CHAPTER 21 OPTION VALUATION

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1、CHAPTER21:OPTIONVALUATION1.Thevalueofaputoptionalsoincreaseswiththevolatilityofthestock.Weseethisfromtheput-callparitytheoremasfollows:P=C–S0+PV(X)+PV(Dividends)GivenavalueforSandarisk-freeinterestrate,then,ifCincreasesbecauseofanincreaseinvolatility,Pmustalsoincreaseinordert

2、omaintaintheequalityoftheparityrelationship.2.a.PutAmustbewrittenonthestockwiththelowerprice.Otherwise,giventhelowervolatilityofStockA,PutAwouldsellforlessthanPutB.b.PutBmustbewrittenonthestockwiththelowerprice.Thiswouldexplainitshigherprice.c.CallBmustbewrittenonthestockwith

3、thelowertimetomaturity.DespitethehigherpriceofStockB,CallBischeaperthanCallA.Thiscanbeexplainedbyalowertimetomaturity.d.CallBmustbewrittenonthestockwithhighervolatility.Thiswouldexplainitshigherprice.e.CallAmustbewrittenonthestockwithhighervolatility.Thiswouldexplainthehigher

4、optionpremium.3.ExercisePriceHedgeRatio11585/150=0.567100100/150=0.66775125/150=0.83350150/150=1.00025150/150=1.00010150/150=1.000Astheoptionbecomesmoreinthemoney,thehedgeratioincreasestoamaximumof1.0.4.Sd1N(d1)45-0.02680.4893500.50000.6915550.97660.835621-165.a.uS0=130ÞPu=0d

5、S0=80ÞPd=30Thehedgeratiois:b.RisklessPortfolioS=80S=130Buy3shares240390Buy5puts1500Total390390Presentvalue=$390/1.10=$354.545c.Theportfoliocostis:3S+5P=300+5PThevalueoftheportfoliois:$354.545Therefore:P=$54.545/5=$10.916.Thehedgeratioforthecallis:RisklessPortfolioS=80S=130Buy

6、2shares160260Write5calls0-100Total160160Presentvalue=$160/1.10=$145.455Theportfoliocostis:2S–5C=$200–5CThevalueoftheportfoliois:$145.455Therefore:C=$54.545/5=$10.91DoesP=C+PV(X)–S?10.91=10.91+110/1.10–10010.91=10.917.d1=0.3182ÞN(d1)=0.6248d2=–0.0354ÞN(d2)=0.4859Xe-rT=47.56C=$

7、8.1321-168.P=$5.69ThisvalueisderivedfromourBlack-Scholesspreadsheet,butnotethatwecouldhavederivedthevaluefromput-callparity:P=C+PV(X)–S0=$8.13+$47.56-$50=$5.699.a.Cfallsto$5.5541b.Cfallsto$4.7911c.Cfallsto$6.0778d.Crisesto$11.5066e.Crisesto$8.718710.AccordingtotheBlack-Schole

8、smodel,thecalloptionshouldbepricedat:[$55´N(d1)]–[50´N(d2)]=($55´0.6