Lecture18 Valuing Options(公司金融讲义(北大,沈明高).pdf

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1、20-2PrinciplesofTopicsCoveredCorporateFinance®OptionValuation18.ValuingOptions®SimpleValuationModelSeventhEdition®BinomialModelRichardA.BrealeyStewartC.Myers®Black-ScholesModel®BlackScholesvs.BinomialSlidesbyMatthewWillSlidesEditedbyMinggaoShenMcGrawHill/IrwinCopyri

2、ght©2003byTheMcGraw-HillCompanies,Inc.Allrightsreserved20-320-4ValuingOptionValuingOption:OptionEquivalentApp.WhyDCFdoesn’tworkforoptions?OptionEquivalentApproach:ThebasicideaistoconstructoptionequivalentsfromcommonOurstandardproceduretovalueanassetisstocksandborrow

3、ing.(1)FigureoutexpectedcashflowsExample:AssumethatthecurrentpriceofAOLis$60.Over(2)Discountthemattheopportunitycostoftheoption’ssix-monthlifeitwillbeeither$73.33(up22.22%)or$41.25(down31.25%).Theoption’sexercisepriceis$55.capitalThefollowingtwoalternativesyieldthes

4、amepayoffs:P=$41.25P=$73.331calloption0$18.33Itisimpossibletofindtherightopportunitycostofcapitalbecausetheriskinessofanoption0.5714shares$23.57$41.90changeseverytimethestockpricemoves.Repaymentofloan+interest-$23.57-$23.570$18.33McGrawHill/IrwinCopyright©2003byTheM

5、cGraw-HillCompanies,Inc.AllrightsreservedMcGrawHill/IrwinCopyright©2003byTheMcGraw-HillCompanies,Inc.Allrightsreserved20-520-6ValuingOption:OptionEquivalentApp.ValuingOption:Risk-NeutralApproachValueofcall=optiondelta*thecurrentprice–Risk-NeutralApproach:Assumingtha

6、tbankloan=0.5714*60-23.11=$11.17investorsareindifferenttorisk,theexpectedreturnonthestockmustbeequaltotherisk-freerateofreturn.WhereOptiondelta=spreadofpossibleoptionprices/spreadofpossiblesharepriceExpectedreturnonastock=risk-freeinterestrate=(15.33-0)/(73.33-41.25

7、)=0.5714(2)Theamounttoborrowfromthebankissimplythepresentvalueofthepaymentaftersixmonths:23.57/1.02=23.11.McGrawHill/IrwinCopyright©2003byTheMcGraw-HillCompanies,Inc.AllrightsreservedMcGrawHill/IrwinCopyright©2003byTheMcGraw-HillCompanies,Inc.Allrightsreserved120-72

8、0-8ValuingOption:Risk-NeutralApproachValuingOptions:BinomialPricingTheAOLexample:ad−ExpectedreturnonAOLstock=pU=ppD=−1U[Prob.ofrise×22.22%