第二十二章 期权与公司理财：基本概念(PPT 67页)

ChapterOutline,22.1Options22.2CallOptions22.3PutOptions22.4SellingOptions22.5ReadingTheWallStreetJournal22.6CombinationsofOptions22.7ValuingOptions22.8AnOptionPricingFormula22.9StocksandBondsasOptions22.10Capital-StructurePolicyandOptions22.11MergersandOptions22.12InvestmentinRealProjectsandOptions22.13SummaryandConclusions,22.1Options,Manycorporatesecuritiesaresimilartothestockoptionsthataretradedonorganizedexchanges.Almosteveryissueofcorporatestocksandbondshasoptionfeatures.Inaddition,capitalstructureandcapitalbudgetingdecisionscanbeviewedintermsofoptions.,22.1OptionsContracts:Preliminaries,Anoptiongivestheholdertheright,butnottheobligation,tobuyorsellagivenquantityofanasseton(orperhapsbefore)agivendate,atpricesagreedupontoday.CallsversusPutsCalloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetatsometimeinthefuture,atpricesagreedupontoday.Whenexercisingacalloption,you“callin”theasset.Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofanassetatsometimeinthefuture,atpricesagreedupontoday.Whenexercisingaput,you“put”theassettosomeone.,22.1OptionsContracts:Preliminaries,ExercisingtheOptionTheactofbuyingorsellingtheunderlyingassetthroughtheoptioncontract.StrikePriceorExercisePriceReferstothefixedpriceintheoptioncontractatwhichtheholdercanbuyorselltheunderlyingasset.ExpiryThematuritydateoftheoptionisreferredtoastheexpirationdate,ortheexpiry.EuropeanversusAmericanoptionsEuropeanoptionscanbeexercisedonlyatexpiry.Americanoptionscanbeexercisedatanytimeuptoexpiry.,OptionsContracts:Preliminaries,In-the-MoneyTheexercisepriceislessthanthespotpriceoftheunderlyingasset.At-the-MoneyTheexercisepriceisequaltothespotpriceoftheunderlyingasset.Out-of-the-MoneyTheexercisepriceismorethanthespotpriceoftheunderlyingasset.,OptionsContracts:Preliminaries,IntrinsicValueThedifferencebetweentheexercisepriceoftheoptionandthespotpriceoftheunderlyingasset.SpeculativeValueThedifferencebetweentheoptionpremiumandtheintrinsicvalueoftheoption.,OptionPremium,=,IntrinsicValue,SpeculativeValue,+,22.2CallOptions,Calloptionsgivestheholdertheright,butnottheobligation,tobuyagivenquantityofsomeassetonorbeforesometimeinthefuture,atpricesagreedupontoday.Whenexercisingacalloption,you“callin”theasset.,BasicCallOptionPricingRelationshipsatExpiry,Atexpiry,anAmericancalloptionisworththesameasaEuropeanoptionwiththesamecharacteristics.Ifthecallisin-the-money,itisworthST-E.Ifthecallisout-of-the-money,itisworthless.CaT=CeT=MaxST-E,0WhereSTisthevalueofthestockatexpiry(timeT)Eistheexerciseprice.CaTisthevalueofanAmericancallatexpiryCeTisthevalueofaEuropeancallatexpiry,CallOptionPayoffs,-20,100,90,80,70,60,0,10,20,30,40,50,-40,20,0,-60,40,60,Stockprice($),Optionpayoffs($),Buyacall,Exerciseprice=$50,CallOptionPayoffs,Writeacall,Exerciseprice=$50,CallOptionProfits,Writeacall,Buyacall,Exerciseprice=$50;optionpremium=$10,22.3PutOptions,Putoptionsgivestheholdertheright,butnottheobligation,tosellagivenquantityofanassetonorbeforesometimeinthefuture,atpricesagreedupontoday.Whenexercisingaput,you“put”theassettosomeone.,BasicPutOptionPricingRelationshipsatExpiry,Atexpiry,anAmericanputoptionisworththesameasaEuropeanoptionwiththesamecharacteristics.Iftheputisin-the-money,itisworthE-ST.Iftheputisout-of-the-money,itisworthless.PaT=PeT=MaxE-ST,0,PutOptionPayoffs,-20,100,90,80,70,60,0,10,20,30,40,50,-40,20,0,-60,40,60,Stockprice($),Optionpayoffs($),Buyaput,Exerciseprice=$50,PutOptionPayoffs,-20,100,90,80,70,60,0,10,20,30,40,50,-40,20,0,-60,40,60,Optionpayoffs($),writeaput,Exerciseprice=$50,Stockprice($),PutOptionProfits,-20,100,90,80,70,60,0,10,20,30,40,50,-40,20,0,-60,40,60,Stockprice($),Optionprofits($),Buyaput,Writeaput,Exerciseprice=$50;optionpremium=$10,10,-10,22.4SellingOptions,Theseller(orwriter)ofanoptionhasanobligation.,Thepurchaserofanoptionhasanoption.,22.5ReadingTheWallStreetJournal,22.5ReadingTheWallStreetJournal,Thisoptionhasastrikepriceof$135;,arecentpriceforthestockis$138.25,Julyistheexpirationmonth,22.5ReadingTheWallStreetJournal,Thismakesacalloptionwiththisexercisepricein-the-moneyby$3.25=$138$135.,Putswiththisexercisepriceareout-of-the-money.,22.5ReadingTheWallStreetJournal,Onthisday,2,365calloptionswiththisexercisepriceweretraded.,22.5ReadingTheWallStreetJournal,TheCALLoptionwithastrikepriceof$135istradingfor$4.75.,Sincetheoptionison100sharesofstock,buyingthisoptionwouldcost$475pluscommissions.,22.5ReadingTheWallStreetJournal,Onthisday,2,431putoptionswiththisexercisepriceweretraded.,22.5ReadingTheWallStreetJournal,ThePUToptionwithastrikepriceof$135istradingfor$.8125.,Sincetheoptionison100sharesofstock,buyingthisoptionwouldcost$81.25pluscommissions.,22.6CombinationsofOptions,Putsandcallscanserveasthebuildingblocksformorecomplexoptioncontracts.Ifyouunderstandthis,youcanbecomeafinancialengineer,tailoringtherisk-returnprofiletomeetyourclientsneeds.,ProtectivePutStrategy:BuyaPutandBuytheUnderlyingStock:PayoffsatExpiry,Buyaputwithanexercisepriceof$50,Buythestock,ProtectivePutstrategyhasdownsideprotectionandupsidepotential,$50,$0,$50,Valueatexpiry,Valueofstockatexpiry,ProtectivePutStrategyProfits,Buyaputwithexercisepriceof$50for$10,Buythestockat$40,$40,ProtectivePutstrategyhasdownsideprotectionandupsidepotential,$40,$0,-$40,$50,Valueatexpiry,Valueofstockatexpiry,CoveredCallStrategy,Sellacallwithexercisepriceof$50for$10,Buythestockat$40,$40,Coveredcall,$40,$0,-$40,$10,-$30,$30,$50,Valueofstockatexpiry,Valueatexpiry,LongStraddle:BuyaCallandaPut,Buyaputwithanexercisepriceof$50for$10,$40,ALongStraddleonlymakesmoneyifthestockpricemoves$20awayfrom$50.,$40,$0,-$20,$50,Buyacallwithanexercisepriceof$50for$10,-$10,$30,$60,$30,$70,Valueofstockatexpiry,Valueatexpiry,ShortStraddle:SellaCallandaPut,Sellaputwithexercisepriceof$50for$10,$40,AShortStraddleonlylosesmoneyifthestockpricemoves$20awayfrom$50.,-$40,$0,-$30,$50,Sellacallwithanexercisepriceof$50for$10,$10,$20,$60,$30,$70,Valueofstockatexpiry,Valueatexpiry,LongCallSpread,Sellacallwithexercisepriceof$55for$5,$55,longcallspread,$5,$0,$50,Buyacallwithanexercisepriceof$50for$10,-$10,-$5,$60,Valueofstockatexpiry,Valueatexpiry,Put-CallParity,Sellaputwithanexercisepriceof$40,Buythestockat$40financedwithsomedebt:FV=$X,Buyacalloptionwithanexercisepriceof$40,$0,-$40,$40-P0,$40,Buythestockat$40,-$40-P0,Inmarketequilibrium,itmastbethecasethatoptionpricesaresetsuchthat:,Otherwise,risklessportfolioswithpositivepayoffsexist.,Valueofstockatexpiry,Valueatexpiry,22.7ValuingOptions,Thelastsectionconcerneditselfwiththevalueofanoptionatexpiry.,Thissectionconsidersthevalueofanoptionpriortotheexpirationdate.Amuchmoreinterestingquestion.,OptionValueDeterminants,CallPutStockprice+Exerciseprice+Interestrate+Volatilityinthestockprice+Expirationdate+ThevalueofacalloptionC0mustfallwithinmax(S0E,0)C0MaxST-E,0,Profit,loss,E,ST,MarketValue,Intrinsicvalue,ST-E,Timevalue,Out-of-the-money,In-the-money,ST,ThevalueofacalloptionC0mustfallwithinmax(S0E,0)C0S0.,22.8AnOptionPricingFormula,Wewillstartwithabinomialoptionpricingformulatobuildourintuition.,Thenwewillgraduatetothenormalapproximationtothebinomialforsomereal-worldoptionvaluation.,BinomialOptionPricingModel,Supposeastockisworth$25todayandinoneperiodwilleitherbeworth15%moreor15%less.S0=$25todayandinoneyearS1iseither$28.75or$21.25.Therisk-freerateis5%.Whatisthevalueofanat-the-moneycalloption?,$25,$21.25,$28.75,S1,S0,BinomialOptionPricingModel,Acalloptiononthisstockwithexercisepriceof$25willhavethefollowingpayoffs.Wecanreplicatethepayoffsofthecalloption.Withaleveredpositioninthestock.,$25,$21.25,$28.75,S1,S0,C1,$3.75,$0,BinomialOptionPricingModel,Borrowthepresentvalueof$21.25todayandbuy1share.Thenetpayoffforthisleveredequityportfolioinoneperiodiseither$7.50or$0.Theleveredequityportfoliohastwicetheoptionspayoffsotheportfolioisworthtwicethecalloptionvalue.,$25,$21.25,$28.75,S1,S0,debt,-$21.25,portfolio,$7.50,$0,(-)=,=,=,C1,$3.75,$0,-$21.25,BinomialOptionPricingModel,Theleveredequityportfoliovaluetodayistodaysvalueofonesharelessthepresentvalueofa$21.25debt:,$25,$21.25,$28.75,S1,S0,debt,-$21.25,portfolio,$7.50,$0,(-)=,=,=,C1,$3.75,$0,-$21.25,BinomialOptionPricingModel,Wecanvaluetheoptiontodayashalfofthevalueoftheleveredequityportfolio:,$25,$21.25,$28.75,S1,S0,debt,-$21.25,portfolio,$7.50,$0,(-)=,=,=,C1,$3.75,$0,-$21.25,Iftheinterestrateis5%,thecallisworth:,TheBinomialOptionPricingModel,$25,$21.25,$28.75,S1,S0,debt,-$21.25,portfolio,$7.50,$0,(-)=,=,=,C1,$3.75,$0,-$21.25,Iftheinterestrateis5%,thecallisworth:,TheBinomialOptionPricingModel,$25,$21.25,$28.75,S1,S0,debt,-$21.25,portfolio,$7.50,$0,(-)=,=,=,C1,$3.75,$0,-$21.25,BinomialOptionPricingModel,thereplicatingportfoliointuition.,Manyderivativesecuritiescanbevaluedbyvaluingportfoliosofprimitivesecuritieswhenthoseportfolioshavethesamepayoffsasthederivativesecurities.,Themostimportantlesson(sofar)fromthebinomialoptionpricingmodelis:,TheRisk-NeutralApproachtoValuation,WecouldvalueV(0)asthevalueofthereplicatingportfolio.Anequivalentmethodisrisk-neutralvaluation,S(0),V(0),S(U),V(U),S(D),V(D),q,1-q,TheRisk-NeutralApproachtoValuation,S(0)isthevalueoftheunderlyingassettoday.,S(0),V(0),S(U),V(U),S(D),V(D),S(U)andS(D)arethevaluesoftheassetinthenextperiodfollowinganupmoveandadownmove,respectively.,q,1-q,V(U)andV(D)arethevaluesoftheassetinthenextperiodfollowinganupmoveandadownmove,respectively.,qistherisk-neutralprobabilityofan“up”move.,TheRisk-NeutralApproachtoValuation,Thekeytofindingqistonotethatitisalreadyimpoundedintoanobservablesecurityprice:thevalueofS(0):,Aminorbitofalgebrayields:,ExampleoftheRisk-NeutralValuationofaCall:,$21.25,C(D),q,1-q,Supposeastockisworth$25todayandinoneperiodwilleitherbeworth15%moreor15%less.Therisk-freerateis5%.Whatisthevalueofanat-the-moneycalloption?Thebinomialtreewouldlooklikethis:,$25,C(0),$28.75,C(D),ExampleoftheRisk-NeutralValuationofaCall:,$21.25,C(D),2/3,1/3,Thenextstepwouldbetocomputetheriskneutralprobabilities,$25,C(0),$28.75,C(D),ExampleoftheRisk-NeutralValuationofaCall:,$21.25,$0,2/3,1/3,Afterthat,findthevalueofthecallintheupstateanddownstate.,$25,C(0),$28.75,$3.75,ExampleoftheRisk-NeutralValuationofaCall:,Finally,findthevalueofthecallattime0:,$25,$2.38,Thisrisk-neutralresultisconsistentwithvaluingthecallusingareplicatingportfolio.,Risk-NeutralValuationandtheReplicatingPortfolio,TheBlack-ScholesModel,TheBlack-ScholesModelis,WhereC0=thevalueofaEuropeanoptionattimet=0,r=therisk-freeinterestrate.,N(d)=Probabilitythatastandardized,normallydistributed,randomvariablewillbelessthanorequaltod.,TheBlack-ScholesModelallowsustovalueoptionsintherealworldjustaswehavedoneinthe2-stateworld.,TheBlack-ScholesModel,Findthevalueofasix-monthcalloptionontheMicrosoftwithanexercisepriceof$150ThecurrentvalueofashareofMicrosoftis$160TheinterestrateavailableintheU.S.isr=5%.Theoptionmaturityis6months(halfofayear).Thevolatilityoftheunderlyingassetis30%perannum.Beforewestart,notethattheintrinsicvalueoftheoptionis$10ouranswermustbeatleastthatamount.,TheBlack-ScholesModel,Letstryourhandatusingthemodel.Ifyouhaveacalculatorhandy,followalong.,Then,Firstcalculated1andd2,TheBlack-ScholesModel,N(d1)=N(0.52815)=0.7013N(d2)=N(0.31602)=0.62401,AssumeS=$50,X=$45,T=6months,r=10%,and=28%,calculatethevalueofacallandaput.,Fromastandardnormalprobabilitytable,lookupN(d1)=0.812andN(d2)=0.754(oruseExcels“normsdist”function),AnotherBlack-ScholesExample,22.9StocksandBondsasOptions,LeveredEquityisaCallOption.Theunderlyingassetcomprisetheassetsofthefirm.Thestrikepriceisthepayoffofthebond.Ifatthematurityoftheirdebt,theassetsofthefirmaregreaterinvaluethanthedebt,theshareholdershaveanin-the-moneycall,theywillpaythebondholdersand“callin”theassetsofthefirm.Ifatthematurityofthedebttheshareholdershaveanout-of-the-moneycall,theywillnotpaythebondholders(i.e.theshareholderswilldeclarebankruptcy)andletthecallexpire.,22.9StocksandBondsasOptions,LeveredEquityisaPutOption.Theunderlyingassetcomprisetheassetsofthefirm.Thestrikepriceisthepayoffofthebond.Ifatthematurityoftheirdebt,theassetsofthefirmarelessinvaluethanthedebt,shareholdershaveanin-the-moneyput.Theywillputthefirmtothebondholders.Ifatthematurityofthedebttheshareholdershaveanout-of-the-moneyput,theywillnotexercisetheoption(i.e.NOTdeclarebankruptcy)andlettheputexpire.,22.9StocksandBondsasOptions,Itallcomesdowntoput-callparity.,Stockholderspositionintermsofcalloptions,Stockholderspositionintermsofputoptions,22.10Capital-StructurePolicyandOptions,Recallsomeoftheagencycostsofdebt:theycanallbeseenintermsofoptions.Forexample,recalltheincentiveshareholdersinaleveredfirmhavetotakelargerisks.,BalanceSheetforaCompanyinDistress,AssetsBVMVLiabilitiesBVMVCash$200$200LTbonds$300?FixedAsset$400$0Equity$300?Total$600$200Total$600$200Whathappensifthefirmisliquidatedtoday?,Thebondholdersget$200;theshareholdersgetnothing.,SelfishStrategy1:TakeLargeRisks(ThinkofaCallOption),TheGambleProbabilityPayoffWinBig10%$1,000LoseBig90%$0Costofinvestmentis$200(allthefirmscash)Requiredreturnis50%ExpectedCFfromtheGamble=$1