期权期货及其衍生品第18弹.ppt

Chapter18TheGreekLetters Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 1 Example Abankhassoldfor 300 000aEuropeancalloptionon100 000sharesofanon dividendpayingstockS0 49 K 50 r 5 s 20 T 20weeks m 13 TheBlack Scholes Mertonvalueoftheoptionis 240 000Howdoesthebankhedgeitsrisktolockina 60 000profit Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 2 Naked CoveredPositions NakedpositionTakenoactionCoveredpositionBuy100 000sharestodayWhataretherisksassociatedwiththesestrategies Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 3 Stop LossStrategy Thisinvolves Buying100 000sharesassoonaspricereaches 50Selling100 000sharesassoonaspricefallsbelow 50 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 4 Stop LossStrategycontinued Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 5 Ignoringdiscounting thecostofwritingandhedgingtheoptionappearstobemax S0 K 0 Whatareweoverlooking Delta SeeFigure18 2 page381 Delta D istherateofchangeoftheoptionpricewithrespecttotheunderlying Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 6 Hedge Traderwouldbehedgedwiththeposition short1000optionsbuy600sharesGain lossontheoptionpositionisoffsetbyloss gainonstockpositionDeltachangesasstockpricechangesandtimepassesHedgepositionmustthereforeberebalanced Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 7 DeltaHedging ThisinvolvesmaintainingadeltaneutralportfolioThedeltaofaEuropeancallonanon dividendpayingstockisN d1 ThedeltaofaEuropeanputonthestockisN d1 1 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 8 TheCostsinDeltaHedgingcontinued Deltahedgingawrittenoptioninvolvesa buyhigh selllow tradingrule Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 9 FirstScenariofortheExample Table18 2page384 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 10 SecondScenariofortheExampleTable18 3 page385 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 11 Theta Theta Q ofaderivative orportfolioofderivatives istherateofchangeofthevaluewithrespecttothepassageoftimeThethetaofacallorputisusuallynegative Thismeansthat iftimepasseswiththepriceoftheunderlyingassetanditsvolatilityremainingthesame thevalueofalongcallorputoptiondeclines Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 12 ThetaforCallOption K 50 s 25 r 5 T 1 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 13 Gamma Gamma G istherateofchangeofdelta D withrespecttothepriceoftheunderlyingassetGammaisgreatestforoptionsthatareclosetothemoney Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 14 GammaforCallorPutOption K 50 s 25 r 5 T 1 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 15 GammaAddressesDeltaHedgingErrorsCausedByCurvature Figure18 7 page389 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 16 S C Stockprice S Callprice C C InterpretationofGamma Foradeltaneutralportfolio DP QDt GDS2 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 17 RelationshipBetweenDelta Gamma andTheta page393 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 18 ForaportfolioofderivativesonastockpayingacontinuousdividendyieldatrateqitfollowsfromtheBlack Scholes Mertondifferentialequationthat Vega Vega n istherateofchangeofthevalueofaderivativesportfoliowithrespecttovolatility Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 19 VegaforCallorPutOption K 50 s 25 r 5 T 1 Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 20 TaylorSeriesExpansion AppendixtoChapter18 ThevalueofaportfolioofderivativesdependentonanassetisafunctionofoftheassetpriceS itsvolatilitys andtimet Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 21 ManagingDelta Gamma Vega DeltacanbechangedbytakingapositionintheunderlyingassetToadjustgammaandvegaitisnecessarytotakeapositioninanoptionorotherderivative Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 22 Example Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 23 Whatpositioninoption1andtheunderlyingassetwillmaketheportfoliodeltaandgammaneutral Answer Long10 000options short6000oftheassetWhatpositioninoption1andtheunderlyingassetwillmaketheportfoliodeltaandveganeutral Answer Long4000options short2400oftheasset Examplecontinued Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 24 Whatpositioninoption1 option2 andtheassetwillmaketheportfoliodelta gamma andveganeutral Wesolve 5000 0 5w1 0 8w2 0 8000 2 0w1 1 2w2 0togetw1 400andw2 6000 Werequirelongpositionsof400and6000inoption1andoption2 Ashortpositionof3240intheassetisthenrequiredtomaketheportfoliodeltaneutral Rho Rhoistherateofchangeofthevalueofaderivativewithrespecttotheinterestrate Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 25 HedginginPractice Tradersusuallyensurethattheirportfoliosaredelta neutralatleastonceadayWhenevertheopportunityarises theyimprovegammaandvegaThereareeconomiesofscaleAsportfoliobecomeslargerhedgingbecomeslessexpensiveperoptionintheportfolio Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 26 ScenarioAnalysis Ascenarioanalysisinvolvestestingtheeffectonthevalueofaportfolioofdifferentassumptionsconcerningassetpricesandtheirvolatilities Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 27 GreekLettersforEuropeanOptionsonanAssetthatProvidesaYieldatRateq Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 28 FuturesContractCanBeUsedforHedging Thedeltaofafuturescontractonanassetpayingayieldatrateqise r q TtimesthedeltaofaspotcontractThepositionrequiredinfuturesfordeltahedgingisthereforee r q Ttimesthepositionrequiredinthecorrespondingspotcontract Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 29 HedgingvsCreationofanOptionSynthetically Whenwearehedgingwetakepositionsthatoffsetdelta gamma vega etcWhenwecreateanoptionsyntheticallywetakepositionsthatmatchdelta gamma vega etc Options Futures andOtherDerivatives 8thEdition Copyright JohnC Hull2012 30 PortfolioInsurance InOcto