期权 期货以及其他衍生品(5)

Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.1DeterminationofForwardandFuturesPricesChapter3Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.2ConsumptionvsInvestmentAssets•Investmentassetsareassetsheldbysignificantnumbersofpeoplepurelyforinvestmentpurposes(Examples:gold,silver)•Consumptionassetsareassetsheldprimarilyforconsumption(Examples:copper,oil)Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.3ShortSelling(Page41-42)•Shortsellinginvolvessellingsecuritiesyoudonotown•YourbrokerborrowsthesecuritiesfromanotherclientandsellstheminthemarketintheusualwayOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.4ShortSelling(continued)•Atsomestageyoumustbuythesecuritiesbacksotheycanbereplacedintheaccountoftheclient•YoumustpaydividendsandotherbenefitstheownerofthesecuritiesreceivesOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.5MeasuringInterestRates•Thecompoundingfrequencyusedforaninterestrateistheunitofmeasurement•ThedifferencebetweenquarterlyandannualcompoundingisanalogoustothedifferencebetweenmilesandkilometersOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.6ContinuousCompounding(Page43)•Inthelimitaswecompoundmoreandmorefrequentlyweobtaincontinuouslycompoundedinterestrates•$100growsto$100eRTwheninvestedatacontinuouslycompoundedrateRfortimeT•$100receivedattimeTdiscountsto$100e-RTattimezerowhenthecontinuouslycompoundeddiscountrateisROptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.7ConversionFormulas(Page44)DefineRc:continuouslycompoundedrateRm:sameratewithcompoundingmtimesperyearRmRmRmecmmRmcln/11Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.8NotationS0:SpotpricetodayF0:FuturesorforwardpricetodayT:Timeuntildeliverydater:Risk-freeinterestrateformaturityTOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.9GoldExample(FromChapter1)•ForgoldF0=S0(1+r)T(assumingnostoragecosts)•IfriscompoundedcontinuouslyinsteadofannuallyF0=S0erTOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.10ExtensionoftheGoldExample(Page46,equation3.5)•ForanyinvestmentassetthatprovidesnoincomeandhasnostoragecostsF0=S0erTOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.11WhenanInvestmentAssetProvidesaKnownDollarIncome(page48,equation3.6)F0=(S0–I)erTwhereIisthepresentvalueoftheincomeOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.12WhenanInvestmentAssetProvidesaKnownYield(Page49,equation3.7)F0=S0e(r–q)Twhereqistheaverageyieldduringthelifeofthecontract(expressedwithcontinuouscompounding)Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.13ValuingaForwardContractPage50•SupposethatKisdeliverypriceinaforwardcontractF0isforwardpricethatwouldapplytothecontracttoday•Thevalueofalongforwardcontract,ƒ,isƒ=(F0–K)e–rT•Similarly,thevalueofashortforwardcontractis(K–F0)e–rTOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.14ForwardvsFuturesPrices•Forwardandfuturespricesareusuallyassumedtobethesame.Wheninterestratesareuncertaintheyare,intheory,slightlydifferent:•Astrongpositivecorrelationbetweeninterestratesandtheassetpriceimpliesthefuturespriceisslightlyhigherthantheforwardprice•AstrongnegativecorrelationimpliesthereverseOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.15StockIndex(Page52)•Canbeviewedasaninvestmentassetpayingadividendyield•ThefuturespriceandspotpricerelationshipisthereforeF0=S0e(r–q)TwhereqisthedividendyieldontheportfoliorepresentedbytheindexOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.16StockIndex(continued)•Fortheformulatobetrueitisimportantthattheindexrepresentaninvestmentasset•Inotherwords,changesintheindexmustcorrespondtochangesinthevalueofatradableportfolio•TheNikkeiindexviewedasadollarnumberdoesnotrepresentaninvestmentassetOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.17IndexArbitrage•WhenF0S0e(r-q)Tanarbitrageurbuysthestocksunderlyingtheindexandsellsfutures•WhenF0S0e(r-q)TanarbitrageurbuysfuturesandshortsorsellsthestocksunderlyingtheindexOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.18IndexArbitrage(continued)•Indexarbitrageinvolvessimultaneoustradesinfuturesandmanydifferentstocks•Veryoftenacomputerisusedtogeneratethetrades•Occasionally(e.g.,onBlackMonday)simultaneoustradesarenotpossibleandthetheoreticalno-arbitragerelationshipbetweenF0andS0doesnotholdOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.19•Aforeigncurrencyisanalogoustoasecurityprovidingadividendyield•Thecontinuousdividendyieldistheforeignrisk-freeinterestrate•Itfollowsthatifrfistheforeignrisk-freeinterestrateFuturesandForwardsonCurrencies(Page55-58)FSerrTf00()Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull3.20FuturesonConsumptionAssets(Page59)F0S0e(r+u)Twhereuisthestoragecostperunittimeasapercentoftheassetvalue.Alternatively,F0(S0+U)erTwhereUisthepresentvalueofthestoragecosts.Options,Futures,andOtherDerivatives,5thedition©2002byJohnC