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chap020ise
CHAPTER20:
OPTIONSMARKETS:
INTRODUCTION
1.
Cost
Payoff
Profit
a.
Calloption,X=$80.00
$4.40
$5.00
$0.60
b.
Putoption,X=$80.00
$0.75
$0.00
-$0.75
c.
Calloption,X=$85.00
$1.35
$0.00
-$1.35
d.
Putoption,X=$85.00
$2.90
$0.00
-$2.90
e.
Calloption,X=$90.00
$0.25
$0.00
-$0.25
f.
Putoption,X=$90.00
$6.80
$5.00
-$1.80
2.Intermsofmonetaryreturns,basedona£1,000investment:
PriceofStock6MonthsfromNow
StockPrice
£4
£5
£6
£7
Allstocks（200shares）
£800
£1,000
£1,200
£1,400
Alloptions（2,000options）
£0
£0
£2,000
£4,000
MMFund+200options
£936
£936
£1,136
£1,336
Intermsofrateofreturn,basedona£1,000investment:
PriceofStock6MonthsfromNow
StockPrice
£4
£5
£6
£7
Allstocks（200shares）
-20%
0%
20%
40%
Alloptions（2,000options）
-100%
-100%
100%
300%
MMFund+200options
-6.4%
-6.4%
13.6%
33.6%
3.a.Fromput-callparity:
P=C–S0+[X/（1+rf）T]=2–20+[20/（1.10）1/4]=C$1.53
b.Purchaseastraddle,i.e.,bothaputandacallonthestock.Thetotalcostofthestraddleis:
C$2+C$1.53=C$3.53
Thisistheamountbywhichthestockwouldhavetomoveineitherdirectionfortheprofitonthecallorputtocovertheinvestmentcost（notincludingtimevalueofmoneyconsiderations）.Accountingfortimevalue,thestockpricewouldhavetomoveineitherdirectionby:
C$3.53⨯1.101/4=C$3.62
4.a.Fromput-callparity:
C=P+S0–[X/（l+rf）T]=560+7,000–[7,000/（1.10）1/4]=¥724.82
b.Sellastraddle,i.e.,sellacallandaputtorealizepremiumincomeof:
¥724.82+¥560=¥1,284.82
Ifthestockendsupat¥7,000,bothoftheoptionswillbeworthlessandyourprofitwillbe¥1,284.82.Thisisyourmaximumpossibleprofitsince,atanyotherstockprice,youwillhavetopayoffoneitherthecallortheput.Thestockpricecanmoveby¥1,284.82ineitherdirectionbeforeyourprofitsbecomenegative.
c.Buythecall,sell（write）theput,lend:
¥7,000/（1.10）1/4
Thepayoffisasfollows:
Position
ImmediateCF
CFin3months
ST≤X
ST>X
Call（long）
C=724.82
0
ST–7,000
Put（short）
–P=560.00
–（7,000–ST）
0
Lendingposition
7,000
7,000
Total
C–P+
ST
ST
Bytheput-callparitytheorem,theinitialoutlayequalsthestockprice:
S0=¥7,000
Ineitherscenario,youendupwiththesamepayoffasyouwouldifyouboughtthestockitself.
5.a.
Outcome
ST≤X
ST>X
Stock
ST+D
ST+D
Put
X–ST
0
Total
X+D
ST+D
b.
Outcome
ST≤X
ST>X
Call
0
ST–X
Zeros
X+D
X+D
Total
X+D
ST+D
ThetotalpayoffsforthetwostrategiesareequalregardlessofwhetherSTexceedsX.
c.Thecostofestablishingthestock-plus-putportfoliois:
S0+P
Thecostofestablishingthecall-plus-zeroportfoliois:
C+PV（X+D）
Therefore:
S0+P=C+PV（X+D）
Thisresultisidenticaltoequation20.2.
6.a.Bywritingcoveredcalloptions,Jonesreceivespremiumincomeof€30,000.If,inJanuary,thepriceofthestockislessthanorequalto€45,thenJoneswillhavehisstockplusthepremiumincome.Butthemosthecanhaveatthattimeis（€450,000+€30,000）becausethestockwillbecalledawayfromhimifthestockpriceexceeds€45.（Weareignoringhereanyinterestearnedoverthisshortperiodoftimeonthepremiumincomereceivedfromwritingtheoption.）Thepayoffstructureis:
StockpricePortfoliovalue
lessthan€4510,000timesstockprice+€30,000
greaterthan€45€450,000+€30,000=€480,000
ThisstrategyofferssomeextrapremiumincomebutleavesJonessubjecttosubstantialdownsiderisk.Atanextreme,ifthestockpricefelltozero,Joneswouldbeleftwithonly€30,000.Thisstrategyalsoputsacaponthefinalvalueat€480,000,butthisismorethansufficienttopurchasethehouse.
b.Bybuyingputoptionswitha€35strikeprice,Joneswillbepaying€30,000inpremiumsinordertoinsureaminimumlevelforthefinalvalueofhisposition.Thatminimumvalueis:
（€35⨯10,000）–€30,000=€320,000
Thisstrategyallowsforupsidegain,butexposesJonestothepossibilityofamoderatelossequaltothecostoftheputs.Thepayoffstructureis:
StockpricePortfoliovalue
lessthan€35€350,000–€30,000=€320,000
greaterthan€3510,000timesstockprice–€30,000
c.Thenetcostofthecollariszero.Thevalueoftheportfoliowillbeasfollows:
StockpricePortfoliovalue
lessthan€35€350,000
between€35and€4510,000timesstockprice
greaterthan€45€450,000
Ifthestockpriceislessthanorequalto€35,thenthecollarpreservesthe€350,000principal.Ifthepriceexceeds€45,thenJonesgainsuptoacapof€450,000.Inbetween€35and€45,hisproceedsequal10,000timesthestockprice.
Thebeststrategyinthiscasewouldbe（c）sinceitsatisfiesthetworequirementsofpreservingthe€350,000inprincipalwhileofferingachanceofgetting€450,000.Strategy（a）shouldberuledoutsinceitleavesJonesexposedtotheriskofsubstantiallossofprincipal.
Ourrankingwouldbe:
（1）strategyc;
（2）strategyb;（3）strategya.
7.a.
Position
STX1STX2
X2X3Longcall（X1）
0
ST–X1
ST–X1
ST–X1
Short2calls（X2）
0
0
–2（ST–X2）
–2（ST–X2）
Longcall（X3）
0
0
0
ST–X3
Total
0
ST–X1
2X2–X1–ST
（X2–X1）–（X3–X2）=0
b.
Position
STX1STX2X2X2XX2X2X2X2X2
X2Buycall（X2）
0
0
ST–X2
Buyput（X1）
X1–ST
0
0
Total
X1–ST
0
ST–X2
8.
Position
STX1STX2XX2
X2Buycall（X2）
0
0
ST–X2
Sellcall（X1）
0
–（ST–X1）
–（ST–X1）
Total
0
X1–ST
X1–X2
9.Thefarmerhastheoptiontosellthecroptothegovernmentforaguaranteedminimumpriceifthemarketpriceistoolow.IfthesupportpriceisdenotedPSandthemarketpricePmthenthefarmerhasaputoptiontosellthecrop（theasset）atanexercisepriceofPSevenifthepriceoftheunderlyingasset（Pm）islessthanPS.
10.Thebondholdershave,ineffect,madealoanwhichrequiresrepaymentofBdollars,whereBisthefacevalueofbonds.If,however,thevalueofthefirm（V）islessthanB,theloanissatisfiedbythebondholderstakingoverthefirm.Inthisway,thebondholdersareforcedto“pay”B（inthesensethattheloaniscancelled）inreturnforanassetworthonlyV.ItisasthoughthebondholderswroteaputonanassetworthVwithexercisepriceB.Alternatively,onemightviewthebondholdersasgivingtherighttotheequityholderstoreclaimthefirmbypayingofftheBdollardebt.Thebondholdershaveissuedacalltotheequityholders.
11.a.&b.TheExcelspreadsheetforbothparts（a）and（b）isshownonthenextpage,andtheprofitdiagramsareonthefollowingpage.
12.Themanagergetsabonusifthestockpriceexceedsacertainvalueandgetsnothingotherwise.Thisisthesameasthepayofftoacalloption.
13.i.Equityindex-linkednote:
Unliketraditionaldebtsecuritiesthatpayascheduledrateofcouponinterestonaperiodicbasisandtheparamountofprincipalatmaturity,theequityindex-linkednotetypicallypayslittleornocouponinterest;atmaturity,however,aunitholderreceivestheoriginalissuepriceplusasupplementalredemptionamount,thevalueofwhichdependsonwheretheequityindexsettledrelativetoapredeterminedinitiallevel.
ii.Commodity-linkedbearbond:
Unliketraditionaldebtsecuritiesthatpayascheduledrateofcouponinterestonaperiodicbasisandtheparamountofprincipalatmaturity,thecommodity-linkedbearbondallowsaninvestortoparticipateinadeclineinacommodity’sprice.Inexchangeforalowerthanmarketcoupon,buyersofabeartranchereceivearedemptionvaluethatexceedsthepurchasepriceifthecommoditypricehasdeclinedbythematuritydate.
SpreadsheetforProblem11:
StockPrices
BeginningMarketPrice
116.5
EndingMarketPrice
130
X130Straddle
Ending
Profit
BuyingOptions:
StockPrice
-37.20
CallOptionsStrike
Price
Payoff
Profit
Return%
50
42.80
110
22.80
20.00
-2.80
-12.28%
60
32.80
120
16.80
10.00
-6.80
-40.48%
70
22.80
130
13.60
0.00
-13.60
-100.00%
80
12.80
140
10.30
0.00
-10.30
-100.00%
90
2.80
100
-7.20
PutOptionsStrike
Price
Payoff
Profit
Return%
110
-17.20
110
12.60
0.00
-12.60
-100.00%
120
-27.20
120
17.20
0.00
-17.20
-100.00%
130
-37.20
130
23.60
0.00
-23.60
-100.00%
140
-27.20
140
30.50
10.00
-20.50
-67.21%
150
-17.20
160
-7.20
Straddle
Price
Payoff
Profit
Return%
170
2.80
110
35.40
20.00
-15.40
-43.50%
180
12.80
120
34.00
10.00
-24.00
-70.59%
190
22.80
130
37.20
0.00
-37.20
-100.00%
200
32.80
140
40.80
10.00
-30.80
-75.49%
210
42.80
SellingOptions:
Bullish
CallOptionsStrike
Price
Payoff
Profit
Return%
Ending
Spread
110
22.80
-20
2.80
12.28%
StockPrice
6.80
120
16.80
-10
6.80
40.48%
50
-3.2
130
13.60
0
13.60
100.00%
60
-3.2
140
10.30
0
10.30
100.00%
70
-3.2
80
-3.2
PutOptionsStrike
Price
Payoff
Profit
Return%
90
-3.2
110
12.60
0
12.60
100.00%
100
-3.2
120
17.20
0
17.20
100.00%
110
-3.2
130
23.60
0
23.60
100.00%
120
-3.2
140
30.50
10
40.50
132.79%
130
6.8
140
6.8
MoneySpread
Price
Payoff
Profit
150
6.8
BullishSpread
160
6.8
Purchase120Call
16.80
10.00
-6.80
170
6.8
Sell130Call
13.60
0
13.60
180
6.8
CombinedProfit
10.00
6.80
19
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