Options 期权

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1、InvestmentandFinance(ABWL1)SS2010O.Kolokolova/Z.Guo/A.MattesTutorial3:SampleSolutions:OptionsandManagerialFlexibilityHintsCalloption–therighttobuyanassetataspecialexercisepriceon(aEuropeancall)orbefore(anAmericancall)aspecialdate.C=max(S-K,0)Putoption–therighttosellanassetataspecialexercise

2、priceon(aEuropeanput)orbefore(anAmericanput)aspecialdate.P=max(K-S,0)whereS–assetprice,K–exercisepricepayoffoflongcallpayoffoflongputKSSKKpayoffofshortcallpayoffofshortputSSKKKBinomialdistributionisadiscreteprobabilitydistributionwhichdescribesthenumberofsuccessesinasequenceofnindependentye

3、s/noexperiments,eachofwhichyieldingsuccesswithprobabilityp.n!kn−kProbabilityofksuccessesinnexperimentsPr(k)=⋅⋅−pp(1)knk!!()−Ex.1Supposethatyouholdoneshareofstockandoneputoptiononthatshare.Whatisthepayoffwhentheoptionexpiresif(a)thestockpriceisbelowtheexerciseprice?(b)thestockpriceisabovethe

4、exerciseprice?(Solvetheproblemgraphically)-1-InvestmentandFinance(ABWL1)SS2010O.Kolokolova/Z.Guo/A.MattesAnswerpayoffofsharepayoffofput=+KKSSSKKKifSKEx.2Howdoesthepriceofacalloptionrespondtothefollowingchanges,otherthingsequal?Doesthecallpricego

5、upordown?(a)Stockpriceincreases.(b)Strikepriceisincreased.(c)Risk-freerateincreases.(d)Expirationdateoftheoptionisextended.(e)Volatilityofthestockpricefalls.(f)Timepasses,sotheoption’sexpirationdatecomescloser.Answer(a)Valueofcallincreases:C=max(S-K,0).valueofcall(b)Valueofcalldecreases.atm

6、aturity(c)Valueofcallincreases:Thereare2effects:1)Higherdiscountingleadstoalowercallprice.2)Higherriskfreeratealsoleadstohigherexpectedreturnonthestockandthustoahighercallprice.Thesecondeffectisnormallystronger.(d)Valueofcallincreases.KS(e)Valueofcalldecreases.(f)Valueofcalldecreases.Ex.3Yo

7、uhavethefollowinginformation.ThecommonstockoftheOverlandRailroadiscurrentlytradedat$45pershareandhasastandarddeviationof24percent.Findthevaluesofa9-monthEuropeanCalloptionandAmericanPutoptiononthestockbyconstructingabinomialtreeandassumingthatthestockpri