Properties ofStock Option PricesChapter 7

PropertiesofStockOptionPricesChapter7Notation•c:Europeancalloptionprice•p:Europeanputoptionprice•S0:Stockpricetoday•X:Strikeprice•T:Lifeofoption•:Volatilityofstockprice•C:AmericanCalloptionprice•P:AmericanPutoptionprice•ST:StockpriceattimeT•D:Presentvalueofdividendsduringoption’slife•r:Risk-freerateformaturityTwithcontcompEffectofVariablesonOptionPricing(Table7.1,page169)cpCPVariableS0XTrD++–+??+++++++–+––––+–+–+AmericanvsEuropeanOptionsAnAmericanoptionisworthatleastasmuchasthecorrespondingEuropeanoptionCcPpCalls:AnArbitrageOpportunity?•Supposethatc=3S0=20T=1r=10%X=18D=0•Isthereanarbitrageopportunity?LowerBoundforEuropeanCallOptionPrices;NoDividends(Equation7.1,page172)cS0-Xe-rTPuts:AnArbitrageOpportunity?•Supposethatp=1S0=37T=0.5r=5%X=40D=0•Isthereanarbitrageopportunity?LowerBoundforEuropeanPutPrices;NoDividends(Equation7.2,page173)pXe-rT-S0Put-CallParity;NoDividends(Equation7.3,page174)•Considerthefollowing2portfolios:–PortfolioA:Europeancallonastock+PVofthestrikepriceincash–PortfolioB:Europeanputonthestock+thestock•BothareworthMAX(ST,X)atthematurityoftheoptions•Theymustthereforebeworththesametoday–Thismeansthatc+Xe-rT=p+S0ArbitrageOpportunities•Supposethatc=3S0=31T=0.25r=10%X=30D=0•Whatarethearbitragepossibilitieswhenp=2.25?p=1?EarlyExercise•UsuallythereissomechancethatanAmericanoptionwillbeexercisedearly•AnexceptionisanAmericancallonanon-dividendpayingstock•Thisshouldneverbeexercisedearly•ForanAmericancalloption:S0=100;T=0.25;X=60;D=0Shouldyouexerciseimmediately?•Whatshouldyoudoif1Youwanttoholdthestockforthenext3months?2Youdonotfeelthatthestockisworthholdingforthenext3months?AnExtremeSituationReasonsForNotExercisingaCallEarly(NoDividends)•Noincomeissacrificed•Wedelaypayingthestrikeprice•HoldingthecallprovidesinsuranceagainststockpricefallingbelowstrikepriceShouldPutsBeExercisedEarly?ArethereanyadvantagestoexercisinganAmericanputwhenS0=60;T=0.25;r=10%X=100;D=0TheImpactofDividendsonLowerBoundstoOptionPrices(Equations7.5and7.6,page179)rTXeDSc00SXeDprTExtensionsofPut-CallParity•Americanoptions;D=0S0-XC-PS0-Xe-rTEquation7.4p.178•Europeanoptions;D0c+D+Xe-rT=p+S0Equation7.7p.180•Americanoptions;D0S0-D-XC-PS0-Xe-rTEquation7.8p.180