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word格式-可编辑-感谢下载支持CHAPTER7FUTURESANDOPTIONSONFOREIGNEXCHANGESUGGESTEDANSWERSANDSOLUTIONSTOEND-OF-CHAPTERQUESTIONSANDPROBLEMSQUESTIONSExplainthebasicdifferencesbetweentheoperationofacurrencyforwardmarketandafuturesmarket.Answer:TheforwardmarketisanOTCmarketwheretheforwardcontractforpurchaseorsaleofforeigncurrencyistailor-madebetweentheclientanditsinternationalbank.Nomoneychangeshandsuntilthematuritydateofthecontractwhendeliveryandreceiptaretypicallymade.Afuturescontractisanexchange-tradedinstrumentwithstandardizedfeaturesspecifyingcontractsizeanddeliverydate.Futurescontractsaremarked-to-marketdailytoreflectchangesinthesettlementprice.Deliveryisseldommadeinafuturesmarket.Ratherareversingtradeismadetocloseoutalongorshortposition.Inorderforaderivativesmarkettofunctionmostefficientlytwotypesofeconomicagentsareneeded:hedgersandspeculators.Explain.Answer:Twotypesofmarketparticipantsarenecessaryfortheefficientoperationofaderivativesmarket:speculatorsandhedgers.Aspeculatorattemptstoprofitfromachangeinthefuturesprice.Todothisthespeculatorwilltakealongorshortpositioninafuturescontractdependinguponhisexpectationsoffuturepricemovement.Ahedgeron-the-other-handdesirestoavoidpricevariationbylockinginapurchasepriceoftheunderlyingassetthroughalongpositioninafuturescontractorasalespricethroughashortposition.Ineffectthehedgerpassesofftheriskofpricevariationtothespeculatorwhoisbetterableoratleastmorewillingtobearthisrisk.WhyaremostfuturespositionsclosedoutthroughareversingtraderatherthanheldtodeliveryAnswer:Inforwardmarketsapproximately90percentofallcontractsthatareinitiallyestablishedresultintheshortmakingdeliverytothelongoftheassetunderlyingthecontract.Thisisnaturalbecausethetermsofforwardcontractsaretailor-madebetweenthelongandshort.Bycontrastonlyaboutonepercentofcurrencyfuturescontractsresultindelivery.Whilefuturescontractsareusefulforspeculationandhedgingtheirstandardizeddeliverydatesmakethemunlikelytocorrespondtotheactualfuturedateswhenforeignexchangetransactionswilloccur.Thustheyaregenerallyclosedoutinareversingtrade.Infactthecommissionthatbuyersandsellerspaytotransactinthefuturesmarketisasingleamountthatcoverstheround-triptransactionsofinitiatingandclosingouttheposition.word格式-可编辑-感谢下载支持Solution:PaMax[68-7068-
69.50/
1.01750]Max[-2-
1.470]=0centsUsetheEuropeanoption-pricingmodelsdevelopedinthechaptertovaluethecallofproblem9andtheputofproblem
10.AssumetheannualizedvolatilityoftheSwissfrancis
14.2percent.ThisproblemcanbesolvedusingtheFXOPM.xlsspreadsheet.Solution:d1=[ln
69.50/68+.
5.
1422.50]/.142V.50=.2675c2=d1・.142V.50=.2765-.1004=.1671Nd1=.6055Nd2=.5664M-dJ=.3945N-d2=.4336C=[
69.
50.6055-
68.5664]e-.o
35.5o=
3.51centsP=[
68.4336-
69.5O.3945]eo355o=
2.03centsQUsethebinomialoption-pricingmodeldevelopedinthechaptertovaluethecallofproblem
9.ThevolatilityoftheSwissfrancis
14.2percent.Solution:ThespotrateatTwillbeeither
77.39C=
70.
0001.1056or
63.32$=
70.00$.9045whereu=e.u2v.5o=
1.1056andd=1/u=.
9045.AttheexercisepriceofE=68theoptionwillonlybeexercisedattimeTiftheSwissfrancappreciates;itsexercisevaluewouldbeCuT=
9.39C=
77.390-
68.IftheSwissfrancdepreciatesitwouldnotberationaltoexercisetheoption;itsvaluewouldbeC^=
0.Thehedgeratioish=
9.39-0/
77.39-
63.32=.
6674.Thusthecallpremiumis:Co=Max{[
69.
50.6674-6870/
68.6674-1+1]/
1.017570-68}=Max[
1.642]=2centsperSF.word格式-可编辑-感谢下载支持MINICASE:THEOPTIONSSPECULATORAspeculatorisconsideringthepurchaseoffivethree-monthJapaneseyencalloptionswithastrikingpriceof96centsper100yen.Thepremiumis
1.35centsper100yen.Thespotpriceis
95.28centsper100yenandthe90-dayforwardrateis
95.71cents.Thespeculatorbelievestheyenwillappreciateto$
1.00per100yenoverthenextthreemonths.Asthespeculatorsassistantyouhavebeenaskedtopreparethefollowing:
1.Graphthecalloptioncashflowschedule.Determinethespeculatorsprofitiftheyenappreciatesto$
1.00/100yen.Determinethespeculatorsprofitiftheyenonlyappreciatestotheforwardrate.Determinethefuturespotpriceatwhichthespeculatorwillonlybreakeven.SuggestedSolutiontotheOptionsSpeculator:5x¥6250000x[100-96-
1.35]/10000=$
8281.
25.Sincetheoptionexpiresout-of-the-moneythespeculatorwilllettheoptionexpireworthless.Hewillonlylosetheoptionpremium.ST=E+C=96+
1.35=
97.35centsper100yen.HowcantheFXfuturesmarketbeusedforpricediscoveryAnswer:TotheextentthatFXforwardpricesareanunbiasedpredictoroffuturespotexchangeratesthemarketanticipateswhetheronecurrencywillappreciateordepreciateversusanother.BecauseFXfuturescontractstradeinanexpirationcycledifferentcontractsexpireatdifferentperiodicdatesintothefuture.Thepatternofthepricesofthesecontractsprovidesinformationastothemarket9scurrentbeliefabouttherelativefuturevalueofonecurrencyversusanotheratthescheduledexpirationdatesofthecontracts.Onewillgenerallyseeasteadilyappreciatingordepreciatingpattern;howeveritmaybemixedattimes.Thusthefuturesmarketisusefulforpricediscoveryi.e.obtainingthemarketsforecastofthespotexchangerateatdifferentfuturedates.WhatisthemajordifferenceintheobligationofonewithalongpositioninafuturesorforwardcontractincomparisontoanoptionscontractAnswer:Afuturesorforwardcontractisavehicleforbuyingorsellingastatedamountofforeignexchangeatastatedpriceperunitataspecifiedtimeinthefuture.Ifthelongholdsthecontracttothedeliverydatehepaystheeffectivecontractualfuturesorforwardpriceregardlessofwhetheritisanadvantageouspriceincomparisontothespotpriceatthedeliverydate.Bycontrastanoptionisacontractgivingthelongtherighttobuyorsellagivenquantityofanassetataspecifiedpriceatsometimeinthefuturebutnotenforcinganyobligationonhimifthespotpriceismorefavorablethantheexerciseprice.Becausetheoptionownerdoesnothavetoexercisetheoptionifitistohisdisadvantagetheoptionhasapriceorpremiumwhereasnopriceispaidatinceptiontoenterintoafuturesorforwardcontract.Whatismeantbytheterminologythatanoptionisin-at-orout-of-the-moneyAnswe匚AcallputoptionwithStEESisreferredtoastradingin-the-money.IfSt^Etheoptionistradingat-the-money.IfStEESthecallputoptionistradingout-of-the-money.word格式-可编辑-感谢下载支持ListtheargumentsvariablesofwhichanFXcallorputoptionmodelpriceisafunction.HowdoesthecallandputpremiumchangewithrespecttoachangeintheargumentsAnswer:Bothcallandputoptionsarefunctionsofonlysixvariables:StErTando.WhenallelseIIipremainsthesamethepriceofaEuropeanFXcallputoptionwillincrease:thelargersmallerisSthesmallerlargerisEthesmallerlargerisrthelargersmalleristhelargersmallerrjsrelativetorandthegreaterisa.WhenrandrarenottoomuchdifferentinsizeaEuropeanFXcallandputwillincreaseinpricewhentheoptionterm-to-maturityincreases.Howeverwhenqisverymuchlargerthanr.aEuropeanFXcallw川3Iincreaseinpricebuttheputpremiumwilldecreasewhentheoptionterm-to-maturityincreases.Theoppositeistruewhenrisverymuchgreaterthanr$.ForAmericanFXoptionstheanalysisislesscomplicated.SincealongertermAmericanoptioncanbeexercisedonanydatethatashortertermoptioncanbeexercisedorasomelaterdateitfollowsthattheallelseremainingthesamethelongertermAmericanoptionwillsellatapriceatleastaslargeastheshortertermoption.PROBLEMSAssumetodayssettlementpriceonaCMEEURfuturescontractis$
1.3140/EUR.Youhaveashortpositioninonecontract.Yourperformancebondaccountcurrentlyhasabalanceof$
1700.Thenextthreedays9settlementpricesare$
1.3126$
1.3133and$
1.
3049.Calculatethechangesintheperformancebondaccountfromdailymarking-to-marketandthebalanceoftheperformancebondaccountafterthethirdday.Solution:$1700+[$
1.3140-$
1.3126+$
1.3126-$
1.3133+$
1.3133-$
1.3049]xEUR125000=$
2837.50whereEUR125000isthecontractualsizeofoneEURcontract.Doproblem1againassumingyouhavealongpositioninthefuturescontract.Solution:$1700+[$
1.3126-$
1.3140+$
1.3133-$
1.3126+$
1.3049-$
1.3133]xEUR125000=$
562.50whereEUR125000isthecontractualsizeofoneEURcontract.Withonly$
562.50inyourperformancebondaccountyouwouldexperienceamargincallrequestingthatadditionalfundsbeaddedtoyourperformancebondaccounttobringthebalancebackuptotheinitialperformancebondlevel.UsingthequotationsinExhibit
7.3calculatethefacevalueoftheopeninterestintheJune2005Swissfrancfuturescontract.Solution:2101contractsxSF125000=SF
262625000.whereSF125000isthecontractualsizeofoneSFcontract.UsingthequotationsinExhibit
7.3notethattheJune2005Mexicanpesofuturescontracthasapriceof$
0.
08845.YoubelievethespotpriceinJunewillbe$
0.
09500.WhatspeculativepositionwouldyouenterintotoattempttoprofitfromyourbeliefsCalculateyouranticipatedprofitsassumingyoutakeapositioninthreecontracts.WhatisthesizeofyourprofitlossifthefuturespriceisindeedanunbiasedpredictorofthefuturespotpriceandthispricematerializesSolution:IfyouexpecttheMexicanpesotorisefrom$
0.08845to$
0.09500youwouldtakealongpositioninfuturessincethefuturespriceof$
0.08845islessthanyourexpectedspotprice.Youranticipatedprofitfromalongpositioninthreecontractsis:3x$
0.09500-$
0.08845xword格式-可编辑-感谢下载支持MP500Q00=$
9825.00whereMP500000isthecontractualsizeofoneMPcontract.Ifthefuturespriceisanunbiasedpredictoroftheexpectedspotpricetheexpectedspotpriceisthefuturespriceof$
0.08845/MP.Ifthisspotpricematerializesyouwillnothaveanyprofitsorlossesfromyourshortpositioninthreefuturescontracts:3x$
0.08845-$
0.08845xMP500000=
0.Doproblem4againassumingyoubelievetheJune2005spotpricewillbe$
0.
08500.Solution:IfyouexpecttheMexicanpesotodepreciatefrom$
0.08845to$
0.07500youwouldtakeashortpositioninfuturessincethefuturespriceof$
0.08845isgreaterthanyourexpectedspotprice.Youranticipatedprofitfromashortpositioninthreecontractsis:3x$
0.08845-$
0.07500xMP500000=$
20175.
00.Ifthefuturespriceisanunbiasedpredictorofthefuturespotpriceandthispricematerializesyouwillnotprofitorlosefromyourlongfuturesposition.GeorgeJohnsonisconsideringapossiblesix-month$100millionLIBOR-basedfloating-ratebankloantofundaprojectattermsshowninthetablebelow.JohnsonfearsapossibleriseintheLIBORratebyDecemberandwantstousetheDecemberEurodollarfuturescontracttohedgethisrisk.ThecontractexpiresDecember201999hasaUS$1millioncontractsizeandadiscountyieldof
7.3percent.Johnsonwillignorethecashflowimplicationsofmarkingtomarketinitialmarginrequirementsandanytimingmismatchbetweenexchange-tradedfuturescontractcashflowsandtheinterestpaymentsdueinMarch.LoanTermsword格式-可编辑-感谢下载支持FormulateJohnsonsSeptember20floating-to-fixed-ratestrategyusingtheEurodollarfuturecontractsdiscussedinthetextabove.Showthatthisstrategywouldresultinafixed-rateloanassuminganincreaseintheLIBORrateto
7.8percentbyDecember20whichremainsat
7.8percentthroughMarch
20.Showallcalculations.Johnsonisconsideringa12-monthloanasanalternative.Thisapproachwillresultintwoadditionaluncertaincashflowsasfollows:DescribethestriphedgethatJohnsoncoulduseandexplainhowithedgesthe12-monthloanspecifynumberofcontracts.Nocalculationsareneeded.CFAGuidelineAnswerThebasispointvalueBPVofaEurodollarfuturescontractcanbefoundbysubstitutingthecontractspecificationsintothefollowingmoneymarketrelationship:BPVFUT=ChangeinValue=facevaluexdaystomaturity/360xchangeinyield=$1millionx90/360x.0001=$25ThenumberofcontractNcanbefoundby:N=BPVspot/BPVfutures=$2500/$25=100ORN=valueofspotposition/facevalueofeachfuturescontract=$100million/$1million=100ORN=valueofspotposition/valueoffuturesposition=$100000000/$981750wherevalueoffuturesposition=$1000000x[1-
0.073/4]必102contractsThereforeonSeptember20Johnsonwouldsell100or102DecemberEurodollarfuturescontractsatthe
7.3percentyield.TheimpliedLIBORrateinDecemberis
7.3percentasindicatedbytheDecemberEurofuturesdiscountyieldof
7.3percent.Thusaborrowingrateof
9.3percent
7.3percent+200basispointscanbelockedinifthehedgeiscorrectlyimplemented.Ariseintherateto
7.8percentrepresentsa50basispointbpincreaseovertheimpliedLIBORrate.Fora50basispointincreaseinLIBORthecashflowontheshortfuturespositionis:=$25perbasispointpercontractx50bpx100contracts=$
125000.Howeverthecashflowonthefloatingrateliabilityis:=-
0.098x$100000000/4=-$
2450000.Combiningthecashflowfromthehedgewiththecashflowfromtheloanresultsinanetoutflowof$2325000whichtranslatesintoanannualrateof
9.3percent:=$2325000x4/$100000000=
0.093ThisispreciselytheimpliedborrowingratethatJohnsonlockedinonSeptember
20.RegardlessoftheLIBORrateonDecember20thenetcashoutflowwillbe$2325000whichtranslatesintoanannualizedrateof
9.3percent.ConsequentlythefloatingrateliabilityhasbeenconvertedtoafixedrateliabilityinthesensethattheinterestrateuncertaintyassociatedwiththeMarch20paymentusingtheDecember20contracthasbeenremovedasofSeptember
20.InastriphedgeJohnsonwouldsell100DecemberfuturesfortheMarchpayment100MarchfuturesfortheJunepaymentand100JunefuturesfortheSeptemberpayment.Theobjectiveistohedgeeachinterestratepaymentseparatelyusingtheappropriatenumberofcontracts.TheproblemisthesameasinPartAexceptherethreecashflowsaresubjecttorisingratesandastripoffuturesisusedtohedgethisinterestraterisk.Thisproblemissimplifiedsomewhatbecausethecashflowmismatchbetweenthefuturesandtheloanpaymentisignored.ThereforeinordertohedgeeachcashflowJohnsonsimplysells100contractsforeachpayment.Thestriphedgetransformsthefloatingrateloanintoastripoffixedratepayments.AswasdoneinPartAthefixedratesarefoundbyadding200basispointstotheimpliedforwardLIBORrateindicatedbythediscountyieldofthethreedifferentEurodollarfuturescontracts.ThefixedpaymentswillbeequalwhentheLIBORtermstructureisflatforthefirstyear.
7.JacobBowerhasaliabilitythat:hasaprincipalbalanceof$100milliononJune301998accruesinterestquarterlystartingonJune301998paysinterestquarterlyhasaone-yeartermtomaturityandcalculatesinterestduebasedon90-dayLIBORtheLondonInterbankOfferedRate.Bowerwishestohedgehisremaininginterestpaymentsagainstchangesininterestrates.Bowerhascorrectlycalculatedthatheneedstosellshort300Eurodollarfuturescontractstoaccomplishthehedge.Heisconsideringthealternativehedgingstrategiesoutlinedinthefollowingtable.InitialPosition6/30/98in90-DayLIBOREurodollarContractsExplainwhystrategyBisamoreeffectivehedgethanstrategyAwhentheyieldcurveundergoesaninstantaneousnonparallelshift.DiscussaninterestratescenarioinwhichstrategyAwouldbesuperiortostrategyB.CFAGuidelineAnswerStrategyBsSuperiorityStrategyBisastriphedgethatisconstructedbysellingshorting100futurescontractsmaturingineachofthenextthreequarters.Withthestriphedgeinplaceeachquarterofthecomingyearishedgedagainstshiftsininterestratesforthatquarter.ThereasonStrategyBwillbeamoreeffectivehedgethanStrategyAforJacobBoweristhatStrategyBislikelytoworkwellwhetheraparallelshiftoranonparallelshiftoccursovertheone-yeartermofBowersliability.ThatisregardlessofwhathappenstothetermstructureStrategyBstructuresthefutureshedgesothattheratesreflectedbytheEurodollarfuturescashpricematchtheapplicableratesfortheunderlyingliability-the90dayLIBOR-basedrateonBowersliability.ThesameisnottrueforStrategyA.BecauseJacobBowersliabilitycarriesafloatinginterestratethatresetsquarterlyheneedsastrategythatprovidesaseriesofthree-monthhedges.StrategyAwillneedtoberestructuredwhenthethreemonthSeptembercontractexpires.InparticulariftheyieldcurvetwistsupwardfuturesyieldsrisemorefordistantexpirationsthanfornearexpirationsStrategyAwillproduceinferiorhedgeresults.ScenarioinWhichStrategyAisSuperiorStrategyAisastackhedgestrategythatinitiallyinvolvessellingshorting300Septembercontracts.StrategyAisrarelybetterthanStrategyBasahedgingorrisk-reductionstrategy.OnlyfromtheperspectiveoffavorablecashflowsisStrategyAbetterthanStrategyB.Suchcashflowsoccuronlyincertaininterestratescenarios.ForexampleStrategyAwillworkaswellasStrategyBforBowersliabilityifinterestratesinstantaneouslychangeinparallelfashion.AnotherinterestratescenariowhereStrategyAoutperformsStrategyBisoneinwhichtheyieldcurverisesbutwithatwistsothatfuturesyieldsrisemorefornearexpirationsthanfordistantexpirations.UponexpirationoftheSeptembercontractBowerwillhavetorollouthishedgebyselling200Decembercontractstohedgetheremaininginterestpayments.ThisactionwillhavetheeffectthatthecashflowfromStrategyAwillbelargerthanthecashflowfromStrategyBbecausetheappreciationonthe300shortSeptemberfuturescontractswillbelargerthanthecumulativeappreciationinthe300contractsshortedinStrategyBi.e.100September100Decemberand100March.ConsequentlythecashflowfromStrategyAwillmorethanoffsettheincreaseintheinterestpaymentontheliabilitywhereasthecashflowfromStrategyBwillexactlyoffsettheincreaseintheinterestpaymentontheliability.UsethequotationsinExhibit
7.7tocalculatetheintrinsicvalueandthetimevalueofthe97SeptemberJapaneseyenAmericancallandputoptions.Solution:Premium-IntrinsicValue=TimeValue97SepCall
2.08-Max[
95.80-
97.00=-
1.200]=
2.08centsper100yen97SepPut
2.47-Max[
97.00-
95.80=
1.200]=
1.27centsper100yenAssumespotSwissfrancis$
0.7000andthesix-monthforwardrateis$
0.
6950.Whatistheminimumpricethatasix-monthAmericancalloptionwithastrikingpriceof$
0.6800shouldsellforinarationalmarketAssumetheannualizedsix-monthEurodollarrateis31/2percent.Solution:NotetoInstructor:Acompletesolutiontothisproblemreliesontheboundaryexpressionspresentedinfootnote3ofthetextofChapter
7.CMax[70-
6869.50-68/
1.01750]aMax[
21.470]=2centsDoproblem9againassuminganAmericanputoptioninsteadofacalloption.September201999December201999March202000Borrow$100millionatSeptember20LIBOR+200basispointsbpsSeptember20LIBOR=7%PayinterestforfirstthreemonthsRollloanoveratDecember20LIBOR+200bps•PaybackprincipalplusinterestContractMonthStrategyAcontractsStrategyBcontractsSeptember1998300100December19980100March19990100。