期权、期货及其他衍生产品 课件 hull-OFOD11-ppt-11

Options,Futures,andOtherDerivativesEleventhEditionChapter11PropertiesofStockOptionsCopyright©2022,2018,2012PearsonEducation,Inc.AllRightsReservedNotationc:Europeancalloptionpricep:EuropeanputoptionpriceSsub0,StockpricetodayK:StrikepriceT:Lifeofoptionsigma,VolatilityofstockpriceC:AmericancalloptionpriceP:AmericanputoptionpriceSsubT,StockpriceatoptionmaturityD:PVofdividendspaidduringlifeofoptionrRisk-freerateformaturityTwithcont.comp.EffectofVariablesonOptionPricing(Table11.1)VariablecpCPSsub0+minus+minusKminus+minus+T??++sigma++++r+minus+minusDminus+minus+AmericanvsEuropeanOptionsAnAmericanoptionisworthatleastasmuchasthecorrespondingEuropeanoption,

Calls:AnArbitrageOpportunity?Supposethatc=3T=1r=10%K=18D=0Isthereanarbitrageopportunity?LowerBoundforEuropeanCallOptionPrices;NoDividends

(Equation11.4)Puts:AnArbitrageOpportunity?SupposethatP=1T=0.5r=5%K=40D=0Isthereanarbitrageopportunity?LowerBoundforEuropeanPutPrices;NoDividends

(Equation11.5)Put-CallParity:NoDividendsConsiderthefollowing2portfolios:PortfolioA:Europeancallonastock+zero-couponbondthatpaysKattimeTPortfolioC:Europeanputonthestock+thestockValuesofPortfolios(Table11.2)BlankBlankSsubTisgreaterthanKSsubTislessthanKPortfolioACalloptionSsubTminusk0Zero-couponbondKKTotalSsubTKPortfolioCPutOption0KminusSsubTShareSsubTSsubTTotalSsubTKThePut-CallParityResult(Equation11.6)Bothareworthmaxatthematurityoftheoptions.Theymustthereforebeworththesametoday.ThismeansthatArbitrageOpportunitiesSupposethatc=3T=0.25r=10%K=30D=0WhatarethearbitragepossibilitieswhenP=2.25?P=1?EarlyExerciseUsuallythereissomechancethatanAmericanoptionwillbeexercisedearly.AnexceptionisanAmericancallonanon-dividendpayingstock.Thisshouldneverbeexercisedearly.AnExtremeSituationForanAmericancalloption:Shouldyouexerciseimmediately?Whatshouldyoudoif:Youwanttoholdthestockforthenext3months?Youdonotfeelthatthestockisworthholdingforthenext3months?ReasonsForNotExercisingaCallEarly(NoDividends)Noincomeissacrificed.Youdelaypayingthestrikeprice.Holdingthecallprovidesinsuranceagainststockpricefallingbelowstrikeprice.BoundsforEuropeanorAmericanCallOptions(NoDividends)

Figure11.3ShouldPutsBeExercisedEarly?ArethereanyadvantagestoexercisinganAmericanputwhen:T=0.25;r=10%K=100;D=0BoundsforEuropeanandAmericanPutOptions(NoDividends)

Figure11.4TheImpactofDividendsonLowerBoundstoOptionPrices(Equations11.8and11.9)ExtensionsofPut–CallParityAmericanoptions:D=0Equation11.7Europeanoptions:Equation11.10Americanoptions:Equation11.11CopyrightThisworkisprotectedbyUnitedStatescopyrightlawsandis

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