公司理财（英文版·第5版）课件 第20章　金融期权

CorporateFinanceFifthEditionChapter20FinancialOptionsCopyright©2020,2017,2014PearsonEducation,Inc.

AllRightsReservedChapterOutline20.1

OptionBasics20.2OptionPayoffsatExpiration20.3Put-CallParity20.4FactorsAffectingOptionPrices20.5ExercisingOptionsEarly20.6

OptionsandCorporateFinanceLearningObjectives(1of3)Definethefollowingterms:calloption,putoption,exerciseprice,strikeprice,exercisingtheoption,expirationdate,Americanoption,Europeanoption,in-the-money,andout-of-the-money.Computethevalueofacalloraputoptionatexpiration.Listtherightsandobligationsofthebuyeroftheoptionandtheselleroftheoption.LearningObjectives(2of3)Useput-callparitytosolveforthecallpremium,theputpremium,thestockprice,thestrikeprice,orthedividend.Discussthefollowingfactorsthatinfluencecallandputoptionvalues:stockprice,strikeprice,andvolatility.Describearbitrageboundsforoptionprices.LearningObjectives(3of3)ExplainwhyitisneveroptimaltoexerciseanAmericancalloptionearlyonanon-dividend-payingstock,andwhyitissometimesoptimaltoexerciseanAmericanputoptionearly.Explaintheuseofoptionmodelingtovalueequity.Describehowcorporatedebtcanbeviewedasaportfolioofrisklessdebtandashortpositioninaputoption.20.1OptionBasics(1of2)FinancialOptionAcontractthatgivesitsownertheright(butnottheobligation)topurchaseorsellanassetatafixedpriceassomefuturedateCallOptionAfinancialoptionthatgivesitsownertherighttobuyanasset20.1OptionBasics(2of2)PutOptionAfinancialoptionthatgivesitsownertherighttosellanassetOptionWriterThesellerofanoptioncontractUnderstandingOptionContracts(1of3)ExercisinganOptionWhenaholderofanoptionenforcestheagreementandbuysorsellsashareofstockattheagreed-uponpriceStrikePrice(ExercisePrice)ThepriceatwhichanoptionholderbuysorsellsashareofstockwhentheoptionisexercisedExpirationDateThelastdateonwhichanoptionholderhastherighttoexercisetheoptionUnderstandingOptionContracts(2of3)AmericanOptionOptionsthatallowtheirholderstoexercisetheoptiononanydateupto,andincluding,theexpirationdateEuropeanOptionOptionsthatallowtheirholderstoexercisetheoptiononlyontheexpirationdateNote:ThenamesAmericanandEuropeanhavenothingtodowiththelocationwheretheoptionsaretradedUnderstandingOptionContracts(3of3)Theoptionbuyer(holder)HoldstherighttoexercisetheoptionandhasalongpositioninthecontractTheoptionseller(writer)Sells(orwrites)theoptionandhasashortpositioninthecontractBecausethelongsidehastheoptiontoexercise,theshortsidehasanobligationtofulfillthecontractifitisexercised.ThebuyerpaysthewriterapremiumInterpretingStockOptionQuotations(1of3)Stockoptionsaretradedonorganizedexchanges.Byconvention,alltradedoptionsexpireontheSaturdayfollowingthethirdFridayofthemonth.OpenInterestThetotalnumberofcontractsofaparticularoptionthathavebeenwrittenTable20.1OptionQuotesforeBayStockSource:ChicagoBoardOptionsExchangeatInterpretingStockOptionQuotations(2of3)At-the-moneyDescribesanoptionwhoseexercisepriceisequaltothecurrentstockpriceIn-the-moneyDescribesanoptionwhosevalue,ifimmediatelyexercised,wouldbepositiveOut-of-the-moneyDescribesanoptionwhosevalue,ifimmediatelyexercised,wouldbenegativeInterpretingStockOptionQuotations(3of3)Deepin-the-moneyDescribesanoptionthatisin-the-moneyandforwhichthestrikepriceandthestockpriceareveryfarapartDeepout-of-the-moneyDescribesanoptionthatisout-of-the-moneyandforwhichthestrikepriceandthestockpriceareveryfarapartTextbookExample20.1(1of2)PurchasingOptionsProblemItistheafternoonofSeptember10,2018,andyouhavedecidedtopurchase10JanuarycallcontractsoneBaystockwithanexercisepriceof$35.Becauseyouarebuying,youmustpaytheaskprice.Howmuchmoneywillthispurchasecostyou?Isthisoptionin-the-moneyorout-of-the-money?TextbookExample20.1(2of2)SolutionFromTable20.1,theaskpriceofthisoptionis$1.66.Youarepurchasing10contractsandeachcontractison100shares,sothetransactionwillcost(ignoringanybrokeragefees).Becausethisisacalloptionandtheexercisepriceisabovethecurrentstockprice($33.75),theoptioniscurrentlyout-of-the-money.AlternativeExample20.1(1of3)ProblemYouhavedecidedtopurchase2/15/2019putcontractsontheD

J

I

Awithanexercisepriceof$246.Source:CBOE.comAlternativeExample20.1(2of3)ProblemHowmuchmoneywillthispurchasecostyou?Isthisoptionin-the-moneyorout-of-the-money?AlternativeExample20.1(3of3)SolutionTheaskpriceis$3.65percontract.ThetotalcostisBecausethestrikeprice($246)islessthanthecurrentprice($247.06),theputoptionisout-of-the-money.OptionsonOtherFinancialSecurities(1of2)Althoughthemostcommonlytradedoptionsareonstocks,optionsonotherfinancialassets,liketheS&P100index,theS&P500index,theDowJonesIndustrialindex,andtheN

Y

S

Eindex,arealsotraded.OptionsonOtherFinancialSecurities(2of2)HedgeToreduceriskbyholdingcontractsorsecuritieswhosepayoffsarenegativelycorrelatedwithsomeriskexposureSpeculateWheninvestorsusecontractsorsecuritiestoplaceabetonthedirectioninwhichtheybelievethemarketislikelytomove20.2OptionPayoffsatExpiration(1of2)LongPositioninanOptionContractThevalueofacalloptionatexpirationisWhereSisthestockpriceatexpiration,Kistheexerciseprice,Cisthevalueofthecalloption,andmaxisthemaximumofthetwoquantitiesintheparentheses.Figure20.1PayoffofaCallOptionwithaStrikePriceof$20atExpiration20.2OptionPayoffsatExpiration(2of2)LongPositioninanOptionContractThevalueofaputoptionatexpirationisWhereSisthestockpriceatexpiration,Kistheexerciseprice,Pisthevalueoftheputoption,andmaxisthemaximumofthetwoquantitiesintheparentheses.TextbookExample20.2(1of2)PayoffofaPutOptionatMaturityProblemYouownaputoptiononOracleCorporationstockwithanexercisepriceof$20thatexpirestoday.Plotthevalueofthisoptionasafunctionofthestockprice.TextbookExample20.2(2of2)SolutionLetSbethestockpriceandPbethevalueoftheputoption.ThevalueoftheoptionisPlottingthisfunctiongivesAlternativeExample20.2(1of2)ProblemYouownaputoptiononDellstockwithanexercisepriceof$12.50thatexpirestoday.Plotthevalueofthisoptionasafunctionofthestockprice.AlternativeExample20.2(2of2)SolutionLetSbethestockpriceandPbethevalueoftheputoption.ThevalueoftheoptionisShortPositioninanOptionContractAninvestorthatsellsanoptionhasanobligation.Thisinvestortakestheoppositesideofthecontracttotheinvestorwhoboughttheoption.Thustheseller’scashflowsarethenegativeofthebuyer’scashflows.Figure20.2ShortPositioninaCallOptionatExpirationTextbookExample20.3(1of2)PayoffofaShortPositioninaPutOptionProblemYouareshortinaputoptiononOracleCorporationstockwithanexercisepriceof$20thatexpirestoday.Whatisyourpayoffatexpirationasafunctionofthestockprice?TextbookExample20.3(2of2)Solution

IfSisthestockprice,yourcashflowswillbeIfthecurrentstockpriceis$30,thentheputwillnotbeexercisedandyouwillowenothing.Ifthecurrentstockpriceis$15,theputwillbeexercisedandyouwilllose$5.Thefigureplotsyourcashflows:ProfitsforHoldinganOptiontoExpirationAlthoughpayoutsonalongpositioninanoptioncontractarenevernegative,theprofitfrompurchasinganoptionandholdingittoexpirationcouldbenegativebecausethepayoutatexpirationmightbelessthantheinitialcostoftheoption.Figure20.3ProfitfromHoldingaCallOptiontoExpirationTextbookExample20.4(1of2)ProfitonHoldingaPositioninaPutOptionUntilExpirationProblemAssumeyoudecidedtopurchaseeachoftheJanuaryputoptionsquotedinTable20.1onSeptember10,2018,andyoufinancedeachpositionbyshortingatwo-monthbondwithayieldof2.5%.Plottheprofitofeachpositionasafunctionofthestockpriceonexpiration.TextbookExample20.4(2of2)SolutionSupposeSisthestockpriceonexpiration,Kisthestrikeprice,andPisthepriceofeachputoptiononSeptember10th.ThenyourcashflowsontheexpirationdatewillbeTheplotisshownbelow.Notethesametrade-offbetweenthemaximumlossandthepotentialforprofitasforthecalloptions.ReturnsforHoldinganOptiontoExpiration(1of2)Themaximumlossonapurchasedcalloptionis100%(whentheoptionexpiresworthless).Out-of-themoneycalloptionsaremorelikelytoexpireworthless,butifthestockgoesupsufficiently,itwillalsohaveamuchhigherreturnthananin-the-moneycalloption.Calloptionshavemoreextremereturnsthanthestockitself.ReturnsforHoldinganOptiontoExpiration(2of2)Themaximumlossonapurchasedputoptionis100%(whentheoptionexpiresworthless).Putoptionswillhavehigherreturnsinstateswithlowstockprices.Putoptionsaregenerallynotheldasaninvestment,butratherasinsurancetohedgeotherriskinaportfolio.Figure20.4OptionReturnsfromPurchasinganOptionandHoldingIttoExpirationCombinationsofOptions(1of4)StraddleAportfoliothatislongacalloptionandaputoptiononthesamestockwiththesameexercisedateandstrikepriceThisstrategymaybeusedifinvestorsexpectthestocktobeveryvolatileandmoveupordownalargeamountbutdonotnecessarilyhaveaviewonwhichdirectionthestockwillmove.Figure20.5PayoffandProfitfromaStraddleCombinationsofOptions(2of4)StrangleAportfoliothatislongacalloptionandaputoptiononthesamestockwiththesameexercisedatebutthestrikepriceonthecallexceedsthestrikepriceontheputTextbookExample20.5(1of2)StrangleProblemYouarelongbothacalloptionandaputoptiononHewlett-Packardstockwiththesameexpirationdate.Theexercisepriceofthecalloptionis$40;theexercisepriceoftheputoptionis$30.Plotthepayoffofthecombinationatexpiration.TextbookExample20.5(2of2)SolutionTheredlinerepresentstheput’spayoutsandthebluelinerepresentsthecall’spayouts.Inthiscase,youdonotreceivemoneyifthestockpriceisbetweenthetwostrikeprices.Thisoptioncombinationisknownasastrangle.CombinationsofOptions(3of4)ButterflySpreadAportfoliothatislongtwocalloptionswithdifferingstrikepricesandisshorttwocalloptionswithastrikepriceequaltotheaveragestrikepriceofthefirsttwocallsAlthoughastraddlestrategymakesmoneywhenthestockandstrikepricesarefarapart,abutterflyspreadmakesmoneywhenthestockandstrikepricesareclose.Figure20.6ButterflySpreadCombinationsofOptions(4of4)ProtectivePutAlongpositioninaputheldonastockyoualreadyownPortfolioInsuranceAprotectiveputwrittenonaportfolioratherthanasinglestockWhentheputdoesnotitselftrade,itissyntheticallycreatedbyconstructingareplicatingportfolio.PortfolioinsurancecanalsobeachievedbypurchasingabondandacalloptionFigure20.7PortfolioInsuranceTheplotsshowtwodifferentwaystoinsureagainstthepossibilityofthepriceofTripadvisorstockfallingbelow$45.Theorangelinein(a)indicatesthevalueontheexpirationdateofapositionthatislongoneshareofAmazonstockandoneEuropeanputoptionwithastrikeof$45(thebluedashedlineisthepayoffofthestockitself).Theorangelinein(b)showsthevalueontheexpirationdateofapositionthatislongazero-couponriskfreebondwithafacevalueof$45andaEuropeancalloptiononTripadvisorwithastrikepriceof$45(thegreendashedlineisthebondpayoff).20.3Put-CallParity(1of4)ConsiderthetwodifferentwaystoconstructportfolioinsurancediscussedpreviouslyPurchasethestockandaputPurchaseabondandacall.Becausebothpositionsprovideexactlythesamepayoff,theLawofOnePricerequiresthattheymusthavethesameprice.20.3Put-CallParity(2of4)Therefore,WhereKisthestrikepriceoftheoption(thepriceyouwanttoensurethatthestockwillnotdropbelow),Cisthecallprice,Pistheputprice,andSisthestockprice.20.3Put-CallParity(3of4)RearrangingthetermsgivesanexpressionforthepriceofaEuropeancalloptionforanon-dividend-payingstock:Thisrelationshipbetweenthevalueofthestock,thebond,andcallandputoptionsisknownasput-callparity.TextbookExample20.6(1of3)UsingPut-CallParityProblemYouareanoptionsdealerwhodealsinnon-publiclytradedoptions.Oneofyourclientswantstopurchaseaone-yearEuropeancalloptiononH

A

LComputerSystemsstockwithastrikepriceof$20.Anotherdealeriswillingtowriteaone-yearEuropeanputoptiononH

A

Lstockwithastrikepriceof$20,andsellyoutheputoptionforapriceof$3.50pershare.IfH

A

Lpaysnodividendsandiscurrentlytradingfor$18pershare,andiftherisk-freeinterestrateis6%,whatisthelowestpriceyoucanchargefortheoptionandguaranteeyourselfaprofit?TextbookExample20.6(2of3)SolutionUsingput-callparity,wecanreplicatethepayoffoftheone-yearcalloptionwithastrikepriceof$20byholdingthefollowingportfolio:Buytheone-yearputoptionwithastrikepriceof$20fromthedealer,buythestock,andsellaone-yearrisk-freezero-couponbondwithafacevalueof$20.Withthiscombination,wehavethefollowingfinalpayoffdependingonthefinalpriceofH

A

Lstockinoneyear,TextbookExample20.6(3of3)Notethatthefinalpayoffoftheportfolioofthethreesecuritiesmatchesthepayoffofacalloption.Therefore,wecansellthecalloptiontoourclientandhavefuturepayoffofzeronomatterwhathappens.Doingsoisworthwhileaslongaswecansellthecalloptionformorethanthecostoftheportfolio,whichisAlternativeExample20.6(1of2)ProblemAssumeYouwanttobuyaone-yearcalloptionandputoptiononDellibar.Thestrikepriceforeachis$15.ThecurrentpricepershareofDellibaris$14.79.Dellibardoesnotpayadividend.Therisk-freerateis2.5%.Thepriceofeachcallis$2.23.Usingput-callparity,whatshouldbethepriceofeachput?AlternativeExample20.6(2of2)SolutionPut-CallParitystates20.3Put-CallParity(4of4)Ifthestockpaysadividend,put-callparitybecomesTextbookExample20.7(1of2)UsingOptionstoValueNear-TermDividendsProblemItisFebruary2016andyouhavebeenasked,inyourpositionasafinancialanalyst,tocomparetheexpecteddividendsofseveralpopularstockindicesoverthenextseveralyears.Checkingthemarkets,youfindthefollowingclosingpricesforeachindex,aswellasforoptionsexpiringDecember2018.IndexFeb2016IndexValueDec2018Index

Options

StrikePriceDec2018Index

Options

CallPriceDec2018Index

Options

PutPriceDJIA164.8516019.7822.73S&P5001929.801900243.25278.00Nasdaq1004200.664200636.35666.85Russell20001022.081000150.10166.80Ifthecurrentrisk-freeinterestrateis0.90%foraDecember2018maturity,estimatetherelativecontributionofthenear-termdividendstothevalueofeachindex.TextbookExample20.7(2of2)SolutionRearrangingthePut-CallParityrelationgivesApplyingthistotheDJIA,wefindthattheexpectedpresentvalueofitsdividendsoverthenext34monthisTherefore,expecteddividendsthroughDecember2018representofthecurrentvalueofD

J

I

Aindex.Doingasimilarcalculationfortheotherindices,wefindthatnear-termdividendsaccountfor5.8%ofthevalueoftheS&P500,3.2%oftheN

A

S

D

A

Q100,and6.2%oftheRussell2000.20.4FactorsAffectingOptionPrices

(1of2)StrikePriceandStockPriceThevalueofacalloptionincreases(decreases)asthestrikepricedecreases(increases),allotherthingsheldconstant.Thevalueofaputoptionincreases(decreases)asthestrikepriceincreases(decreases),allotherthingsheldconstant.20.4FactorsAffectingOptionPrices(2of2)StrikePriceandStockPriceThevalueofacalloptionincreases(decreases)asthestockpriceincreases(decreases),allotherthingsheldconstant.Thevalueofaputoptionincreases(decreases)asthestockpricedecreases(increases),allotherthingsheldconstant.ArbitrageBoundsonOptionPrices

(1of3)AnAmericanoptioncannotbeworthlessthanitsEuropeancounterpart.Aputoptioncannotbeworthmorethanitsstrikeprice.Acalloptioncannotbeworthmorethanthestockitself.ArbitrageBoundsonOptionPrices

(2of3)IntrinsicValueTheamountbywhichanoptionisin-the-money,orzeroiftheoptionisout-of-the-money.AnAmericanoptioncannotbeworthlessthanitsintrinsicvalue.ArbitrageBoundsonOptionPrices

(3of3)TimeValueThedifferencebetweenanoption’spriceanditsintrinsicvalue.AnAmericanoptioncannothaveanegativetimevalue.OptionPricesandtheExerciseDateForAmericanoptions,thelongerthetimetotheexercisedate,themorevaluabletheoption.AnAmericanoptionwithalaterexercisedatecannotbeworthlessthananotherwiseidenticalAmericanoptionwithanearlierexercisedate.However,aEuropeanoptionwithalaterexercisedatecanbeworthlessthananotherwiseidenticalEuropeanoptionwithanearlierexercisedate.OptionPricesandVolatilityThevalueofanoptiongenerallyincreaseswiththevolatilityofthestock.TextbookExample20.8(1of2)OptionValueandVolatilityProblemTwoEuropeancalloptionswithastrikepriceof$50arewrittenontwodifferentstocks.Supposethattomorrow,thelow-volatilitystockwillhaveapriceof$50forcertain.Thehigh-volatilitystockwillbewortheither$60or$40,witheachpricehavingequalprobability.Iftheexercisedateofbothoptionsistomorrow,whichoptionwillbeworthmoretoday?TextbookExample20.8(2of2)SolutionTheexpectedvalueofbothstockstomorrowis$50̶thelow-volatilitystockwillbeworththisamountforsure,andthehigh-high-volatilitystockhasanexpectedvalueofHowever,theoptionshaveverydifferentvalues.Theoptiononthelow-volatilitystockisworthnothingbecausethereisnochanceitwillexpirein-the-money(thelow-volatilitystockwillbeworth$50andthestrikepriceis$50).Theoptiononthehigh-volatilitystockisworthapositiveamountbecausethereisa50%chancethatitwillbeworthanda50%chancethatitwillbeworthless.Thevaluetodayofa50%chanceofapositivepayoff(withnochanceofaloss)ispositive.AlternativeExample20.8(1of2)ProblemYouareconsideringinvestinginFinray,whichcurrentlytradesat$13.10pershare.Aone-yearcalloptionwithastrikepriceof$13costs$0.87,whileaputoptionwiththesamestrikepriceandexpirationcosts$0.98.Iftherisk-freerateis0.10%,whatisFinray’sexpecteddividend?AlternativeExample20.8(2of2)SolutionPut-CallParitystatesSolvingforPV(Div)yields20.5ExercisingOptionsEarlyAlthoughanAmericanoptioncannotbeworthlessthanitsEuropeancounterpart,theymayhaveequalvalue.Non-Dividend-PayingStocks(1of5)Foranon-dividendpayingstock,Put-CallParitycanbewrittenasWheredis(K)istheamountofthediscountfromfacevalueofthezero-couponbondK.Non-Dividend-PayingStocks(2of5)Becausedis(K)andPmustbepositivebeforetheexpirationdate,aEuropeancallalwayshasapositivetimevalue.BecauseanAmericanoptionisworthatleastasmuchasaEuropeanoption,itmustalsohaveapositivetimevaluebeforeexpiration.Thus,thepriceofanycalloptiononanon-dividend-payingstockalwaysexceedsitsintrinsicvaluepriortoexpiration.Non-Dividend-PayingStocks(3of5)Thisimpliesthatitisneveroptimaltoexerciseacalloptiononanon-dividendpayingstockearly.Youarealwaysbetteroffjustsellingtheoption.BecauseitisneveroptimaltoexerciseanAmericancallonanon-dividend-payingstockearly,anAmericancallonanon-dividendpayingstockhasthesamepriceasitsEuropeancounterpart.Non-Dividend-PayingStocks(4of5)However,itmaybeoptimaltoexerciseaputoptiononanon-dividendpayingstockearlyNon-Dividend-PayingStocks(5of5)Whenaputoptionissufficientlydeepin-the-money,dis(K)willbelargerelativetothevalueofthecall,andthetimevalueofaEuropeanputoptionwillbenegative.Inthatcase,theEuropeanputwillsellforlessthanitsintrinsicvalue.However,itsAmericancounterpartcannotsellforlessthanitsintrinsicvalue,whichimpliesthatanAmericanputoptioncanbeworthmorethananotherwiseidenticalEuropeanoption.TextbookExample20.9(1of2)EarlyExerciseofaPutOptiononaNon-Dividend-PayingStockProblemTable20.2liststhequotesfromtheC

B

O

EonJuly20,2018,foroptionsonAlphabetstock(Google’sholdingcompany)expiringinSeptember2018.Alphabetwillnotpayadividendduringthisperiod.Identifyanyoptionforwhichexercisingtheoptionearlyisbetterthansellingit.TextbookExample20.9(2of2)SolutionBecauseAlphabetpaysnodividendsduringthelifeoftheseoptions(July2018toSeptember2018),itshouldnotbeoptimaltoexercisethecalloptionsearly.Infact,wecancheckthatthebidpriceforeachcalloptionexceedsthatoption’sintrinsicvalue,soitwouldbebettertosellthecallthantoexerciseit.Forexample,thepayofffromexercisingacallwithastrikeof1000earlyiswhiletheoptioncanbesoldfor$204.90.Ontheotherhand,anAlphabetshareholderholdingaputoptionwithastrikepriceof$1360orhigherwouldbebetteroffexercising—ratherthanselling—theoption.Forexample,byexercisingthe1400puttheshareholderwouldreceive$1400forherstock,whereasbysellingthestockandtheoptionshewouldonlyreceiveThesameisnottrueoftheputswithstrikesbelow$1360,however.Forexample,theholderofthe1320putoptionwhoexercisesitearlywouldreceive$1320forherstock,butwouldnetbysellingthestockandtheputinstead.Thus,earlyexerciseisonlyoptimalforthedeepin-the-moneyputoptions.Table20.2AlphabetOptionQuotesSource:ChicagoBoardOptionsExchangeatDividend-PayingStocks(1of3)Theput-callparityrelationshipforadividend-payingstockcanbewrittenasIfPV(Div)islargeenough,thetimevalueofaEuropeancalloptioncanbenegative,implyingthatitspricecouldbelessthanitsintrinsicvalue.BecauseanAmericanoptioncanneverbeworthlessthanitsintrinsicvalue,thepriceoftheAmericanoptioncanexceedthepriceofaEuropeanoption.Dividend-PayingStocks(2of3)Withadividendpayingstock,itmaybeoptimaltoexercisetheAmericancalloptionearly.Whenacompanypaysadividend,investorsexpectthepriceofthestocktodrop.Whenthestockpricefalls,theownerofacalloptionloses.Unliketheownerofthestock,theoptionholderdoesnotgetthedividendascompensation.However,byexercisingearlyandholdingthestock,theownerofthecalloptioncancapturethedividend.TextbookExample20.10(1of2)EarlyExerciseofOptionsonaDividend-PayingStockProblemGeneralElectric(G

E)stockwentex-dividendonDecember22,2005(onlyequityholdersonthepreviousdayareentitledtothedividend).Thedividendamountwas$0.25.Table20.3liststhequotesforG

EoptionsonDecember21,2005.Fromthequotes,identifytheoptionsthatshouldbeexercisedearlyratherthansold.TextbookExample20.10(2of2)SolutionTheholderofacalloptiononG

Estockwithastrikepriceof$32.50orlessisbetteroffexercising̶ratherthanselling̶theoption.Forexample,exercisingthe06January10callandimmediatelysellingthestockwouldnetTheoptionitselfcanbesoldfor$25.40,sotheholderisbetteroffby$0.12byexercisingthecallratherthansellingit.Tounderstandwhyearlyexercisecanbeoptimalinthiscase,notethatinterestrateswereabout0.33%permonth,sothevalueofdelayingpaymentofthe$10strikepriceuntilJanuarywasworthonly$0.033,andtheputoptionwasworthlessthan$0.05.Thus,fromEq.20.7,thebenefitofdelaywasmuchlessthanthe$0.25valueofthedividend.Ontheotherhand,alloftheputoptionslistedhaveapositivetimevalueandthusshouldnotbeexercisedearly.Inthiscase,waitingforthestocktogoex-dividendismorevaluablethanthecostofdelayingthereceiptofthestrikeprice.Table20.3OptionQuotesforG

EonDecember21,2005(G

Epaid$0.25dividendwithex-dividenddateofDecember22,2005)Source:ChicagoBoardOptionsExchangeatDividend-PayingStocks(3of3)Theput-callparityrelationshipforputscanbewrittenasAsstatedearlier,Europeanoptionsmaytradeforlessthantheirintrinsicvalue.Onthenextslide,notethatalltheputswithastrikepriceof$1400orhighertradeforlessthantheirexercisevalue.Table20.4Two-YearCallandPutOptionsontheS&P500IndexSource:ChicagoBoardOptionsExchangeat20.6OptionsandCorporateFinanceEquityasaCallOptionAshareofstockcanbethoughtofasacalloptionontheassetsofthefirmwithastrikepriceequaltothevalueofdebtoutstanding.Ifthefirm’svaluedoesnotexceedthevalueofdebtoutstandingattheendoftheperiod,thefirmmustdeclarebankruptcyandtheequityholdersreceivenothing.Ifthevalueexceedsthevalueofdebtoutstanding,theequityholdersgetwhateverisleftoncethedebthasbeenrepaid.Figure20.8EquityasaCallOptionDebtasanOptionPortfolio(1of2)Debtholderscanbeviewedasownersofthefirmhavingsoldacalloptionwithastrikepriceequaltotherequireddebtpayment.Ifthevalueofthefirmexceedstherequireddebtpayment,thecallwillbeexercised;thedebtholderswillthereforerec