecreaseastheobservationsbecomeolder.2.TheGARCH(1,1)modeldiffersfromtheEWMAmodelinthatsomeweightisalsoassignedtothe.3.Whenthecurrentvolatilityisabovethelong-termvolatility,theGARCH(1,1)modelestimatesavolatilitytermstructure.4.Supposethatλis0.8,thevolatilityestimatedforamarketvariablefordayn-1is2%perday,andduringdayn-1themarketvariableincreasedby3%.Thentheestimateofthevolatilityfordaynis.5.Supposethatλ=0.9,andtheestimateofthecorrelationbetweentwovariablesXandYondayn-1is0.7.Supposeσx,n−1=2%,σy,n−1=3%,ux,n−1=0.4%,uy,n−1=2.5%.Thecovariancefordaynwouledbe.6.ForanAmericanoption,thevalueatanodeisthegreaterof,andthediscountedexpectedvalueifitisheldforafurtherperiodoftimeδt.7.Finitedifferencemethodssolvetheunderlyingbycovertittoadifferenceequation.8.Theexplicitmethodisfunctionallythesameasusinga.9.involvesdividingthedistributionintorangesorintervalsandsamplingfromeachintervalaccordingtoitsprobability.1218SIMPLEIMPLEMENTINGOFOPTIONORICINGMODELS10.Currenciesandfuturescontractscan,forthepurposesofoptionevaluation,becon-sideredasassetsprovidingknownyields.Inthecaseofacurrency,therelevantyieldisthe;inthecaseofafuturescontract,itisthe.!K(3zKoY¥J(YŁW\K)S)1.Whichmodelisnotusedtoproduceestimatesofvolatilities()A.EWMAB.ARCHC.CRRD.GARCH2.InanEWMAmodel,theweightsoftheuideclinesatrateaswemovebackthroughtime.()A.λB.1λC.λ2D.1−λ3.WhenusevariancetargetingapproachtoestimateparametersinGARCH(1,1),thereareonlyparametershavetobeestimated.()A.1B.2C.3D.44.TheparametersofaGARCH(1,1)modelareestimatedasω=0.000004,α=0.05,β=0.92.Whatisthelong-runaveragevolatility?()A.0.00013B.0.013C.0.00025D.0.0255.ThemostrecentestimateofthedailyvolatilityofUSD\GBPexchangerateis0.55%andtheexchangerateat4p.m.yesterdaywas1.4950.TheparameterλintheEWMAmodelis0.95.Supposethattheexchangerateat4p.m.todayprovestobe1.4850,theestimateofthedailyvolatilityis()A.2.900B.2.874C.0.2874D.0.29006.WhichofthefollowingcanbeestimatedforanAmericanoptionbyconstructingasinglebinomialtree?()A.DeltaB.VegaC.GammaD.Theta7.WhichisnotparticularlyusefulwhentheholderhasearlyexercisedecisionsinAmer-icanoptions?()A.MonteCarloSimulationB.BinomialFreesmodelC.FiniteDifferenceMethodsD.TrinomialTreesmodel38.WhichmodelcanbeusedwhenthepayoffdependsonthepathfollowedbytheunderlyingvariableSaswellaswhenitdependsonlyonthefinalvalueofS?()A.BinomialTreesmodelB.TrinomialTreesmodelC.FiniteDifferenceMethodsD.MonteCarloSimulation9.Considerafour-monthAmericancalloptiononindexfutureswheretherisk-freeinterestrateis9%perannum,andthevolatilityoftheindexis40%perannum.Wedividethelifeoftheoptionintofourone-monthperiodsforthepurposesofcon-structingthetree.Thenthegrowthfactoraequals:()A.1B.e9%×0.0833C.e9%D.e40%×t0.083310.Inabinomialmodelforadividend-payingstock,whenthedollaramountdividendisknown,therearenodesonthetreeattimeiδt.()A.i+1B.iC.2iD.i2n!K(3(K)Sy”√”§K)Sy”×”)1.Black-Scholesmodelassumethatthevolatilityoftheunderlyingassetisnotconstant.()2.IntheEWMAmodel,someweightisassignedtothelong-runaveragevariancerate.()3.Whenwebuildupmodelstoforecastvolatility,uisassumedtobezero.()4.IntheARCH(m)model,theolderanobservation,thelessweightitisgiven.()5.TheEWMAapproachhastheattractivefeaturethatrelativelylittledateneedtobestored.Atanygiventime,weneedtorememberonlythecurrentestimateofthevariancerateandthemostrecentobservationonthevalueofthemarketvariable.()6.ForastableGARCH(1,1)process,werequireα+β1,thentheGARCH(1,1)processis’meanreverting’ratherthan’meanfleeing’.()7.TheEWMAmodelincorporatesmeanreversion,whereastheGARH(1,1)modeldosenot.()8.Foraseriesxi,theautocorrelationwithalagofkisthecoefficientofcorrelationbetweenxiandxi+k.()418SIMPLEIMPLEMENTINGOFOPTIONORICINGMODELS9.Whenthecurrentvolatilityisbelowthelong-termvolatility,itestimatesandownward-slopingvolatilitytermstructure.()10.Supposethereisabigmoveinthemarketvariableondayn-1,theestimateofthecurrentvolatilitymovesupward.()11.MonteCarlosimulationisusedprimarilyforderivativeswherethepayoffisdepen-dentonthehistoryoftheunderlyingvariableorwherethereareseveralunderlyingvariables.()12.Binomialtreesandfinitedifferencemethodsarenotusefulwhentheholderhasearlyexercisedecisionstomakepriortomaturity.()13.Inbinomialtreesmodel,thederivativescanbevaluebydiscountingtheirexpectedvaluesattherisk-freeinterestrate.()14.Currenciescanbeconsideredasassetsprovidingknownyields,andtherelevantyieldisdomesticrisk-freeinterestrate.()15.Thetreedoesnotrecombinewhenthedividendyieldisknown.()16.ThecontrolvariatetechniqueusedbybinomialtreesneedstocalculatetheBlank-ScholespriceoftheEuropeanoption.()17.TheCRRistheonlywaytoconstructbinomialtrees.()18.TheadvantageofMonteCarlosimulationisthatitiscomputationallyverytime-saving.()19.InMonteCarlosimulationtheuncertaintyaboutthevalueofthederivativeisin-verselyproportionaltothesquarerootofthenumberoftrials.()20.Theimplicitfinitedifferencehastheadvantageofbeingveryrobust.Italwayscon-vergestothesolutionofthedifferentialequationas4sand4tappro