金融机构管理习题答案025.docx
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金融机构管理习题答案025.docx
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金融机构管理习题答案025
ChapterTwentyFive
Options,Caps,Floors,andCollars
ChapterOutline
Introduction
BasicFeaturesofOptions
∙BuyingaCallOptiononaBond
∙WritingaCallOptiononaBond
∙BuyingaPutOptiononaBond
∙WritingaPutOptiononaBond
WritingversusBuyingOptions
∙EconomicReasonsforNotWritingOptions
∙RegulatoryReasons
∙FuturesversusOptionsHedging
TheMechanicsofHedgingaBondorBondPortfolio
∙HedgingwithBondOptionsUsingtheBinomialModel
ActualBondOptions
UsingOptionstoHedgeInterestRateRiskontheBalanceSheet
UsingOptionstoHedgeForeignExchangeRisk
HedgingCreditRiskwithOptions
HedgingCatastropheRiskwithCallSpreadOptions
Caps,Floors,andCollars
∙Caps
∙Floors
∙Collars
∙Caps,Floors,Collars,andCreditRisk
Summary
SolutionstoEnd-of-ChapterQuestionsandProblems:
ChapterTwentyFive
1.Howdoesusingoptionsdifferfromusingforwardorfuturescontracts?
Bothoptionsandfuturescontractsareusefulinmanagingrisk.Otherthanthepuremechanics,theprimarydifferencebetweenthesecontractsliesintherequirementofwhatmustbedoneonorbeforematurity.Futuresandforwardcontractsrequirethatthebuyerorsellerofthecontractsmustexecutesometransaction.Thebuyerofanoptionhasthechoicetoexecutetheoptionortoletitexpirewithoutexecution.Thewriterofanoptionmustperformatransactiononlyifthebuyerchoosestoexecutetheoption.
2.Whatisacalloption?
Acalloptionisaninstrumentthatallowstheownertobuysomeunderlyingassetataprespecifiedpriceonorbeforeaspecifiedmaturitydate.
3.Whatmusthappentointerestratesforthepurchaserofacalloptiononabondtomakemoney?
Howdoesthewriterofthecalloptionmakemoney?
Thecalloptiononabondallowstheownertobuyabondataspecificprice.Fortheowneroftheoptiontomakemoney,heshouldbeabletoimmediatelysellthebondatahigherprice.Thus,forthebondpricetoincrease,interestratesmustdecreasebetweenthetimetheoptionispurchasedandthetimeitisexecuted.Thewriterofthecalloptionmakesapremiumfromthesaleoftheoption.Iftheoptionisnotexercised,thewritermaximizesprofitintheamountofthepremium.Iftheoptionisexercised,thewriterstandstoloseaportionortheentirepremium,andmayloseadditionalmoneyifthepriceontheunderlyingassetmovessufficientlyfar.
4.Whatisaputoption?
Aputoptionisaninstrumentthatallowstheownertosellsomeunderlyingassetataprespecifiedpriceonorbeforeaspecifiedmaturitydate.
5.Whatmusthappentointerestratesforthepurchaserofaputoptiononabondtomakemoney?
Howdoesthewriteroftheputoptionmakemoney?
Theputoptiononabondallowstheownertosellabondataspecificprice.Fortheowneroftheoptiontomakemoney,heshouldbeabletobuythebondatalowerpriceimmediatelypriortoexercisingtheoption.Thus,forthebondpricetodecrease,interestratesmustincreasebetweenthetimetheoptionispurchasedandthetimeitisexecuted.Thewriteroftheputoptionmakesapremiumfromthesaleoftheoption.Iftheoptionisnotexercised,thewritermaximizesprofitintheamountofthepremium.Iftheoptionisexercised,thewriterstandstoloseaportionortheentirepremium,andmayloseadditionalmoneyifthepriceontheunderlyingassetmovessufficientlyfar.
6.Considerthefollowing:
a.WhatarethetwowaystousecallandputoptionsonT-bondstogeneratepositivecashflowswheninterestratesdecline?
Verifyyouranswerwithadiagram.
TheFIcaneither(a)buyacalloption,or(b)sellaputoptiononinterestrateinstruments,suchasT-bonds,togeneratepositivecashflowsintheeventthatinterestratesdecline.Inthecaseofacalloption,positivecashflowswillincreaseaslongasinterestratescontinuetodecrease.SeeFigure25-1inthetextasanexampleofpositivecashflowsminusthepremiumpaidfortheoption.Althoughnotlabeledinthisdiagram,interestratesareassumedtobedecreasingasyoumovefromlefttorightonthex-axis.Thusbondpricesareincreasing.
Thesaleofaputoptiongeneratespositivecashflowsfromthepremiumreceived.Figure25-4showsthatthepayoffwilldecreaseasthepriceofthebondfalls.Ofcoursethiscanonlyhappenifinterestratesareincreasing.Again,althoughnotlabeledinthisdiagram,interestratesareassumedtobeincreasingasyoumovefromrighttoleftonthex-axis.
b.UnderwhatbalancesheetconditionscananFIuseoptionsonT-bondstohedgeitsassetsand/orliabilitiesagainstinterestratedeclines?
AnFIcanusecalloptionsonT-bondstohedgeanunderlyingcashpositionthatdecreasesinvalueasinterestratesdecline.Thiswouldbetrueif,inthecaseofamacrohedge,theFI'sdurationgapisnegativeandtherepricinggapispositive.Inthecaseofamicrohedge,theFIcanhedgeasinglefixed-rateliabilityagainstinterestratedeclines.
c.IsitmoreappropriateforFIstohedgeagainstadeclineininterestrateswithlongcallsorshortputs?
AnFIisbetteroffpurchasingcallsasopposedtowritingputsfortworeasons.First,regulatoryrestrictionslimitanFI'sabilitytowritenakedshortoptions.Second,sincethepotentialpositivecashinflowontheshortputoptionislimitedtothesizeoftheputpremium,theremaybeinsufficientcashinflowintheeventofinterestratedeclinestooffsetthelossesintheunderlyingcashposition.
7.Ineachofthefollowingcases,identifywhatriskthemanagerofanFIfacesandwhethertheriskshouldbehedgedbybuyingaputoracalloption.
a.AcommercialbankplanstoissueCDsinthreemonths.
Thebankfacestheriskthatinterestrateswillincrease.TheFIshouldbuyaputoption.Ifratesrise,theCDscanbepurchasedatalowerpriceandsoldimmediatelybyexercisingtheoption.ThegainwilloffsetthehigherinterestratetheFImustpayinthespotmarket.
b.Aninsurancecompanyplanstobuybondsintwomonths.
Theinsurancecompany(IC)isconcernedthatinterestrateswillfall,andthusthepriceofthebondswillrise.TheICshouldbuycalloptionsthatallowthebondpurchaseatthelowerprice.Thebondspurchasedwiththeoptionscanbesoldimmediatelyforagainthatcanbeappliedagainsttheloweryieldrealizedinthemarket.OrthebondscanbekeptandplacedintheIC’sportfolioiftheyarethedesiredtypeofasset.
c.AthriftplanstosellTreasurysecuritiesnextmonth.
Thethriftisafraidthatrateswillriseandthevalueofthebondswillfall.Thethriftshouldbuyaputoptionthatallowsthesaleofthebondsatornearthecurrentprice.
d.AU.S.banklendstoaFrenchcompanywithaloanpayableinfrancs.
TheU.S.bankisafraidthatthedollarwillappreciate(francswilldepreciate).Thusthebankshouldbuyaputtosellfrancsatornearthecurrentexchangerate.
e.AmutualfundplanstosellitsholdingofstockinaBritishcompany.
Thefundisafraidthatthedollarwillappreciate(£willdepreciate).Thusthefundshouldbuyaputtosell£atornearthecurrentexchangerate.
f.Afinancecompanyhasassetswithadurationofsixyearsandliabilitieswithadurationof13years.
TheFIisconcernedthatinterestrateswillfall,causingthevalueoftheliabilitiestorisemorethanthevalueoftheassetswhichwouldcausethevalueoftheequitytodecrease.Thusthebondshouldbuyacalloptiononinterestrates(bonds).
8.ConsideranFIthatwishestousebondoptionstohedgetheinterestrateriskinthebondportfolio.
a.Howdoeswritingcalloptionshedgetheriskwheninterestratesdecrease?
InthecasewheretheFIislongthebond,writingacalloptionwillprovideextracashflowintheformofapremium.Butfallinginterestrateswillcausethevalueofthebondtoincrease,andeventuallytheoptionwillbeexercisedatalosstothewriter.Butthelossisoffsetbytheincreaseinvalueofthelongbond.Thustheinitialgoalofmaintainingtheinterestratereturnonthelongbondcanberealized.
b.Willwritingcalloptionsfullyhedgetheriskwheninterestratesincrease?
Explain.
Writingcalloptionsprovidesapremiumthatcanbeusedtooffsetthelossesinthebondportfoliocausedbyrisingratesuptotheamountofthepremium.Furtherlossesarenotprotected.
c.Howdoesbuyingaputoptionreducethelossesonthebondportfoliowheninterestratesrise?
Wheninterestratesincrease,thevalueofthebondfalls,buttheputallowsthesaleofthebondatorneartheoriginalprice.Thustheprofitpotentialincreasesasinterestratescontinuetoincrease,althoughitistemperedbytheamountofpremiumthatwaspaidfortheput.
d.Diagramthepurchaseofabondcalloptionagainstthecombinationofabondinvestmentandthepurchaseofabondputoption.
TheprofitpayoffofabondcalloptionisgiveninFigure25-1.Ifthepriceofthebondfallsbelowtheexerciseprice,thepurchaserofthecalllosesthepremium.Asthepriceofthebondincreasesbeyondtheexerciseprice,thepurchaserrecoversthepremiumandthenrealizesanetprofit.Figures25-6and25-7givetheindividualandnetprofitpayoffofholdingabondlongandthepurchaseofaputoption.Theputoptionallowsaprofitifbondpricesdrop.Thisprofitwilloffsetthelossonthelongbondcausedbythedecreaseinthebondvalue.Ifbondpricesincrease,theoptionwillnotbeexercisedandtheinvestorwillrealizeagainfromtheincreaseinthebondsvalue.Thusthecalloptionorthecombinationoflongbondandputoptiongivethesamevalue.
9.WhataretheregulatoryreasonsthatFIsseldomwriteoptions?
Regulatorsoftenprohibitt
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