专题四期权估价英语特训练习cgyy lx0401

专题四期权估价英语特训练习cgyylx0401单项选择题1.Anoptionthatcanbeexercisedonlyattheexpirationdateiscalleda(n)______.A.AmericanoptionB.EuropeanoptionC.BermudanoptionD.AsianoptionAnswer:B.AEuropeanoptioncanbeexercisedonlyattheexpirationdate,whileanAmericanoptioncanbeexercisedatanytimebeforeandincludingtheexpirationdate.ABermudanoptioncanbeexercisedonspecificdatesbeforeexpiration,andanAsianoption'spayoffisbasedontheaveragepriceoftheunderlyingassetoveracertainperiod.2.Thevalueofacalloptionispositivelyrelatedtoallofthefollowingexcept______.A.thecurrentpriceoftheunderlyingassetB.thetimetoexpirationC.theexercisepriceD.thevolatilityoftheunderlyingassetAnswer:C.Thevalueofacalloptionispositivelyrelatedtothecurrentpriceoftheunderlyingasset(higherassetpricemeansmorepotentialprofit),thetimetoexpiration(moretimefortheoptiontobecomeprofitable),andthevolatilityoftheunderlyingasset(highervolatilityincreasesthechanceoflargepricemovementsintheasset).However,itisnegativelyrelatedtotheexerciseprice.Ahigherexercisepricemakesitlesslikelyforthecalloptiontobeinthemoney.3.Ifthepriceoftheunderlyingassetislowerthantheexercisepriceofacalloption,thecalloptionis______.A.inthemoneyB.atthemoneyC.outofthemoneyD.deepinthemoneyAnswer:C.Acalloptionisinthemoneywhenthepriceoftheunderlyingassetishigherthantheexerciseprice.Itisatthemoneywhenthepriceoftheunderlyingassetequalstheexerciseprice.Whenthepriceoftheunderlyingassetislowerthantheexerciseprice,itisoutofthemoney.Deepinthemoneyimpliesasignificantdifferencewheretheassetpriceismuchhigherthantheexerciseprice.4.TheBlackScholesoptionpricingmodelassumesallofthefollowingexcept______.A.theunderlyingassetpricefollowsalognormaldistributionB.therearenotransactioncostsortaxesC.theriskfreeinterestrateisconstantoverthelifeoftheoptionD.theoptioncanbeexercisedatanytimebeforeexpirationAnswer:D.TheBlackScholesmodelisusedforEuropeanoptions,whichcanbeexercisedonlyatexpiration.Itassumesthattheunderlyingassetpricefollowsalognormaldistribution,therearenotransactioncostsortaxes,andtheriskfreeinterestrateisconstantoverthelifeoftheoption.5.Thedeltaofacalloptionmeasures______.A.thechangeintheoptionpriceforaoneunitchangeinthepriceoftheunderlyingassetB.thechangeintheoptionpriceforaoneunitchangeinthetimetoexpirationC.thechangeintheoptionpriceforaoneunitchangeinthevolatilityoftheunderlyingassetD.thechangeintheoptionpriceforaoneunitchangeintheriskfreeinterestrateAnswer:A.Deltaisdefinedasthechangeintheoptionpriceforaoneunitchangeinthepriceoftheunderlyingasset.Gammameasuresthechangeindeltaforaoneunitchangeinthepriceoftheunderlyingasset.Thetameasuresthechangeintheoptionpriceforaoneunitchangeinthetimetoexpiration,Vegameasuresthechangeintheoptionpriceforaoneunitchangeinthevolatilityoftheunderlyingasset,andRhomeasuresthechangeintheoptionpriceforaoneunitchangeintheriskfreeinterestrate.6.Ifthedeltaofacalloptionis0.6,itmeansthatifthepriceoftheunderlyingassetincreasesby$1,thepriceofthecalloptionwillapproximately______.A.increaseby$0.6B.decreaseby$0.6C.increaseby$1D.decreaseby$1Answer:A.Sincedeltameasuresthechangeintheoptionpriceforaoneunitchangeinthepriceoftheunderlyingasset,adeltaof0.6impliesthatifthepriceoftheunderlyingassetincreasesby$1,thepriceofthecalloptionwillincreasebyapproximately$0.6.7.Aputoptiongivestheholdertherightto______.A.buytheunderlyingassetattheexercisepriceB.selltheunderlyingassetattheexercisepriceC.buytheunderlyingassetatthemarketpriceD.selltheunderlyingassetatthemarketpriceAnswer:B.Aputoptiongivestheholdertherighttoselltheunderlyingassetattheexerciseprice.Acalloptiongivestheholdertherighttobuytheunderlyingassetattheexerciseprice.8.Theintrinsicvalueofaputoptioniscalculatedas______.A.Max(0,SX)B.Max(0,XS)C.SXD.XSAnswer:B.Theintrinsicvalueofaputoptionisthemaximumof0andthedifferencebetweentheexerciseprice(X)andthepriceoftheunderlyingasset(S).IfX>S,theputoptionhasintrinsicvalueequaltoXS.IfX≤S,theintrinsicvalueis0.9.Asthetimetoexpirationofanoptiondecreases,thetimevalueoftheoption______.A.increasesB.decreasesC.remainsthesameD.mayincreaseordecreasedependingonotherfactorsAnswer:B.Thetimevalueofanoptionrepresentsthepotentialfortheoptiontogainmorevaluebeforeexpiration.Asthetimetoexpirationdecreases,thereislesstimefortheoptiontobecomeprofitable,sothetimevalueoftheoptiondecreases.10.Thevegaofanoptionmeasures______.A.thesensitivityoftheoptionpricetochangesinthevolatilityoftheunderlyingassetB.thesensitivityoftheoptionpricetochangesinthetimetoexpirationC.thesensitivityoftheoptionpricetochangesintheriskfreeinterestrateD.thesensitivityoftheoptionpricetochangesinthepriceoftheunderlyingassetAnswer:A.Vegameasuresthechangeintheoptionpriceforaoneunitchangeinthevolatilityoftheunderlyingasset.Thetameasuresthechangeintheoptionpriceforaoneunitchangeinthetimetoexpiration,Rhomeasuresthechangeintheoptionpriceforaoneunitchangeintheriskfreeinterestrate,andDeltameasuresthechangeintheoptionpriceforaoneunitchangeinthepriceoftheunderlyingasset.多项选择题1.Whichofthefollowingfactorsaffectthevalueofacalloption?A.ThecurrentpriceoftheunderlyingassetB.TheexercisepriceC.ThetimetoexpirationD.ThevolatilityoftheunderlyingassetAnswer:ABCD.Thevalueofacalloptionispositivelyrelatedtothecurrentpriceoftheunderlyingasset(morepotentialprofit),negativelyrelatedtotheexerciseprice(higherexercisepricereducesprofitpotential),positivelyrelatedtothetimetoexpiration(moretimefortheoptiontobeprofitable),andpositivelyrelatedtothevolatilityoftheunderlyingasset(higherchanceoflargepricemovements).2.TheassumptionsoftheBlackScholesoptionpricingmodelinclude______.A.TheunderlyingassetpricefollowsageometricBrownianmotionB.TherearenodividendspaidontheunderlyingassetC.Themarketisfrictionless(notransactioncosts,notaxes)D.TheriskfreeinterestrateisconstantandknownAnswer:ABCD.TheBlackScholesmodelassumesthattheunderlyingassetpricefollowsageometricBrownianmotion(whichisrelatedtothelognormaldistribution),nodividendsarepaidontheunderlyingasset(abasicversion;thereareextensionsfordividendpayingassets),themarketisfrictionless,andtheriskfreeinterestrateisconstantandknown.3.Foraputcallparityrelationship,whichofthefollowingequationshold?A.CP=SPV(X)B.C+PV(X)=P+SC.PC=PV(X)SD.P+S=C+PV(X)Answer:ABCD.TheputcallparityrelationshipforEuropeanoptionsonnondividendpayingstocksisCP=SPV(X),whereCisthecalloptionprice,Pistheputoptionprice,Sisthepriceoftheunderlyingasset,andPV(X)isthepresentvalueoftheexerciseprice.RearrangingthisequationgivesC+PV(X)=P+S,PC=PV(X)S,andP+S=C+PV(X).4.TheGreeksinoptionpricingareusedtomeasure______.A.ThesensitivityoftheoptionpricetochangesinthepriceoftheunderlyingassetB.ThesensitivityoftheoptionpricetochangesinthetimetoexpirationC.ThesensitivityoftheoptionpricetochangesinthevolatilityoftheunderlyingassetD.ThesensitivityoftheoptionpricetochangesintheriskfreeinterestrateAnswer:ABCD.TheGreeksinoptionpricingincludeDelta(sensitivitytounderlyingassetpricechanges),Theta(sensitivitytotimetoexpirationchanges),Vega(sensitivitytovolatilitychanges),andRho(sensitivitytoriskfreeinterestratechanges).5.WhichofthefollowingstatementsaboutAmericanandEuropeanoptionsarecorrect?A.AmericanoptionscanbeexercisedatanytimebeforeandincludingtheexpirationdateB.EuropeanoptionscanbeexercisedonlyattheexpirationdateC.AmericanoptionsarealwaysmorevaluablethanEuropeanoptionsD.AmericanoptionsonnondividendpayingstockshavethesamevalueasEuropeanoptionsAnswer:ABD.Americanoptionscanbeexercisedatanytimebeforeandincludingtheexpirationdate,whileEuropeanoptionscanbeexercisedonlyattheexpirationdate.AmericanoptionsonnondividendpayingstockshavethesamevalueasEuropeanoptionsbecausethereisnobenefittoearlyexercise.However,Americanoptionsarenotalwaysmorevaluable.Fornondividendpayingassets,theyareequal,andforsomecaseswithspecificmarketconditions,thedifferencemaybeverysmall.TrueFalseQuestions1.Acalloptionisalwaysmorevaluablethanaputoption.Answer:False.Thevalueofacalloptionandaputoptiondependsonvariousfactorssuchasthecurrentpriceoftheunderlyingasset,theexerciseprice,thetimetoexpiration,andthevolatilityoftheunderlyingasset.Insomesituations,aputoptioncanbemorevaluablethanacalloption,forexample,whenthepriceoftheunderlyingassetisexpectedtodecreasesignificantly.2.TheBlackScholesmodelcanbeusedtopriceAmericanoptionsaccurately.Answer:False.TheBlackScholesmodelisdesignedforEuropeanoptions,whichcanbeexercisedonlyatexpiration.Americanoptions,whichcanbeexercisedatanytimebeforeexpiration,mayrequiremorecomplexmodelssuchasbinomialtreestoaccountfortheearlyexercisefeature.3.Thetimevalueofanoptionisthedifferencebetweentheoptionpriceanditsintrinsicvalue.Answer:True.Theoptionpriceconsistsoftwoparts:intrinsicvalueandtimevalue.So,thetimevalueiscalculatedastheoptionpriceminusitsintrinsicvalue.4.Ifthevolatilityoftheunderlyingassetincreases,thevalueofbothcallandputoptionswillincrease.Answer:True.Highervolatilitymeansthereisagreaterchanceoflargepricemovementsintheunderlyingasset.Forcalloptions,thereismorepotentialfortheassetpricetoriseabovetheexerciseprice,andforputoptions,thereismorepotentialfortheassetpricetofallbelowtheexerciseprice.So,thevalueofbothcallandputoptionsincreaseswithanincreaseinvolatility.5.Thedeltaofaputoptionispositive.Answer:False.Thedeltaofaputoptionisnegative.Deltameasuresthechangeintheoptionpriceforaoneunitchangeinthepriceoftheunderlyingasset.Foraputoption,asthepriceoftheunderlyingassetincreases,thevalueoftheputoptiondecreases,sothedeltaisnegative.FillintheBlankQuestions1.The______optioncanbeexercisedatanytimebeforeandincludingtheexpirationdate.Answer:American.Americanoptionshavetheflexibilityofearlyexercise,whileEuropeanoptionscanbeexercisedonlyattheexpirationdate.2.Thepresentvalueoftheexercisepriceisanimportantcomponentinthe______relationship.Answer:putcallparity.TheputcallparityformulaisCP=SPV(X),wherePV(X)isthepresentvalueoftheexerciseprice.3.The______ofanoptionmeasurestherateofchangeofdeltawithrespecttothepriceoftheunderlyingasset.Answer:Gamma.Gammaisusedtomeasurehowdeltachangesasthepriceoftheunderlyingassetchanges.4.Anoptionwithadeltacloseto1islikelytobe______themoney.Answer:in.Acalloptionwithadeltacloseto1isdeepinthemoney,meaningthepriceoftheunderlyingassetismuchhigherthantheexerciseprice,andtheoptionpricewillmovealmostoneforonewiththepriceoftheunderlyingasset.5.The______ofanoptionmeasuresthechangeintheoptionpriceforaoneunitchangeintheriskfreeinterestrate.Answer:Rho.RhoisoneoftheGreeksinoptionpricingandisusedtomeasurethesensitivityoftheoptionpricetochangesintheriskfreeinterestrate.ShortAnswerQuestions1.Explaintheconceptofintrinsicvalueandtimevalueofanoption.Answer:Theintrinsicvalueofanoptionistheimmediatevalueoftheoptionifitweretobeexercisedrightaway.Foracalloption,itisMax(0,SX),whereSisthepriceoftheunderlyingassetandXistheexerciseprice.Foraputoption,itisMax(0,XS).Thetimevalueofanoptionisthedifferencebetweentheoptionpriceanditsintrinsicvalue.Itrepresentsthepotentialfortheoptiontogainmorevaluebeforeexpirationduetofactorssuchaschangesinthepriceoftheunderlyingasset,volatility,andtimeremaininguntilexpiration.2.Describetheputcallparityrelationship.Answer:TheputcallparityrelationshipholdsforEuropeanoptionsonnondividendpayingstocks.ThebasicequationisCP=SPV(X),whereCisthecalloptionprice,Pistheputoptionprice,Sisthepriceoftheunderlyingasset,andPV(X)isthepresentvalueoftheexerciseprice.Thisrelationshipisbasedontheprincipleofnoarbitrage.Iftherelationshipdoesnothold,anarbitrageopportunityexists,andtraderscanmakeriskfreeprofitsbybuyingandsellingtheappropriatecombinationoftheunderlyingasset,calloption,putoption,andariskfreebond.3.WhatarethemainassumptionsoftheBlackScholesoptionpricingmodel?Answer:ThemainassumptionsoftheBlackScholesmodelare:1)TheunderlyingassetpricefollowsageometricBrownianmotion,whichimpliesthatthelogarithmoftheassetpricechangesarenormallydistributed.2)Therearenotransactioncostsortaxes.3)Theriskfreeinterestrateisconstantandknownoverthelifeoftheoption.4)Theoptioncanbeexercisedonlyattheexpirationdate(itisforEuropeanoptions).5)Theunderlyingassetpaysnodividendsduringthelifeoftheoption(abasicversion;thereareextensionsfordividendpayingassets).4.ExplainthesignificanceoftheGreeksinoptionpricing.Answer:TheGreeksinoptionpricingareusedtomeasurethesensitivityoftheoptionpricetovariousfactors.Deltameasuresthechangeintheoptionpriceforaoneunitchangeinthepriceoftheunderlyingasset,whichhelpsinhedgingtheoptionpositionagainstpricemovementsoftheunderlying.Thetameasuresthechangeintheoptionpriceastimepasses,whichisimportantforunderstandingthetimedecayoftheoption.Vegameasuresthesensitivitytochangesinthevolatilityoftheunderlyingasset,whichiscrucialasvolatilityaffectstheprobabilityoftheoptionbeinginthemoney.Rhomeasuresthesensitivitytochangesintheriskfreeinterestrate,whichcanimpactthepresentvaluecalculationsinoptionpricing.5.CompareAmericanandEuropeanoptions.Answer:Americanoptionscanbeexercisedatanytimebeforeandincludingtheexpirationdate,whileEuropeanoptionscanbeexercisedonlyattheexpirationdate.Americanoptionsprovidemoreflexibilitytotheholder.However,fornondividendpayingstocks,AmericanandEuropeanoptionshavethesamevaluebecausethereisnobenefittoearlyexercise.Fordividendpayingstocks,Americanoptionsmaybemorevaluableasearlyexercisecanbebeneficialtocapturedividends.CaseStudyQuestions1.CompanyXYZ'sstockiscurrentlytradingat$50.Acalloptiononthisstockwithanexercisepriceof$45andanexpirationin3monthsispricedat$7.Aputoptionwiththesameexercisepriceandexpirationispricedat$2.Theriskfreeinterestrateis5%perannum.a.Checkiftheputcallparityholds.b.Ifnot,suggestanarbitragestrategy.Answer:a.First,calculatethepresentvalueoftheexerciseprice.TheexercisepriceX=$45,andthetimetoexpirationt=3/12=0.25years.UsingtheformulaPV(X)=Xe^(rt),wherer=0.05,wehavePV(X)=45e^(0.050.25)≈450.9876=$44.44.ThelefthandsideoftheputcallparityisCP=72=$5.TherighthandsideisSPV(X)=5044.44=$5.56.Since5≠5.56,theputcallparitydoesnothold.b.SinceCP<SPV(X),wecanusethefollowingarbitragestrategy:Buythecalloptionfor$7andselltheputoptionfor$2.Thenetinflowfromoptionsis72=$5.Shortsellthestockandreceive$50.Investthepresentvalueoftheexerciseprice,$44.44,attheriskfreerate.Atexpiration,ifS>45,thecalloptionwillbeexercised,andwewillbuythestockat$45.Wecanusethemoneyfromtheinvestment(whichwillgrowto$45)tobuythestockandclosetheshortsaleposition.IfS<45,theputoptionwillbeexercisedagainstus,andwewillbuythestockat$45,againusingthemoneyfromtheinvestment.Ineithercase,wemakeariskfreeprofitof5.565=$0.56.2.Aninvestorholdsacalloptiononastock.Thecurrentstockpriceis$60,theexercisepriceis$55,thetimetoexpirationis6months,thevolatilityofthestockis30%,andtheriskfreeinterestrateis4%.a.Estimatethedeltaofthecalloption.b.Explainwhatthedeltavaluemeansinthiscontext.Answer:a.Toestimatethedeltaofthecalloption,wecanusetheBlackScholesformula.TheformulafordeltaofacalloptionisN(d1),whered1=[ln(S/X)+(r+σ²/2)t]/(σ√t).Here,S=60,X=55,r=0.04,σ=0.3,t=0.5.First,calculated1:ln(S/X)=ln(60/55)≈0.087.(r+σ²/2)t=(0.04+0.3²/2)0.5=(0.04+0.045)0.5=0.0425.σ√t=0.3√0.5≈0.212.d1=(0.087+0.0425)/0.212≈0.61.LookingupN(0.61)inthestandardnormaldistributiontable,wegetN(0.61)≈0.73.So,thedeltaofthecalloptionisapproximately0.73.b.Thedeltavalueof0.73mea