HullFund8eCh09ProblemSolutions.docx

HullFund8eCh09ProblemSolutions.docx

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HullFund8eCh09ProblemSolutions

CHAPTER9

MechanicsofOptionsMarkets

PracticeQuestions

Problem9.8.

Acorporatetreasurerisdesigningahedgingprograminvolvingforeigncurrencyoptions.Whataretheprosandconsofusing（a）theNASDAQOMXand（b）theover—the—countermarketfortrading？

TheNASDAQOMXoffersoptionswithstandardstrikepricesandtimestomaturity。

Optionsintheover-the-countermarkethavetheadvantagethattheycanbetailoredtomeetthepreciseneedsofthetreasurer.Theirdisadvantageisthattheyexposethetreasurertosomecreditrisk.Exchangesorganizetheirtradingsothatthereisvirtuallynocreditrisk。

Problem9.9.

SupposethataEuropeancalloptiontobuyasharefor＄100。

00costs$5.00andishelduntilmaturity。

Underwhatcircumstanceswilltheholderoftheoptionmakeaprofit?

Underwhatcircumstanceswilltheoptionbeexercised？

Drawadiagramillustratinghowtheprofitfromalongpositionintheoptiondependsonthestockpriceatmaturityoftheoption。

Ignoringthetimevalueofmoney，theholderoftheoptionwillmakeaprofitifthestockpriceatmaturityoftheoptionisgreaterthan＄105。

Thisisbecausethepayofftotheholderoftheoptionis,inthesecircumstances，greaterthanthe＄5paidfortheoption.Theoptionwillbeexercisedifthestockpriceatmaturityisgreaterthan＄100.Notethatifthestockpriceisbetween$100and$105theoptionisexercised,buttheholderoftheoptiontakesalossoverall。

TheprofitfromalongpositionisasshowninFigureS9.1。

FigureS9。

1ProfitfromlongpositioninProblem9。

9

Problem9。

10。

SupposethataEuropeanputoptiontosellasharefor＄60costs$8andishelduntilmaturity.Underwhatcircumstanceswilltheselleroftheoption（thepartywiththeshortposition）makeaprofit？

Underwhatcircumstanceswilltheoptionbeexercised？

Drawadiagramillustratinghowtheprofitfromashortpositionintheoptiondependsonthestockpriceatmaturityoftheoption.

Ignoringthetimevalueofmoney，theselleroftheoptionwillmakeaprofitifthestockpriceatmaturityisgreaterthan$52.00。

Thisisbecausethecosttotheselleroftheoptionisinthesecircumstanceslessthanthepricereceivedfortheoption。

Theoptionwillbeexercisedifthestockpriceatmaturityislessthan＄60。

00.Notethatifthestockpriceisbetween$52.00and$60.00theselleroftheoptionmakesaprofiteventhoughtheoptionisexercised。

TheprofitfromtheshortpositionisasshowninFigureS9。

2.

FigureS9.2ProfitfromshortpositioninProblem9.10

Problem9.11.

Describetheterminalvalueofthefollowingportfolio：

anewlyentered-intolongforwardcontractonanassetandalongpositioninaEuropeanputoptionontheassetwiththesamematurityastheforwardcontractandastrikepricethatisequaltotheforwardpriceoftheassetatthetimetheportfolioissetup。

ShowthattheEuropeanputoptionhasthesamevalueasaEuropeancalloptionwiththesamestrikepriceandmaturity.

Theterminalvalueofthelongforwardcontractis:

where

isthepriceoftheassetatmaturityand

istheforwardpriceoftheassetatthetimetheportfolioissetup。

（Thedeliverypriceintheforwardcontractisalso

.）

Theterminalvalueoftheputoptionis：

Theterminalvalueoftheportfolioistherefore

ThisisthesameastheterminalvalueofaEuropeancalloptionwiththesamematurityastheforwardcontractandanexercisepriceequalto

.ThisresultisillustratedintheFigureS9。

3.

FigureS9。

3ProfitfromportfolioinProblem9.11

Wehaveshownthattheforwardcontractplustheputisworththesameasacallwiththesamestrikepriceandtimetomaturityastheput。

Theforwardcontractisworthzeroatthetimetheportfolioissetup.Itfollowsthattheputisworththesameasthecallatthetimetheportfolioissetup。

Problem9.12.

Atraderbuysacalloptionwithastrikepriceof$45andaputoptionwithastrikepriceof＄40.Bothoptionshavethesamematurity。

Thecallcosts$3andtheputcosts＄4.Drawadiagramshowingthevariationofthetrader'sprofitwiththeassetprice。

FigureS9。

4showsthevariationofthetrader’spositionwiththeassetprice。

Wecandividethealternativeassetpricesintothreeranges:

a）Whentheassetpricelessthan＄40，theputoptionprovidesapayoffof

andthecalloptionprovidesnopayoff.Theoptionscost＄7andsothetotalprofitis

.

b）Whentheassetpriceisbetween$40and$45,neitheroptionprovidesapayoff.Thereisanetlossof$7。

c）Whentheassetpricegreaterthan＄45，thecalloptionprovidesapayoffof

andtheputoptionprovidesnopayoff.Takingintoaccountthe$7costoftheoptions,thetotalprofitis

。

Thetradermakesaprofit（ignoringthetimevalueofmoney）ifthestockpriceislessthan$33orgreaterthan$52。

ThistypeoftradingstrategyisknownasastrangleandisdiscussedinChapter11.

FigureS9。

4ProfitfromtradingstrategyinProblem9。

12

Problem9。

13.

ExplainwhyanAmericanoptionisalwaysworthatleastasmuchasaEuropeanoptiononthesameassetwiththesamestrikepriceandexercisedate。

TheholderofanAmericanoptionhasallthesamerightsastheholderofaEuropeanoptionandmore。

Itmustthereforebeworthatleastasmuch。

Ifitwerenot，anarbitrageurcouldshorttheEuropeanoptionandtakealongpositionintheAmericanoption.

Problem9。

14。

ExplainwhyanAmericanoptionisalwaysworthatleastasmuchasitsintrinsicvalue。

TheholderofanAmericanoptionhastherighttoexerciseitimmediately。

TheAmericanoptionmustthereforebeworthatleastasmuchasitsintrinsicvalue.Ifitwerenotanarbitrageurcouldlockinasureprofitbybuyingtheoptionandexercisingitimmediately.

Problem9.15。

Explaincarefullythedifferencebetweenwritingaputoptionandbuyingacalloption。

Writingaputgivesapayoffof

.Buyingacallgivesapayoffof

。

Inbothcasesthepotentialpayoffis

.Thedifferenceisthatforawrittenputthecounterpartychooseswhetheryougetthepayoff（andwillallowyoutogetitonlywhenitisnegativetoyou）。

Foralongcallyoudecidewhetheryougetthepayoff（andyouchoosetogetitwhenitispositivetoyou。

）

Problem9.16。

Thetreasurerofacorporationistryingtochoosebetweenoptionsandforwardcontractstohedgethecorporation'sforeignexchangerisk.Discusstheadvantagesanddisadvantagesofeach。

Forwardcontractslockintheexchangeratethatwillapplytoaparticulartransactioninthefuture.Optionsprovideinsurancethattheexchangeratewillnotbeworsethansomelevel.Theadvantageofaforwardcontractisthatuncertaintyiseliminatedasfaraspossible。

Thedisadvantageisthattheoutcomewithhedgingcanbesignificantlyworsethantheoutcomewithnohedging.Thisdisadvantageisnotasmarkedwithoptions.However，unlikeforwardcontracts,optionsinvolveanup-frontcost.

Problem9.17。

Consideranexchange—tradedcalloptioncontracttobuy500shareswithastrikepriceof＄40andmaturityinfourmonths。

Explainhowthetermsoftheoptioncontractchangewhenthereis

a）A10%stockdividend

b）A10%cashdividend

c）A4—for—1stocksplit

a）Theoptioncontractbecomesonetobuy

shareswithanexerciseprice

。

b）Thereisnoeffect.Thetermsofanoptionscontractarenotnormallyadjustedforcashdividends。

c）Theoptioncontractbecomesonetobuy

shareswithanexercisepriceof40/4=＄10.

Problem9.18.

“Ifmostofthecalloptionsonastockareinthemoney，itislikelythatthestockpricehasrisenrapidlyinthelastfewmonths."Discussthisstatement.

Theexchangehascertainrulesgoverningwhentradinginanewoptionisinitiated。

Thesemeanthattheoptionisclose—to-the—moneywhenitisfirsttraded.Ifallcalloptionsareinthemoney，itisthereforelikelythatthestockpricehasrisensincetradingintheoptionbegan。

Problem9.19.

Whatistheeffectofanunexpectedcashdividendon（a）acalloptionpriceand（b）aputoptionprice?

Anunexpectedcashdividendwouldreducethestockpriceontheex—dividenddate.Thisstockpricereductionwouldnotbeanticipatedbyoptionholders.Asaresulttherewouldbeareductioninthevalueofacalloptionandanincreasethevalueofaputoption。

（Notethatthetermsofanoptionareadjustedforcashdividendsonlyinexceptionalcircumstances.）

Problem9.20.

OptionsonGeneralMotorsstockareonaMarch,June，September，andDecembercycle.Whatoptionstradeon（a）March1,（b）June30,and（c）August5？

a）March,April,JuneandSeptember

b）July，August,September,December

c）August,September,December,March。

Longerdatedoptionsmayalsotrade.

Problem9.21.

Explainwhythemarketmaker’sbid-offerspreadrepresentsarealcosttooptionsinvestors。

A“fair”pricefortheoptioncanreasonablybeassumedtobehalfwaybetweenthebidandtheofferpricequotedbyamarketmaker。

Aninvestortypicallybuysatthemarketmaker’sofferandsellsatthemarketmaker’sbid。

Eachtimeheorshedoesthisthereisahiddencostequaltohalfthebid-offerspread。

Problem9。

22.

AUnitedStatesinvestorwritesfivenakedcalloptioncontracts。

Theoptionpriceis＄3。

50，thestrikepriceis$60。

00，andthestockpriceis＄57.00。

Whatistheinitialmarginrequirement？

Thetwocalculationsarenecessarytodeterminetheinitialmargin.Thefirstgives

Thesecondgives

Theinitialmarginisthegreaterofthese,or＄5,950。

Partofthiscanbeprovidedbytheinitialamountof500×3.5=$1，750receivedfortheoptions.

FurtherQuestions

Problem9。

23.

Calculatetheintrinsicvalueandtimevaluefromthemid—market（averageof