Options Futures and Other Derivatives 8t CH16 17讲义ppt课件

1 Chapter16OptionsonStockIndicesandCurrenciesChapter17FuturesOptions Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 1 2 EuropeanOptionsonStocksProvidingaDividendYield WegetthesameprobabilitydistributionforthestockpriceattimeTineachofthefollowingcases 1 ThestockstartsatpriceS0andprovidesadividendyield q2 ThestockstartsatpriceS0e qTandprovidesnoincome 3 EuropeanOptionsonStocksProvidingDividendYieldcontinued WecanvalueEuropeanoptionsbyreducingthestockpricetoS0e qTandthenbehavingasthoughthereisnodividend 4 ExtensionofChapter10Results Equations16 1to16 3 LowerBoundforcalls LowerBoundforputs PutCallParity 5 ExtensionofChapter14Results Equations16 4and16 5 6 TheBinomialModel S0u u S0d d S0 p 1 p f e rT pfu 1 p fd 7 TheBinomialModelcontinued Inarisk neutralworldthestockpricegrowsatr qratherthanatrwhenthereisadividendyieldatrateqTheprobability p ofanupmovementmustthereforesatisfypS0u 1 p S0d S0e r q Tsothat 8 IndexOptions page345 347 ThemostpopularunderlyingindicesintheU S areTheStheXEOandallothersareEuropean Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 8 9 IndexOptionExample Consideracalloptiononanindexwithastrikepriceof880Suppose1contractisexercisedwhentheindexlevelis900Whatisthepayoff 10 UsingIndexOptionsforPortfolioInsurance SupposethevalueoftheindexisS0andthestrikepriceisKIfaportfoliohasabof1 0 theportfolioinsuranceisobtainedbybuying1putoptioncontractontheindexforeach100S0dollarsheldIfthebisnot1 0 theportfoliomanagerbuysbputoptionsforeach100S0dollarsheldInbothcases Kischosentogivetheappropriateinsurancelevel 11 Example1 Portfoliohasabetaof1 0Itiscurrentlyworth 500 000Theindexcurrentlystandsat1000Whattradeisnecessarytoprovideinsuranceagainsttheportfoliovaluefallingbelow 450 000 12 Example2 Portfoliohasabetaof2 0Itiscurrentlyworth 500 000andindexstandsat1000Therisk freerateis12 perannumThedividendyieldonboththeportfolioandtheindexis4 Howmanyputoptioncontractsshouldbepurchasedforportfolioinsurance 13 Ifindexrisesto1040 itprovidesa40 1000or4 returnin3monthsTotalreturn incldividends 5 Excessreturnoverrisk freerate 2 Excessreturnforportfolio 4 IncreaseinPortfolioValue 4 3 1 6 Portfoliovalue 530 000 CalculatingRelationBetweenIndexLevelandPortfolioValuein3months 14 DeterminingtheStrikePrice Table16 2 page347 Anoptionwithastrikepriceof960willprovideprotectionagainsta10 declineintheportfoliovalue 15 ValuingEuropeanIndexOptions WecanusetheformulaforanoptiononastockpayingadividendyieldSetS0 currentindexlevelSetq averagedividendyieldexpectedduringthelifeoftheoption 16 CurrencyOptions CurrencyoptionstradeonNASDAQOMXTherealsoexistsaveryactiveover the counter OTC marketCurrencyoptionsareusedbycorporationstobuyinsurancewhentheyhaveanFXexposure Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 16 17 FormulasforEuropeanCurrencyOptions Equations16 11and16 12 page355 18 TheForeignInterestRate F0 S0e r q T E ST IfF0 S0e r q T thenbuyaforwardcontractandsellthespot YoumaygetoneunitofthestockwithadividendyieldqworthSTatT Withoutdividend oneunitofthestockworthonlyS0e qTnow Ifyousellnowoneunitofthestockandinvestthemoneyinthebank youcangetS0e qTerT S0e r q TatT Hence youmayearn S0e r q T F0 19 ValuingEuropeanCurrencyOptions F0 S0e r rf T E ST IfF0 S0e r rf T thenbuyaforwardcontractandsellthespot YoumaygetoneunitoftheforeigncurrencyworthSTatT However oneunitoftheforeigncurrencyonlyworth 1 e rfT now Ifyouselloneunitoftheforeigncurrencynow youcanget 1 e rfT S0 unitsofthedomesticcurrency Thenyoucaninvesttheminthedomesticbankandearne rfTS0erT S0e r rf TatT Hence youmayearn S0e r rf T F0 20 AlternativeFormulas Equations16 13and16 14 page356 Using 21 ThePayoffs Ifthefuturespositionisclosedoutimmediately Payofffromcall F0 KPayofffromput K F0whereF0isfuturespriceattimeofexercise 22 Put CallParityforFuturesOptions Equation17 1 page365 Considerthefollowingtwoportfolios 1 EuropeancallplusKe rTofcash2 EuropeanputpluslongfuturespluscashequaltoF0e rTTheymustbeworththesameattimeTsothatc Ke rT p F0e rT 23 FuturesPrice 33OptionPrice 4 FuturesPrice 28OptionPrice 0 Futuresprice 30OptionPrice BinomialTreeExample A1 monthcalloptiononfutureshasastrikepriceof29 24 ConsiderthePortfolio longDfuturesshort1calloptionPortfolioisrisklesswhen3D 4 2DorD 0 8 SettingUpaRisklessPortfolio 25 ValuingthePortfolio Risk FreeRateis6 26 GeneralizationofBinomialTreeExample Figure17 2 page368 AderivativelastsfortimeTandisdependentonafuturesprice F0u u F0d d F0 27 Generalization continued ConsidertheportfoliothatislongDfuturesandshort1derivativeTheportfolioisrisklesswhen F0uD F0D u F0dD F0D d 28 Generalization continued ValueoftheportfolioattimeTisF0uD F0D uValueofportfoliotodayis Hence F0uD F0D u e rT 29 Generalization continued SubstitutingforDweobtain p u 1 p d e rTwhere 30 ValuingEuropeanFuturesOptions WecanusetheformulaforanoptiononastockpayingadividendyieldSetS0 currentfuturesprice F0 Setq domesticrisk freerate r Settingq rensuresthattheexpectedgrowthofFinarisk neutralworldiszero 31 Black sFormula Equations17 9and17 10 page3