期權(quán)、期貨及其他衍生產(chǎn)品 課件 hull-OFOD11-ppt-18

Options,Futures,andOtherDerivativesEleventhEditionChapter18FuturesOptionsandBlack’sModelCopyright?2022,2018,2012PearsonEducation,Inc.AllRightsReservedOptionsonFuturesReferredtobythematuritymonthoftheunderlyingfutures.TheoptionisAmericanandusuallyexpiresonorafewdaysbeforetheearliestdeliverydateoftheunderlyingfuturescontract.MechanicsofCallFuturesOptionsWhenacallfuturesoptionisexercisedtheholderacquires:Alongpositioninthefutures.Acashamountequaltotheexcessofthefuturespriceatthetimeofthemostrecentsettlementoverthestrikeprice.MechanicsofPutFuturesOptionWhenaputfuturesoptionisexercisedtheholderacquires:Ashortpositioninthefutures.Acashamountequaltotheexcessofthestrikepriceoverthefuturespriceatthetimeofthemostrecentsettlement.Example18.1Septembercalloptioncontractoncopperfutureshasastrikeof320centsperpound.Itisexercisedwhenfuturespriceis331centsandmostrecentsettlementis330.Onecontractison25,000pounds.Traderreceives:LongSeptemberfuturescontractoncopper25,000times10centsor$2,500incashExample18.2Decemberputoptioncontractoncornfutureshasastrikepriceof600centsperbushel.Itisexercisedwhenthefuturespriceis580centsperbushelandthemostrecentsettlementpriceis579centsperbushel.Onecontractison5000bushels.Traderreceives:ShortDecemberfuturescontractoncorn$1,050incashThePayoffsIfthefuturespositionisclosedoutimmediately:Payofffromcall=Payofffromput=whereFisfuturespriceattimeofexercise.InterestRateFuturesOptionsOptionsonT-Bondfutures(quotedaspercentageoffacevaluetothenearestOptionson3-monthS

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RfuturesorEurodollarfutures.Eachonebasispointinthequoterepresents$25.Ifyouthinkinterestrateswillgoup,shouldyoubuycallorputoptions?PotentialAdvantagesofFuturesOptionsOverSpotOptionsFuturescontractsmaybeeasiertotradeandmoreliquidthantheunderlyingasset.Exerciseofoptiondoesnotleadtodeliveryofunderlyingasset.Futuresoptionsandfuturesusuallytradeonsameexchange.Futuresoptionsmayentaillowertransactionscosts.EuropeanFuturesOptionsEuropeanfuturesoptionsandEuropeanspotoptionsareequivalentwhenfuturescontractmaturesatthesametimeastheoption.ItiscommontoregardEuropeanspotoptionsasEuropeanfuturesoptionswhentheyarevalued.Put–CallParityforFuturesOptions(Equation18.1)Considerthefollowingtwoportfolios:EuropeancallplusofcashEuropeanputpluslongfuturespluscashequaltoTheymustbeworththesameattimeTsothatOtherRelations(Equations18.2to18.4)GrowthRatesforFuturesPricesAfuturescontractrequiresnoinitialinvestment.Inarisk-neutralworld,theexpectedreturnshouldbezero.Theexpectedgrowthrateofthefuturespriceisthereforezero.Thefuturespricecanthereforebetreatedlikeastockpayingadividendyieldofr.ValuingEuropeanFuturesOptionsWecanusetheformulaforanoptiononastockpayingadividendyield:

=currentfuturesprice,q

=domesticrisk-freerate,r

Settingq=rensuresthattheexpectedgrowthofFinarisk-neutralworldiszero.TheresultisreferredtoasBlack’smodelbecauseitwasfirstsuggestedinapaperbyFischerBlackin1976.Black’sModel(Equations18.7and18.8)whereHowBlack’sModelIsUsedinPracticeBlack’smodelisfrequentlyusedtovalueEuropeanoptionsonthespotpriceofanasset.Thisavoidstheneedtoestimateincomeontheasset.UsingBlack’sModelInsteadofBlack–Scholes–Merton(Example18.7)Considera6-monthEuropeancalloptiononspotgold.6-monthfuturespriceis1,240,6-monthrisk-freerateis5%,strikepriceis1,200,andvolatilityoffuturespriceis20%.ValueofoptionisgivenbyBlack’smodelwithK=1,200,r=0.05,T=0.5,andItis88.37.BinomialTreeExample(Figure18.1)A1-monthcalloptiononfutureshasastrikepriceof29.SettingUpaRisklessPortfolioConsiderthePortfolio:longfuturesshort1calloptionPortfolioisrisklesswhenValuingthePortfolio

(Risk-FreeRateis6%)Therisklessportfoliois:long0.8futuresshort1calloptionThevalueoftheportfolioin1monthis:Thevalueoftheportfoliotodayis:ValuingtheOptionTheportfoliothatislong0.8futuresshort1optionisworthThevalueofthefuturesiszeroThevalueoftheoptionmustthereforebe1.592GeneralizationofBinomialTreeExample(Figure18.2)AderivativelastsfortimeTandisdependentonafuturesprice.Generalization(1of3)Considertheportfoliothatislongfuturesandshort1derivativeTheportfolioisrisklesswhenGeneralization(2of3)ValueoftheportfolioattimeTisValueofportfoliotodayisHence,Generalization(3of3)SubstitutingforweobtainWhereFuturesOptionPriceversusSpotOptionPriceIffuturespricesarehigherthanspotprices(normalmarket),anAmericancallonfuturesisworthmorethanasimilarAmericancallonspot.AnAmericanputonfuturesisworthlessthanasimilarAmericanputonspot.Whenfuturespricesarelowerthanspotprices(invertedmarket)thereverseistrue.FuturesStyleOptionsAfutures-styleoptionisafuturescontractontheoptionpayoff.Someexchangestradetheseinpreferencetoregularfuturesoptions.Thefuturespriceforacallfutures-styleoptionis:Thefuturespriceforaputfutures-styleoptionis:Summary:Put–CallParityResults(1of2)Non-dividend-payingstock:Indices:Foreignexchange:Summary:Put–CallParityResults(2of2)Futures:Futuresstyle:SummaryofKeyResultsfromChapters17and18Wecantreatstockindices,currencies,andfutureslikeastockpayingadividendyieldofq.Forstockindices,qisaveragedividendyieldontheindexovertheoptionlife.Forcur