Derivatives and risk managementWord文档下载推荐.docx
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Derivatives and risk managementWord文档下载推荐.docx
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▪Whydoyouenterthecontract?
∙Forabuyer–toensurehe/shecangetthesupplyoftheblackpepper
∙Foraseller–toensurethereisareadybuyerforhis/herblackpepper
oFuturescontract
▪Similartoforwardcontractexceptthatthecontractsarestandardizedandtradedonformalexchanges
oOption
▪Acontractthatgivesitsholdertherighttobuyorsaleanassetatapredeterminedpricewithinaspecifiedperiodoftime
▪CallOption
∙Anoptiontobuyor“call”ashareofstockatacertainpricewithinaspecifiedperiod
∙Forexample,youbuyacalloptionatthepriceofRM7,withanexerciseprice(strikeprice)ofRM25,3monthsfromnow
∙Exerciseprice(strikeprice)–thepricethatmustbepaidforashareofcommonstockwhenanoptionisexercised
▪
MarketPrice
Optionprice
Strikeprice
Exerciseornot?
40
7
25
-25-7+40=8
43
-25-7+43=11
100
-25-7+100=68
32
Exercise-25-7+32=0
Don’texercise
=-7
30
Exercise-7-25+30=-2
Don’texercise=-7
28
Exercise-7-25+28=-4
Exercise-7-25+25=-7
23
Exercise-7-25+23=-9
20
-7
15
1.5
0.1
∙Putoption
oAnoptiontosellashareofstockatacertain(exercise/strikeprice)pricewithinaspecifiedperiod
∙Forexample,youbuyaputoptionatthepriceofRM7,withanexerciseprice(strikeprice)ofRM25,3monthsfromnow
o
Exerciseornot?
Ifexercise=
-7-100+25=-82
90
50
34
exercise=
-7-34+25=-16
-7-25+25=-7
24
-7-24+25=-6
18
-7-18+25=0
-7-15+25=3
10
-7-10+25=8
0.5
-7-0.5+25=17.5
∙TheBlack-ScholesOptionPricingModel(OPM)
oV=P[N(d1)]–Xe(-rrf)(t)[N(d2)]
od1=
od2=d1-
owhere
▪V=currentvalueofthecalloption
▪P=currentpriceoftheunderlyingstock
▪N(d1)=probabilitythatadeviationlessthand1willoccurinastandardnormaldistribution.Thus,N(d1)andN(d2)representareasunderastandardnormaldistribution
▪X=exercise(strike)priceoftheoption
▪rrf=riskfreeinterestrate
▪e=2.7183
▪t=timeuntiltheoptionexpires(theoptionperiod)
▪ln(P/X)=naturallogarithmofP/X
▪δ2=varianceoftherateofreturnonthestock
oexampleP=RM21,X=RM21t=0.36yearrrf=5%andδ2=0.09
ocalculated1,d2andV
=0.19
od2=0.19-
=0.01
oV=21[N(0.19)]–21e(-0.05)(0.36)[N(0.01)]
oV=21[0.5753]–21(0.98216)[0.504]
oV=12.081-10.395=1.686
1.AnanalystisinterestedinusingBlack-ScholesmodeltovaluecalloptionsonthestockofABCLtd.Theanalysthasaccumulatedthefollowinginformation
∙Thepriceofthestock=33
∙Thestrikeprice=33
∙Optionmaturesin6months=(t=0.5)
∙Theriskfreerate=10%
Giventheinformation,theanalystisabletocalculatesomeothernecessarycomponentsoftheBlack-Scholesmodel:
∙d1=0.34177
∙d2=0.12964
∙N(d1)=0.63369
∙N(d2)=0.55155
∙N(d1)andN(d2)representareasunderastandardnormaldistributionfunction.UsingaBlack-Scholesmodel,whatisthevalueofthecalloption?
oV=33[0.63336]–33e(-0.1)(0.5)[0.55155]
oV=20.91–17.31
oV=3.60
2.AssumethatyouhavebeengiventhefollowinginformationonParagonLtd:
Currentstockprice=$15
Exercisepriceofoption=$15
Timetomaturityofoption=6months
Riskfreerate=10%
Varianceofstockprice=0.12
d1=0.32660d2=0.08165
N(d1)=0.62795
N(d2)=0.53252
UsingtheBlack–ScholesOptionPricingModel,whatisthevalueoftheoption?
oV=15[0.62795]–15e(-0.1)(0.5)[0.53252]
oV=9.4193–7.5982
oV=1.82
3.AcalloptiononBCGstockhasamarketpriceof$7.Thestocksellsfor$30ashare,andtheoptionhasanexercisepriceof$25ashare.
a.Whatistheexercisevalueofthecalloption?
ExerciseValue=Currentstockprice–Exerciseprice
ExerciseValue=30–25=5
b.Whatisthepremiumontheoption?
Premiumvalue=option’smarketprice–ExerciseValue
Premiumvalue=7–5=2
4.TheexercisepriceononeofECF‘scalloptionis$15,itsexercisevalueis$22anditspremiumis$5.Whataretheoption’smarketvalueandthestock’scurrentprice?
option’smarketprice=Premiumvalue+ExerciseValue
option’smarketprice=5+22=27
stockprice=22+15=37
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