期权期货习题.docx
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期权期货习题.docx
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期权期货习题
FutureOptionandother
derivatives
exercises
1.What5sthediffereneebetweenenteringintoalongforwardcontactwhentheforwardpriceis$50andtakingalongpositioninacallwithastrikepriceof$50?
2.Aninvestorentersintoashortforwardcontracttosell100,000BritishpoundsforUSdollarsatanexchangerateof1.5000USdollarsperpound.Howmuchdoestheinvestorgainorloseiftheexchangerateattheendofthecontractis1.4900and1.5200?
❖3.Youwouldliketospeculateonariseinthepriceofacertainstock.Thecurrentstockpriceis$29,anda3-monthcallwithastrikepriceof$30costs$2.90.Youhave$5,800toinvest.Identifytwoalternativeinvestmentstrategies,oneinthestockandtheotherinanoptiononthestock.Whatarethepotentialgainsandlossesfromeach?
❖4.SupposethataMarchcalloptiontobuyasharefor$50costs$2.5andishelduntilMarch.Underwhatcircumstanceswilltheholderoftheoptionmakeaprofit?
Underwhatcircumstanceswilltheoptionbeexercised?
Drawadiagramillustratinghowtheprofitfromalongpositionintheoptiondependsonthestockpriceatmaturityoftheoption.
•5.Explainwhyaforwardcontractcanbe
usedforeitherspeculationorhedging.
•6.SupposethataJuneputoptiontosellasharefor$60costs$4andishelduntilJune.Underwhatcircumstanceswilltheoptionbeexercised?
Drawadiagramillustratinghowtheprofitfromashortpositionintheoptiondependsonthestockpriceatmaturityoftheoption.
•7」tisMayandatraderwritesaSeptembercalloptionwithastrikepriceof$20.Thestockpriceis$18andtheoptionpriceis$2.Describethetrader'scashflowsiftheoptionishelduntilSeptemberandthestockpriceis$25atthattime.
❖8.AtraderwritesaDecemberputoptionwithastrikepriceof$30.Thepriceoftheoptionis$4.Underwhatcircumstancesdoesthetradermakeagain?
❖9.Acompanyknowsthatitisduetoreceiveacertainamountofaforeigncurrencyin4months.Whattypeofoptioncontractisappropriateforhedging?
❖10.Thepriceofgoldiscurrently$500perounce.Theforwardpricefordeliveryin1yearis$700.Anarbitrageurcanborrowmoneyat10%perannum.Whatshouldthearbitrageurdo?
Assumethatthecostofstoringgoldiszeroandthatgoldprovidesnoincome.
11.SupposethatyouenterintoashortfuturescontracttosellJulysilverfor$5.20perounceontheNewYorkCommodityExchange.Thesizeofthecontractis5,000ounces.Theinitialmarginis$4,000,andthemaintenancemarginis$3,000.Whatchangeinfuturespricewillleadtoamargincall?
Whathappensifyoudonotmeetthemargincall?
12.AninvestorentersintotwolongJulyfuturescontractsonorangejuice.Eachcontractisforthedeliveryof15,000pounds.Thecurrentfuturespriceis160centsperpound,theinitialmarginis$6,000percontract,andthemaintenancemarginis$4,500percontract.Whatpricechangewouldleadtoamargincall?
Underwhatcircumstancescould$2,000bewithdrawnfromthemarginaccount?
13.Attheendofonedayaclearinghousememberislong100contracts,andthesettlementpriceis$50,000percontract.Theoriginalmarginis$2,000percontract.Onthefollowingdaythememberbecomesresponsibleforclearinganadditional20longcontracts,enteredintoatapriceof$51,000percontract.Thesettlementpriceattheendofthisdayis$50,200.Howmuchdoesthememberhavetoaddtoitsmarginaccountwiththeexchangeclearinghouse?
❖14.Describetheprofitfromthefollowingportfolio:
alongforwardcontractonanassetandalongEuropeanputoptionontheassetwiththesamematurityastheforwardcontractandastrikepricethatisequaltotheforwardpriceoftheassetatthetimetheportfolioissetup.
❖15.ThecurrentPriceofastockis$94,and3-monthEuropeancalloptionswithastrikepriceof$95currentlysellfor$4.70.AninvestorwhofeelsthatthePriceofthestockwillincreaseistryingtodecidebetweenbuying100sharesandbuying2,000calloptions(=20contracts).Bothstrategiesinvolveaninvestmentof$9,400.Whatadvicewouldyougive?
Howhighdoesthestockpricehavetorisefortheoptionstrategytobemoreprofitable?
TableDatafortheexampleonrollingoilhedgeforward.
DateApr.04Sept.04
Feb.05i
June05
Oct.04futuresprice
18.20
17.40
Mar.O5futuresprice
17.00
16.50
July.O5futuresprice
16.30
15.90
Spotprice
19.00
16.00
•16.Supposethatthestandarddeviationofquarterlychangesinthepricesofacommodityis$0.65,thestandarddeviationofquarterlychangesinafuturespriceonthecommodityis$0.81,andthecoefficientofcorrelationbetweenthetwochangesis0.8.Whatistheoptimalhedgeratiofora3-monthcontract?
Whatdoesitmean?
❖17/1ftheminimunrivariancehedgeratioiscalculatedas1.0,thehedgemustbeperfect.5,Isthisstatementtrue?
Explainyouranswer.
❖18.Thestandarddeviationofmonthlychangesinthespotpriceoflivecattleis(incentsperpound)12Thestandarddeviationofmonthlychangesinthefuturespriceoflivecattlefortheclosestcontractis14Thecorrelationbetweenthefuturespricechangesandthespotpricechangesis0・7」tisnowOctober15.Abeefproduceriscommittedtopurchasing200,000poundsoflivecattleonNovember15.TheproducerwantstousetheDecemberlivecattlefuturescontractstohedgeitsrisk・Eachcontractisforthedeliveryof40,000poundsofcattle・Whatstrategyshouldthebeefproducerfollow?
❖19.Alongforwardcontractonanon・dividend-payingstockwasenteredintosometimeago.Itcurrentlyhas6monthstomaturity.Therisk-freerateofinterest(withcontinuouscompounding)is10%perannum,thestockpriceis$25,andthedeliverypriceis$24.
❖20.Considera3-monthfuturescontractontheS&P500.Supposethatthestocksunderlyingtheindexprovideadividendyieldof1%perQrinum,thatthecurrentvalueoftheindexis800,andthatthecontinuouslycompoundedrisk-freeinterestrateis6%perQrinum.
♦21.Supposethatyouenterintoa6・monthforwardcontractonanon-dividend-payingstockwhenthestockpriceis$30andtherisk-freeinterestrate(withcontinuouscompounding)is12%perannuin.Whatistheforwardprice?
•22.A1-yearlongforwardcontractonanorvdividend-payingstockisenteredintowhenthestockPriceis$40andtherisk-freerateofinterestis10%perannumwithcontinuouscompounding.
(a)Whataretheforwardpriceandtheinitialvalueoftheforwardcontract?
(b)Sixmonthslater,thepriceofthestockis$45andtherisk-freeinterestrateisstill10%Whataretheforwardpriceandthevalueoftheforwardcontract?
23.Supposethattherisk-freeinterestrateis10%perannumwithcontinuouscompoundingandthatthedividendyieldonastockindexis4%perannum.Theindexisstandingat400,andthefuturespriceforacontractdeliverableinfourmonthsis4O5.Whatarbitrageopportunitiesdoesthiscreate?
24.Assumethattherisk-freeinterestrateis9%perannumwithcontinuouscompoundingandthatthedividendyieldonastockindexvariesthroughouttheyear.InFebruary,May,August,andNovember,dividendsarepaidatarateof5%perannum.Inothermonths,dividendsarepaidatarateof2%perannurn.SupposethatthevalueoftheindexonJuly31,2006,is300.WhatisthefuturespriceforacontractdeliverableonDecember31,2006?
25.The2-monthinterestratesinSwitzerlandandtheUnitedStatesare,respectively,3%and8%perannumwithcontinuouscompounding.ThespotpriceoftheSwissfrancis$0.6500.Thefuturespriceforacontractdeliverabein2monthsis$0.6600.Whatarbitrageopportunitiesdoesthiscreate?
26.Thespotpriceofsilveris$9perounce.The-storagecostsare$0.24perounce;peryearpayablequarterlyinadvanee.Assumingthatinterestratesare10%perannumforallmaturities,calculatethefuturespriceofsilverfordeliveryin9months.
•27.SupposethattheTreasurybondfuturespriceis101-12.Whichofthefollowingfourbondsischeapesttodeliver?
Bond
Price
Conversionfactor
1
125-05
1.2131
2
142-15.
1.3792
3
115-31
1.1149
4
144-02
1.4026
❖28.Thepriceofa90-dayTreasurybillisquotedas10.OO.WhatcontinuouslycompoundedreturndoesaninvestorearnontheTreasurybillforthe90-dayperiod?
29.ltisMay5,2005.Thequotedpriceofagovernmentbondwitha12%couponthatmaturesonJuly27,2011,is110-17.Whatisthecashprice?
•31・Supposethat,inaTreasurybondfuturescontract,itisknownthatthecheapest-to-deliverbondwillbea12%couponbondwithaconversionfactorof1.4000.Supposealsothatitisknownthatdeliverywilltakeplacein270days・Couponsarepayablesemiannuallyonthebond・AsillustratedinFigure5thelastcoupondatewas60daysago5thenextcoupondateisin122days5andthecoupondatethereafterisin305days・Thetermstructureisflat,andtherateofinterest(withcontinuouscompounding)is10%perannum.Assumethecurrentquotedbondpricetheproportionofthenextcouponpaymentthataccruestotheholder.
60days
122days
148days
35days
Figure.TimechartforExample31
CouponCurrentCouponMaturityCoupon
Paymenttimepaymentofpayment
futures
contract
Anumberoffactorsdeterminethecheapest-to-deliverbond.Whenbondyields
areinexcess6%,theconversionfactorsystemtendstofavorthedeliveryofbonds.
❖32lt5sJuly30,2005.Thecheapest-to-deliverbondinaSeptember2005Treasurybondfuturescontractisa13%couponbond,anddeliveryisexpectedtobemadeonSeptember30,2005.CouponpaymentsonthebondaremadeonFebruary4andAugust
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