HullOFOD8eSolutionsCh09

CHAPTER9MechanicsofOptionsMarketsPracticeQuestionsProblem9.1.AninvestorbuysaEuropeanputonasharefor$3.Thestockpriceis$42andthestrikepriceis$40.Underwhatcircumstancesdoestheinvestormakeaprofit?Underwhatcircumstanceswilltheoptionbeexercised?Drawadiagramshowingthevariationoftheinvestor’sprofitwiththestockpriceatthematurityoftheoption.Theinvestormakesaprofitifthepriceofthestockontheexpirationdateislessthan$37.Inthesecircumstancesthegainfromexercisingtheoptionisgreaterthan$3.Theoptionwillbeexercisedifthestockpriceislessthan$40atthematurityoftheoption.Thevariationoftheinvestor’sprofitwiththestockpriceinFigureS9.1.FigureS9.1Investor’sprofitinProblem9.1Problem9.2.AninvestorsellsaEuropeancallonasharefor$4.Thestockpriceis$47andthestrikepriceis$50.Underwhatcircumstancesdoestheinvestormakeaprofit?Underwhatcircumstanceswilltheoptionbeexercised?Drawadiagramshowingthevariationoftheinvestor’sprofitwiththestockpriceatthematurityoftheoption.Theinvestormakesaprofitifthepriceofthestockisbelow$54ontheexpirationdate.Ifthestockpriceisbelow$50,theoptionwillnotbeexercised,andtheinvestormakesaprofitof$4.Ifthestockpriceisbetween$50and$54,theoptionisexercisedandtheinvestormakesaprofitbetween$0and$4.Thevariationoftheinvestor’sprofitwiththestockpriceisasshowninFigureS9.2.FigureS9.2Investor’sprofitinProblem9.2Problem9.3.AninvestorsellsaEuropeancalloptionwithstrikepriceofKandmaturityTandbuysaputwiththesamestrikepriceandmaturity.Describetheinvestor’sposition.Thepayofftotheinvestorismax(0)max(0)TTSKKS−−,+−,ThisisTKS−inallcircumstances.Theinvestor’spositionisthesameasashortpositioninaforwardcontractwithdeliverypriceK.Problem9.4.Explainwhymarginsarerequiredwhenclientswriteoptionsbutnotwhentheybuyoptions.Whenaninvestorbuysanoption,cashmustbepaidupfront.Thereisnopossibilityoffutureliabilitiesandthereforenoneedforamarginaccount.Whenaninvestorsellsanoption,therearepotentialfutureliabilities.Toprotectagainsttheriskofadefault,marginsarerequired.Problem9.5.AstockoptionisonaFebruary,May,August,andNovembercycle.Whatoptionstradeon(a)April1and(b)May30?OnApril1optionstradewithexpirationmonthsofApril,May,August,andNovember.OnMay30optionstradewithexpirationmonthsofJune,July,August,andNovember.Problem9.6.Acompanydeclaresa2-for-1stocksplit.Explainhowthetermschangeforacalloptionwithastrikepriceof$60.Thestrikepriceisreducedto$30,andtheoptiongivestheholdertherighttopurchasetwiceasmanyshares.Problem9.7.“Employeestockoptionsissuedbyacompanyaredifferentfromregularexchange-tradedcalloptionsonthecompany’sstockbecausetheycanaffectthecapitalstructureofthecompany.”Explainthisstatement.Theexerciseofemployeestockoptionsusuallyleadstonewsharesbeingissuedbythecompanyandsoldtotheemployee.Thischangestheamountofequityinthecapitalstructure.Whenaregularexchange-tradedoptionisexercisednonewsharesareissuedandthecompany’scapitalstructureisnotaffected.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.TheprofitfromalongpositionisasshowninFigureS9.3.FigureS9.3ProfitfromlongpositioninProblem9.9Problem9.10.SupposethataEuropeanputoptiontosellasharefor$60costs$8andishelduntilmaturity.Underwhatcircumstanceswilltheselleroftheoption(thepartywiththeshortposition)makeaprofit?Underwhatcircumstanceswilltheoptionbeexercised?Drawadiagramillustratinghowtheprofitfromashortpositionintheoptiondependsonthestockpriceatmaturityoftheoption.Ignoringthetimevalueofmoney,theselleroftheoptionwillmakeaprofitifthestockpriceatmaturityisgreaterthan$52.00.Thisisbecausethecosttotheselleroftheoptionisinthesecircumstanceslessthanthepricereceivedfortheoption.Theoptionwillbeexercisedifthestockpriceatmaturityislessthan$60.00.Notethatifthestockpriceisbetween$52.00and$60.00theselleroftheoptionmakesaprofiteventhoughtheoptionisexercised.TheprofitfromtheshortpositionisasshowninFigureS9.4.FigureS9.4ProfitfromshortpositioninProblem9.10Problem9.11.Describetheterminalvalueofthefollowingportfolio:anewlyentered-intolongforwardcontr