博迪教學(xué)課件15

Chapter15:

MarketsforOptions andContingentClaimsObjectiveOptionsPricingrelationshipsPricingmodelsFinancialdecisionsanalyzedthroughoptions1Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallChapter15Contents15.1HowOptionsWork15.2InvestingwithOptions15.3ThePut-CallParityRelationship15.4Volatility&OptionPrices15.5Two-State(Binomial)OptionPricing15.6DynamicReplication&theBinomialModel15.7TheBlack-ScholesModel15.8ImpliedVolatility15.9ContingentClaimsAnalysisofCorporateDebtandEquity15.10CreditGuarantees15.11OtherApplicationsofOption-PricingMethodology2Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallObjectivesHowtouseoptionstomodifyone’sexposuretoinvestmentrisk.Tounderstandthepricingrelationshipsthatexistamongcalls,puts,stocks,andbonds.ToexplainthebinomialandBlack-Scholesoption-pricingmodelsandapplythemtothevaluationofcorporatebondsandothercontingentclaims.Toexploretherangeoffinancialdecisionsthatcanbefruitfullyanalyzedintermsofoptions.3Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallIntroductionThischapterexploreshowoptionpricesareaffectedbythevolatilityoftheunderlyingsecurityExchangetradedoptionsappearedin1973,enablingustodeterminethemarket’sestimateoffuturevolatility,ratherthanrelyingonhistoricalvalues4Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDefinitionofanOptionRecallthatanAmerican{European}call(put)optionistheright,butnottheobligationtobuy(sell)anassetataspecifiedpriceanytimebeforeitsexpirationdate{onitsexpirationdate}5Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallUbiquitousOptionsThischapterfocusesontradedoptions,butitwouldbeamistaketobelievethatthetoolswewillbedevelopingarerestrictedtotradedoptionsSomeexamplesofoptionsaregivenonthenextfewslides6Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallGovernmentPriceSupportsGovernmentssometimesprovideassistancetofarmersbyofferingtopurchaseagriculturalproductsataspecifiedsupportpriceIfthemarketpriceislowerthanthesupport,thenafarmerwillexerciseherrightto‘put’hercroptothegovernmentatthehigherprice7Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallOldMortgageTraditionalUSmortgagesgivethehouseholdertherighttocallthemortgageatastrikeequaltotheoutstandingprincipleIfinterestrateshavefallenbelowthenote’srate,thenthehomeownerwillconsiderrefinancingthemortgage8Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallNewMortgageYoupaysome‘points’tolock-inaninterestrateonamortgageIfratesfall,youmayrenegotiatethemortgage,andthenpaymorepointstolockinthenewlowerrateIfratesrise,thenyouwillgotothesettlementtablewithalower-than-marketinterestrate9Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTenureandSeniorityInacompanythathasapolicyoflast-infirst-out,aworkerwithsenioritymayforegoahighersalaryinanothercompanybecauseofthelossofjobsecurityTheworkerhasbeengiventheright,butnottheobligation,tohaveworkunderasetofadverseeconomicconditions10Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallCopperPennies,SilverCoinSilverandcoppercoinagehasbeenreplacedbyzincandcooperalloys/compositestoreducetheirmintingcostsTheoldcoinsareoftenlegalcurrency,andsocontainanoptionfeature:Ifthepriceoftheunderlyingmetalfallsbelowitslegalvalue,Ihavetherighttoreturnthecoinintocirculation11Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallInsuranceInsurancepoliciesoftengiveyoutheright,butnottheobligationtodosomething,itisthereforeoption-likeTherenewablerideronatermlifepolicyisanoptionIfsomebody:isterminallyill,thentheriderisveryvaluableremainsingoodhealth,thenitisnotvaluable12Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSupplyContractsAnuclearpowerplantsupplieroncegotintoserioustroublebyguaranteeingtosupplyenricheduraniumatafixedpriceThemarketpriceofenricheduraniumroseprecipitously13Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTechnologicalLeasesAcomputerleasingcompanyhadaclauseinitsleasestatingthatthecustomerhadtherighttocancelThecomputermanufacturerintroducednextgenerationofcomputers,andtheleasingcompany’scustomer’scanceledtheirleases,resultinginamassiveinventoryofobsoletecomputers14Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallLimitedLiabilityTheownersofalimitedliabilitycorporationhavetheright,butnottheobligation,to‘put’thecompanytothecorporation’screditorsandbondholdersLimitedliabilityis,ineffect,aputoption15Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTradingonCommissionYouareatraderwithacontractgivingyouacommissionof20%ofeachmonthstradingprofitsIfyoumakealoss,thenyouwalkaway,butifyoumakeaprofit,youstayYoumaybetemptedtoincreaseyourvolatilitytoboostthevalueofyouroption16Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.1HowOptionsWorkTheLanguageofOptionsContingentClaim:Anyassetwhosefuturepay-offdependsupontheoutcomeofanuncertaineventCall:anoptiontobuyPut:anoptiontosellStrikeorExercisePrice:thefixedpricespecifiedinanoptioncontractExpirationorMaturityDate:Thedateafterwhichanoptioncan’tbeexercisedAmericanOption:anoptionthatcanbeexercisedatanytimeuptoandincludingmaturitydate17Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallEuropeanOption:anoptionthatcanonlybeexercisedonthematuritydateTangibleValue:ThehypotheticalvalueofanoptionifitwereexercisedimmediatelyAt-the-Money:anoptionwithastrikepriceequaltothevalueoftheunderlyingassetOut-of-the-Money:anoptionthat’snotat-the-money,buthasnotangiblevalueIn-the-Money:anoptionwithatangiblevalueTimeValue:thedifferencebetweenanoption’smarketvalueanditstangiblevalueExchange-TradedOption:AstandardizedoptionthatanexchangestandsbehindinthecaseofadefaultOvertheCounterOption:Anoptiononasecuritythatisnotanexchange-tradedoption18Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall19Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall20Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.2InvestingwithOptionsThepayoffdiagram(terminalconditions,boundaryconditions)foracallandaputoption,eachwithastrike(exerciseprice)of$100,isderivednext21Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallOptionPayoffDiagramsThevalueofanoptionatexpirationfollowsimmediatelyfromitsdefinitionInthecaseofacalloptionwithstrikeof$100,ifthestockpriceis$90($110),thenexercisingtheoptionresultspurchasingthesharefor$100,whichis$10moreexpensive($10lessexpensive)thanbuyingit,soyouwouldn't(would)exerciseyourright22Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall

CallOptionPayoffDiagram23Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPutOptionPayoffDiagram24Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPayoffDiagramsforAlternativeBullishStockStrategies25Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall26Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.3ThePut-CallParityRelationConsiderthefollowingtwostrategiesPurchaseaputwithastrikepriceof$100,andtheunderlyingsharePurchaseacallwithastrikepriceof$100andabondthatmaturesatthesamedatewithafaceof$100Thematurityvaluesaretabulatedandplottedagainstshareprice:27Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPayoffDiagramforPureDiscountBondPlusCall28Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall29Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall30Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallObservationThemostimportantpointtoobserveisthatthevalueofthe“call+bond”strategy,isidentical(atmaturity)withtheprotective-putstrategy“put+share”So,iftheputandthecallhavethesamestrikeprice,weobtaintheput-callparityrelationship:put+share=call+bond31Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTechnicalNoteTheaboverelationshipistrue,ingeneral,fordividend-lessEuropeanoptions,buttheactualproofrequirestakingexpectationsoftheoptionandsecurityboundaryconditionsTheargumentisthereforeaheuristicforrememberingand‘seeing’therelationshipThefullproofisleftforyourinvestmentclass32Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPut-CallParityforAmericanandEuropeanOptionsAEuropeanoptionthatpaysnodividendduringitslifefullysatisfiestherequirementsofput-callparityInthecaseofAmericanoptions,therelationshipisfullyaccurateonlyatmaturity,becauseAmericanputsaresometimesexercisedearly33Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPut-CallParityEquation34Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSyntheticSecuritiesTheput-callparityrelationshipmaybesolvedforanyofthefoursecurityvariablestocreatesyntheticsecurities:C=S+P-BS=C-P+BP=C-S+BB=S+P-C35Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSyntheticSecuritiesC=S+P-BandP=C-S+BmaybeusedbyfloortraderstoflipbetweenacallandaputS=C-P+Bmaybeusedbyshort-termtraderswishingtotakeadvantageoflowertransactioncostsB=S+P-Cmaybeusedtocreateasyntheticbondsaidtopayaslightlyhigherreturnthanthephysicalbond36Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallOptionsandForwardsWesawinthelastchapterthatthediscountedvalueoftheforwardwasequaltothecurrentspotTherelationshipbecomes37Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallImplicationsforEuropeanOptionsIftheforwardpriceoftheunderlyingstockisequaltothestrikeprice,thenthevalueofthecallisequaltothevalueoftheputThisrelationshipissoimportant,thatsomeoptiontradersdefine‘a(chǎn)t-the-money’intermsoftheforwardratherthanthespot38Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallImplicationsforEuropeanOptionsIf(F>E)then(C>P)If(F=E)then(C=P)If(F<E)then(C<P)EisthecommonstrikepriceFistheforwardpriceofunderlyingshareCisthecallpricePistheputprice39Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallStrike=ForwardCall=Put40Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall41Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPVStrikeStrike42Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.4VolatilityandOptionPrices

WenextexplorewhathappenstothevalueofanoptionwhenthevolatilityoftheunderlyingstockincreasesWeassumeaworldinwhichthestockpricemovesduringtheyearfrom$100tooneoftwonewvaluesattheendoftheyearwhentheoptionmaturesAssumeriskneutrality43Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall44Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallIllustrationExplainedThestockvolatilityinthesecondscenarioishigher,andtheexpectedpayoffsforboththeputandthecallarealsohigherThisistheresultoftruncation,andholdsinallempiricallyreasonablecasesConclusion:Volatilityincreasesalloptionprices45Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.5Two-State(Binomial)Option-PricingWearenowgoingtoderivearelativelysimplemodelforevaluatingoptionsTheassumptionswillatfirstappeartotallyunrealistic,butusingsomeunderhandmathematics,themodelmaybemadetopriceoptionstoanydesiredlevelofaccuracyTheadvantageofthemethodisthatitdoesnotrequirelearningstochasticcalculus,andyetitillustratesallthekeystepsnecessarytoderiveanyoptionevaluationmodel46Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModelAssumptionsAssume:theexercisepriceisequaltotheforwardpriceoftheunderlyingstockoptionpricesthendependonlyonthevolatilityandtimetomaturity,anddonotdependoninterestratestheputandcallhavethesameprice47Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModelAssumptionsMorespecificallyweassume:shareprice=strikeprice=$100timetomaturity=1yeardividendrate=interestrate=0stockpriceseitherriseorfallby20%intheyear,andsoareeither$80or$120atyearend48Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModel:CallStrategy:replicatethecallusingaportfoliooftheunderlyingstocktherisklessbondbythelawofoneprice,thepriceoftheactualcallmustequalthepriceofthesyntheticcall49Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModel:CallImplementation:thesyntheticcall,C,iscreatedbybuyingafractionxofshares,ofthestock,S,andsimultaneouslysellingshortriskfreebondswithamarketvalueythefractionxiscalledthehedgeratio50Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModel:CallSpecification:Wehaveanequation,andgiventhevalueoftheterminalshareprice,weknowtheterminaloptionvaluefortwocases:Byinspection,thesolutionisx=1/2,y=4051Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModel:CallSolution:Wenowsubstitutethevalueoftheparametersx=1/2,y=40intotheequationtoobtain:52Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModel:PutStrategy:replicatetheputusingaportfoliooftheunderlyingstockandrisklessbondbythelawofoneprice,thepriceoftheactualputmustequalthepriceofthesyntheticputreplicatedaboveMinorchangestothecallargumentaremadeinthenextfewslidesfortheput53Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModel:PutImplementation:thesyntheticput,P,iscreatedbysellshortafractionxofshares,ofthestock,S,andsimultaneouslybuyriskfreebondswithamarketvalueythefractionxiscalledthehedgeratio54Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDecisionTreeforDynamicReplication

ofCallOption55Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModel:PutSpecification:Wehaveanequation,andgiventhevalueoftheterminalshareprice,weknowtheterminaloptionvaluefortwocases:Byinspection,thesolutionisx=1/2,y=6056Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallBinaryModel:PutSolution:Wenowsubstitutethevalueoftheparametersx=1/2,y=60intotheequationtoobtain:57Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.6DynamicReplicationandtheBinomialModelWenowtakethenextsteptowardsgreaterrealismbydividingtheyearinto2sub-periodsofhalfayeareach.Thisgives3possibleoutcomesOurfirsttaskistofindaself-financinginvestmentstrategythatdoesnotrequireinjectionorwithdrawalofnewfundsduringthelifeoftheoptionWefirstcreateadecisiontree:58Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDecisionTreeforDynamicReplicationofaCallOption($120*100%)+(-$100)=$2059Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallReadingtheDecisionTreeThetreeisconstructedbackwardsbecauseweknowonlythefuturecontingentcallpricesForExample,whenconstructingtheweightsfortime6-months,theoptionpricesfor12-monthsareusedForconsistencywiththenextmodel,thediscretestockpricesareusuallyfixedratios,i.e.121,110,100,90.91,82.6460Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallThePowerofLatticeModelsLatticemodels,ofwhichthebinarymodelisthesimplest,areveryimportanttotradersbecausetheymaybemodifiedtohandledifferentdistributions,thepossibilityofearlyexercise,anddiscretedividendpaymentsToseehoweasyitistochangethedistributionalassumption,theaboveillustrationresultsinstockpricesbeingnormallydistributed,andthemodificationresultsinalognormaldistributionofprices61Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.7TheBlack-ScholesModel

ThemostwidelyusedmodelforpricingoptionsistheBlack-ScholesmodelThismodeliscompletelyconsistentwiththebinarymodelastheintervalbetweenstockpricesdecreasestozeroThemodelprovidestheoreticalinsightsintooptionbehaviorTheassumptionsareelegant,simple,andquiterealistic62Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheBlack-ScholesModel

WewillworkwiththegeneralizedformofthemodelbecausethesmalladditionalcomplexityresultsinconsiderableadditionalpowerandflexibilityFirst,notation:63Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheBlack-ScholesModel:Notation

C=priceofcallP=priceofputS=priceofstockE=exercisepriceT=timetomaturityln(.)=naturallogarithme=2.71828...N(.)=cum.norm.dist’nThefollowingareannual,compoundedcontinuously:r=domesticriskfreerateofinterestd=foreignriskfreerateorconstantdividendyieldσ=volatility64Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheNormalProblemItisnotunusualforastudenttohaveaproblemcomputingthecumulativenormaldistributionusingtablestablestructuresvary,sobecarefulusingstandard-issuenormaltablesdegradescomputedoptionvaluesbecauseoferrorscausedbycatastrophicsubtraction{ManyprofessionalsuseHasting’sformulaasreportedinAbramowitzandStegunasequation26.2.19(never,neveruse26.2.18).Itscertificatevalidin0<=x<Inf,sousesymmetrytoget-Inf<x<0}65Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheNormalProblemThefunctionsthatcomewithExcelhaveadequateaccuracy,soconsiderusing‘Normsdist()’inthestatisticalfunctions(notethesinNormsdist)66Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheBlack-ScholesModel:What’smissingTherearenoexpectationsaboutfuturereturnsinthemodelThemodelispreference-freeσ-risk,notb-risk,istherelevantrisk67Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheBlack-ScholesModel:Equations68Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheBlack-ScholesModel:Equations(ForwardForm)69Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallTheBlack-ScholesModel:Equations(Simplified)70Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallSoWhatDoesitMean?Youcannowobtainthevalueofnon-dividendpayingEuropeanoptionsWithalittleskill,youcanwidenthistoobtainapproximatevaluesofEuropeanoptionsonsharespayingadividend,andtosomeAmericanoptions71Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall72Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall73Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallImpliedVolatilitySPX

(July2005-June2006)74Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall75Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallObservableVariablesAllthevariablesaredirectlyobservable,exceptingthevolatility,σ,andpossibly,thenextcashdividend,dWedonothavetodelveintothepsycheofinvestorstoevaluateoptionsWedonotforecastfuturepricestoobtainoptionvalues76Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.8ImpliedVolatilityThefollowingslidesshowhowtoestimatevolatilityusingExcelTheoptionmostcommonlyusedtoestimatevolatilityistheoneclosesttothepresentvalueofthestrikeprice:Thatis,theoptionthatishasastrikeclosesttotheforwardpriceThisoptionhasthemost“oomph”77Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallInsertanynumbertostartFormulaforoptionvalueminustheactualcallvalue78Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall79Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPat’sPlanPathasaplantogetrichwithnorisk:Setupspecialportfolio,(Patcallsthisa“selffinancing,deltaneutralportfoliowithpositivecurvature,”butPathasthisthingwithwords)80Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPat,theStrategistShortsomeshares,andoff-setsmallpricechangesaboutthecurrentpricewithsomecalloptions,theninvestthedifferenceinbonds81Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall82Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPat,theCartographerApparently,whatPathasdoneistofindthetangent(attoday’sshareprice)ofthecallvaluecurve,usingbondsandstockintherightproportionsThisiswhatwedidearlierwhenweconstructedthebinarypricingmodelAtthecurrentpriceof$103,thetangentmimicsthecallcurve83Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPat(Continued)Patthenwentshortthetangencyportfolio,andlongthecalltocreatethethickblackportfolioObservethattheminimumvalueoftheportfolioiszero,andthisoccursatthecurrentprice,soitisself-financingPatmakesmoneyifsharepricesmoveupordown84Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPatTriumphantThisclearlydefeatsthelawofoneprice:Thereisnodownsiderisk,noconstructioncosts,andyetwillyieldapositiveprofitalmostallthetimeWhat’swrongwithPat’sanalysis?85Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPatDejectedTheansweristhatittakestimeforapricetomove,andduringthattime,allotherthingsbeingequal,thevalueoftheoptionwilldecayThinkofadownwardssloping,veryslick,rain-guttercontainingacritter:Thecrittermayclimbthewallsofthegutter,butitisconstantlyslidingdownthegutter86Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPatinDespairThenextdiagramshowsthevalueoftheportfoliotodayandoneweekhenceTheconstructionlineshavebeenremoved,andthegraphhasbeenre-scaled87Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall88Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallPatCondemnedtoPovertyThediagramshowsthat,ifnextweek’ssharepricesfallbetweenabout$97and$105.5,PatwillenjoyalossAstimepasses,decaywillmakethisstrategyaveryriskyoneAnotherfactorPatdidnottakeintoaccountisthatvolatilityisitselfvolatile,sothehedgemaydisintegrate89Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15.9ContingentClaimsAnalysisofCorporateDebtandEquityTheCCAapproachusesadifferentsetofinformationalassumptionsthanthediscountedcashflow(DCF)method:itusestherisk-freerateratherthanarisk-adjusteddiscountrateitusesknowledgeofthepricesofoneormorerelatedassetsandtheirvolatilities90Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallContingent-ClaimsAnalysisofStockandBonds:DebtcoDebtcoisareal-estateholdingcompanyandhasissued1,000,000commonshares80,000purediscountbonds,face$,1000,maturity1-year91Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDebtco,ContinuedThetotalmarketvalueofDebtcois$100,000,000Therisk-freerate,(andtherefore,bythelawofoneprice,Debtco’sbondrate,)is4%92Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDebtco,NotationEthemarketvalueofthestockissueDthemarketvalueofthedebtissueVthetotalcurrentmarketvalue;V=E+DV1thetotalmarketvalueoneyearhence(ThelawofonepriceensuresthatV=E+Dmustbetrue,otherwisetherewillbeanarbitrageopportunity)93Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDebtco,SecurityValuationValueofthebondsBytheruleofoneprice,thevalueofthebondsmustequaltheirfacevaluediscountedattherisk-freerateforayearD=80,000*$1,000/1.04=$76,923,077Bythetotalvalueofthefirm,V=E+D,thevalueofthestockisE=V-D=$100,000,000-$76,923,077=$23,076,92394Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallDebtco,PayoffAconsequenceofDebtco’shavingbondswitharisk-freerateisthatthecompanyhaseitherpurchasedbonddefaultinsurancefromathirdparty,orthatthefirm’sassetshaveno(downside)riskFormanycompanies,amorerealisticassumptionisthattheassetsdohaverisk,andtoevaluatesuchsecuritiesrequiresapayofffunctionforthebondsorstock:95Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall96Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHallNegativeFirmValuesWehaveassumedthatthevalueofthefirmneverfallsbelowzero,butwhileunusual,itispossibleforthemarketvalueofafirm’sassetstobelessthanzeroConsiderEnviromessInc.,afirmthatforyearspollutedtheHudsonRiverwithabyproductofLifecide?Thecostofcleaninguptherivermaywellgreatlyexceedthefirm’sfinancialresources97Copyright?2009PearsonEducation