Option-期权

金融市场学——期权攀登Buy-LongSell-ShortCallPutKeyElementsExerciseorStrikePricePremiumorPriceMaturityorExpirationOptionTerminologyIntheMoney-exerciseoftheoptionwouldbeprofitableCall:marketpriceexercisepricePut:exercisepricemarketpriceOutoftheMoney-exerciseoftheoptionwouldnotbeprofitableCall:marketpriceexercisepricePut:exercisepricemarketpriceAttheMoney-exercisepriceandassetpriceareequalMarketandExercisePriceRelationshipsAmerican-theoptioncanbeexercisedatanytimebeforeexpirationormaturityEuropean-theoptioncanonlybeexercisedontheexpirationormaturitydateAmericanvs.EuropeanOptionsStockOptionsIndexOptionsFuturesOptionsForeignCurrencyOptionsInterestRateOptionsDifferentTypesofOptionsNotationStockPrice=STExercisePrice=XPayofftoCallHolder(ST-X)ifSTX0ifSTXProfittoCallHolderPayoff-PurchasePricePayoffsandProfitsonOptionsatExpiration-CallsPayofftoCallWriter-(ST-X)ifSTX0ifSTXProfittoCallWriterPayoff+PremiumPayoffsandProfitsonOptionsatExpiration-CallsPayoffProfilesforCallsPayoffStockPrice0CallWriterCallHolderPayoffstoPutHolder0ifSTX(X-ST)ifSTXProfittoPutHolderPayoff-PremiumPayoffsandProfitsatExpiration-PutsPayoffstoPutWriter0ifSTX-(X-ST)ifSTXProfitstoPutWriterPayoff+PremiumPayoffsandProfitsatExpiration-PutsPayoffProfilesforPuts0PayoffsStockPricePutWriterPutHolderInvestmentStrategyInvestmentEquityonlyBuystock@100100shares$10,000OptionsonlyBuycalls@101000options$10,000LeveragedBuycalls@10100options$1,000equityBuyT-bills@2%$9,000YieldEquity,Options&LeveragedEquityIBMStockPrice$95$105$115AllStock$9,500$10,500$11,500AllOptions$0$5,000$15,000LevEquity$9,270$9,770$10,770Equity,Options&LeveragedEquity-PayoffsIBMStockPrice$95$105$115AllStock-5.0%5.0%15%AllOptions-100%-50%50%LevEquity-7.3%-2.3%7.7%Equity,Options&LeveragedEquityProtectivePutUse-limitlossPosition-longthestockandlongtheputPayoffSTXSTXStockSTSTPutX-ST0ProtectivePutProfitSTProfit-PStockProtectivePutPortfolioCoveredCallUse-SomedownsideprotectionattheexpenseofgivingupgainpotentialPosition-OwnthestockandwriteacallPayoffSTXSTXStockSTSTCall0-(ST-X)CoveredCallProfitSTProfit-PStockCoveredCallPortfolioStraddle(SameExercisePrice)LongCallandLongPutSpreads-AcombinationoftwoormorecalloptionsorputoptionsonthesameassetwithdifferingexercisepricesortimestoexpirationVerticalormoneyspreadSamematurityDifferentexercisepriceHorizontalortimespreadDifferentmaturitydatesOptionStrategiesSTXSTXPayoffforCallOwned0ST-XPayoffforPutWritten-(X-ST)0TotalPayoffST-XST-XPut-CallParityRelationshipLongCallShortPutPayoffStockPriceCombined=LeveragedEquityPayoffofLongCall&ShortPutSincethepayoffonacombinationofalongcallandashortputareequivalenttoleveragedequity,thepricesmustbeequal.C-P=S0-X/(1+rf)TIfthepricesarenotequalarbitragewillbepossibleArbitrage&PutCallParityStockPrice=110CallPrice=17PutPrice=5RiskFree=10.25%Maturity=.5yrX=105C-PS0-X/(1+rf)T17-5110-(105/1.05)1210Sincetheleveragedequityislessexpensive,acquirethelowcostalternativeandsellthehighcostalternativePutCallParity-DisequilibriumExamplePut-CallParityArbitrageImmediateCashflowinSixMonthsPositionCashflowST105ST105BuyStock-110STSTBorrowX/(1+r)T=100+100-105-105SellCall+170-(ST-105)BuyPut-5105-ST0Total200OptionlikeSecuritiesCallableBondsConvertibleSecuritiesWarrantsCollateralizedLoansExoticOptionsAsianOptionsBarrierOptionsLookbackOptionsCurrencyTranslatedOptionsBinaryOptionsIntrinsicvalue-profitthatcouldbemadeiftheoptionwasimmediatelyexercisedCall:stockprice-exercisepricePut:exerciseprice-stockpriceTimevalue-thedifferencebetweentheoptionpriceandtheintrinsicvalueOptionValuesTimeValueofOptions:CallOptionvalueXStockPriceValueofCallIntrinsicValueTimevalueFactorEffectonvalueStockpriceincreasesExercisepricedecreasesVolatilityofstockpriceincreasesTimetoexpirationincreasesInterestrateincreasesDividendRatedecreasesFactorsInfluencingOptionValues:CallsRestrictionsonOptionValue:CallValuecannotbenegativeValuecannotexceedthestockvalueValueofthecallmustbegreaterthanthevalueofleveredequityCS0-(X+D)/(1+Rf)TCS0-PV(X)-PV(D)AllowableRangeforCallCallValueS0PV(X)+PV(D)LowerBound=S0-PV(X)-PV(D)10020050StockPriceC750CallOptionValueX=125BinomialOptionPricing:TextExampleAlternativePortfolioBuy1shareofstockat$100Borrow$46.30(8%Rate)Netoutlay$53.70PayoffValueofStock50200Repayloan-50-50NetPayoff015053.701500PayoffStructureisexactly2timestheCallBinomialOptionPricing:TextExample53.701500C7502C=$53.70C=$26.85BinomialOptionPricing:TextExampleAlternativePortfolio-oneshareofstockand2callswritten(X=125)PortfolioisperfectlyhedgedStockValue50200CallObligation0-150Netpayoff5050Hence100-2C=46.30orC=26.85AnotherViewofReplicationofPayoffsandOptionValuesGeneralizingtheTwo-StateApproachAssumethatwecanbreaktheyearintotwosix-monthsegmentsIneachsix-monthsegmentthestockcouldincreaseby10%ordecreaseby5%Assumethestockisinitiallysellingat100PossibleoutcomesIncreaseby10%twiceDecreaseby5%twiceIncreaseonceanddecreaseonce(2paths)GeneralizingtheTwo-StateApproach1001101219590.25104.50AssumethatwecanbreaktheyearintothreeintervalsForeachintervalthestockcouldincreaseby5%