HullOFOD8eSolutionsCh01.docx

HullOFOD8eSolutionsCh01.docx

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HullOFOD8eSolutionsCh01

CHAPTER1

Introduction

PracticeQuestions

Problem1.1

Whatisthedifferencebetweenalongforwardpositionandashortforwardposition?

Whenatraderentersintoalongforwardcontract,sheisagreeingtobuytheunderlyingassetforacertainpriceatacertaintimeinthefuture.Whenatraderentersintoashortforwardcontract,sheisagreeingtoselltheunderlyingassetforacertainpriceatacertaintimein

thefuture.

Problem1.2.

Explaincarefullythedifferencebetweenhedging,speculation,andarbitrage.

Atraderishedgingwhenshehasanexposuretothepriceofanassetandtakesapositioninaderivativetooffsettheexposure.Inaspeculationthetraderhasnoexposuretooffset.Sheisbettingonthefuturemovementsinthepriceoftheasset.Arbitrageinvolvestakingapositionintwoormoredifferentmarketstolockinaprofit.

Problem1.3.

Whatisthedifferencebetweenenteringintoalongforwardcontractwhentheforwardpriceis$50andtakingalongpositioninacalloptionwithastrikepriceof$50?

Inthefirstcasethetraderisobligatedtobuytheassetfor$50.（Thetraderdoesnothaveachoice.）Inthesecondcasethetraderhasanoptiontobuytheassetfor$50.（Thetraderdoesnothavetoexercisetheoption.）

Problem1.4.

Explaincarefullythedifferencebetweensellingacalloptionandbuyingaputoption.

Sellingacalloptioninvolvesgivingsomeoneelsetherighttobuyanassetfromyou.Itgivesyouapayoffof

Buyingaputoptioninvolvesbuyinganoptionfromsomeoneelse.Itgivesapayoffof

Inbothcasesthepotentialpayoffis

.Whenyouwriteacalloption,thepayoffisnegativeorzero.（Thisisbecausethecounterpartychooseswhethertoexercise.）Whenyoubuyaputoption,thepayoffiszeroorpositive.（Thisisbecauseyouchoosewhethertoexercise.）

Problem1.5.

Aninvestorentersintoashortforwardcontracttosell100,000BritishpoundsforUSdollarsatanexchangerateof1.4000USdollarsperpound.Howmuchdoestheinvestorgainorloseiftheexchangerateattheendofthecontractis（a）1.3900and（b）1.4200?

（a）Theinvestorisobligatedtosellpoundsfor1.4000whentheyareworth1.3900.Thegainis（1.4000-1.3900）×100,000=$1,000.

（b）Theinvestorisobligatedtosellpoundsfor1.4000whentheyareworth1.4200.Thelossis（1.4200-1.4000）×100,000=$2,000

Problem1.6.

Atraderentersintoashortcottonfuturescontractwhenthefuturespriceis50centsperpound.Thecontractisforthedeliveryof50,000pounds.Howmuchdoesthetradergainorloseifthecottonpriceattheendofthecontractis（a）48.20centsperpound;（b）51.30centsperpound?

（a）Thetradersellsfor50centsperpoundsomethingthatisworth48.20centsperpound.Gain

.

（b）Thetradersellsfor50centsperpoundsomethingthatisworth51.30centsperpound.Loss

.

Problem1.7.

Supposethatyouwriteaputcontractwithastrikepriceof$40andanexpirationdateinthreemonths.Thecurrentstockpriceis$41andthecontractison100shares.Whathaveyoucommittedyourselfto?

Howmuchcouldyougainorlose?

Youhavesoldaputoption.Youhaveagreedtobuy100sharesfor$40pershareifthepartyontheothersideofthecontractchoosestoexercisetherighttosellforthisprice.Theoptionwillbeexercisedonlywhenthepriceofstockisbelow$40.Suppose,forexample,thattheoptionisexercisedwhenthepriceis$30.Youhavetobuyat$40sharesthatareworth$30;youlose$10pershare,or$1,000intotal.Iftheoptionisexercisedwhenthepriceis$20,youlose$20pershare,or$2,000intotal.Theworstthatcanhappenisthatthepriceofthestockdeclinestoalmostzeroduringthethree-monthperiod.Thishighlyunlikelyeventwouldcostyou$4,000.Inreturnforthepossiblefuturelosses,youreceivethepriceoftheoptionfromthepurchaser.

Problem1.8.

Whatisthedifferencebetweentheover-the-countermarketandtheexchange-tradedmarket?

Whatarethebidandofferquotesofamarketmakerintheover-the-countermarket?

Theover-the-countermarketisatelephone-andcomputer-linkednetworkoffinancialinstitutions,fundmanagers,andcorporatetreasurerswheretwoparticipantscanenterintoanymutuallyacceptablecontract.Anexchange-tradedmarketisamarketorganizedbyanexchangewheretraderseithermeetphysicallyorcommunicateelectronicallyandthecontractsthatcanbetradedhavebeendefinedbytheexchange.Whenamarketmakerquotesabidandanoffer,thebidisthepriceatwhichthemarketmakerispreparedtobuyandtheofferisthepriceatwhichthemarketmakerispreparedtosell.

Problem1.9.

Youwouldliketospeculateonariseinthepriceofacertainstock.Thecurrentstockpriceis$29,andathree-monthcallwithastrikeof$30costs$2.90.Youhave$5,800toinvest.Identifytwoalternativestrategies,oneinvolvinganinvestmentinthestockandtheotherinvolvinginvestmentintheoption.Whatarethepotentialgainsandlossesfromeach?

Onestrategywouldbetobuy200shares.Anotherwouldbetobuy2,000options.Ifthesharepricedoeswellthesecondstrategywillgiverisetogreatergains.Forexample,ifthesharepricegoesupto$40yougain

fromthesecondstrategyandonly

fromthefirststrategy.However,ifthesharepricedoesbadly,thesecondstrategygivesgreaterlosses.Forexample,ifthesharepricegoesdownto$25,thefirststrategyleadstoalossof

whereasthesecondstrategyleadstoalossofthewhole$5,800investment.Thisexampleshowsthatoptionscontainbuiltinleverage.

Problem1.10.

Supposeyouown5,000sharesthatareworth$25each.Howcanputoptionsbeusedtoprovideyouwithinsuranceagainstadeclineinthevalueofyourholdingoverthenextfourmonths?

Youcouldbuy50putoptioncontracts（eachon100shares）withastrikepriceof$25andanexpirationdateinfourmonths.Ifattheendoffourmonthsthestockpriceprovestobelessthan$25,youcanexercisetheoptionsandsellthesharesfor$25each.

Problem1.11.

Whenfirstissued,astockprovidesfundsforacompany.Isthesametrueofanexchange-tradedstockoption?

Discuss.

Anexchange-tradedstockoptionprovidesnofundsforthecompany.Itisasecuritysoldbyoneinvestortoanother.Thecompanyisnotinvolved.Bycontrast,astockwhenitisfirstissuedissoldbythecompanytoinvestorsanddoesprovidefundsforthecompany.

Problem1.12.

Explainwhyafuturescontractcanbeusedforeitherspeculationorhedging.

Ifaninvestorhasanexposuretothepriceofanasset,heorshecanhedgewithfuturescontracts.Iftheinvestorwillgainwhenthepricedecreasesandlosewhenthepriceincreases,alongfuturespositionwillhedgetherisk.Iftheinvestorwilllosewhenthepricedecreasesandgainwhenthepriceincreases,ashortfuturespositionwillhedgetherisk.Thuseitheralongorashortfuturespositioncanbeenteredintoforhedgingpurposes.

Iftheinvestorhasnoexposuretothepriceoftheunderlyingasset,enteringintoafuturescontractisspeculation.Iftheinvestortakesalongposition,heorshegainswhentheasset’spriceincreasesandloseswhenitdecreases.Iftheinvestortakesashortposition,heorsheloseswhentheasset’spriceincreasesandgainswhenitdecreases.

Problem1.13.

SupposethataMarchcalloptiontobuyasharefor$50costs$2.50andishelduntilMarch.Underwhatcircumstanceswilltheholderoftheoptionmakeaprofit?

Underwhatcircumstanceswilltheoptionbeexercised?

Drawadiagramshowinghowtheprofitonalongpositionintheoptiondependsonthestockpriceatthematurityoftheoption.

Theholderoftheoptionwillgainifthepriceofthestockisabove$52.50inMarch.（Thisignoresthetimevalueofmoney.）Theoptionwillbeexercisedifthepriceofthestockisabove$50.00inMarch.TheprofitasafunctionofthestockpriceisshowninFigureS1.1.

FigureS1.1ProfitfromlongpositioninProblem1.13

Problem1.14.

SupposethataJuneputoptiontosellasharefor$60costs$4andishelduntilJune.Underwhatcircumstanceswilltheselleroftheoption（i.e.,thepartywithashortposition）makeaprofit?

Underwhatcircumstanceswilltheoptionbeexercised?

Drawadiagramshowinghowtheprofitfromashortpositionintheoptiondependsonthestockpriceatthematurityoftheoption.

Theselleroftheoptionwilllosemoneyifthepriceofthestockisbelow$56.00inJune.（Thisignoresthetimevalueofmoney.）Theoptionwillbeexercisedifthepriceofthestockisbelow$60.00inJune.TheprofitasafunctionofthestockpriceisshowninFigureS1.2.

FigureS1.2ProfitfromshortpositioninProblem1.14

Problem1.15.

ItisMayandatraderwritesaSeptembercalloptionwithastrikepriceof$20.Thestockpriceis$18,andtheoptionpriceis$2.Describetheinvestor’scashflowsiftheoptionishelduntilSeptemberandthestockpriceis$25atthistime.

Thetraderhasaninflowof$2inMayandanoutflowof$5inSeptember.The$2isthecashreceivedfromthesaleoftheoption.The$5istheresultoftheoptionbeingexercised.Theinvestorhastobuythestockfor$25inSeptemberandsellittothepurchaseroftheoptionfor$20.

Problem1.16.

AtraderwritesaDecemberputoptionwithastrikepriceof$30.Thepriceoftheoptionis$4.Underwhatcircumstancesdoesthetradermakeagain?

Thetradermakesagainifthepriceofthestockisabove$26atthetimeofexercise.（Thisignoresthetimevalueofmoney.）

Problem1.17.

Acompanyknowsthatitisduetoreceiveacertainamountofaforeigncurrencyinfourmonths.Whattypeofoptioncontractisappro