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ch09

CHAPTER9FUTURESANDOPTIONSONFOREIGNEXCHANGE

SUGGESTEDANSWERSANDSOLUTIONSTOEND-OF-CHAPTER

QUESTIONSANDPROBLEMS

QUESTIONS

1.Explainthebasicdifferencesbetweentheoperationofacurrencyforwardmarketandafuturesmarket.

Answer:

TheforwardmarketisanOTCmarketwheretheforwardcontractforpurchaseorsaleofforeigncurrencyistailor-madebetweentheclientanditsinternationalbank.Nomoneychangeshandsuntilthematuritydateofthecontractwhendeliveryandreceiptaretypicallymade.Afuturescontractisanexchange-tradedinstrumentwithstandardizedfeaturesspecifyingcontractsizeanddeliverydate.Futurescontractsaremarked-to-marketdailytoreflectchangesinthesettlementprice.Deliveryisseldommadeinafuturesmarket.Ratherareversingtradeismadetocloseoutalongorshortposition.

2.Inorderforaderivativesmarkettofunction,twotypesofeconomicagentsareneeded:

hedgersandspeculators.Explain.

Answer:

Twotypesofmarketparticipantsarenecessaryfortheoperationofaderivativesmarket:

speculatorsandhedgers.Aspeculatorattemptstoprofitfromachangeinthefuturesprice.Todothis,thespeculatorwilltakealongorshortpositioninafuturescontractdependinguponhisexpectationsoffuturepricemovement.Ahedger,on-the-other-hand,desirestoavoidpricevariationbylockinginapurchasepriceoftheunderlyingassetthroughalongpositioninafuturescontractorasalespricethroughashortposition.Ineffect,thehedgerpassesofftheriskofpricevariationtothespeculatorwhoisbetterable,oratleastmorewilling,tobearthisrisk.

3.Whyaremostfuturespositionsclosedoutthroughareversingtraderatherthanheldtodelivery?

Answer:

Inforwardmarkets,approximately90percentofallcontractsthatareinitiallyestablishedresultintheshortmakingdeliverytothelongoftheassetunderlyingthecontract.Thisisnaturalbecausethetermsofforwardcontractsaretailormadebetweenthelongandshort.Bycontrast,onlyaboutonepercentofcurrencyfuturescontractsresultindelivery.Whilefuturescontractsareusefulforspeculationandhedging,theirstandardizeddeliverydatesmakethemunlikelytocorrespondtotheactualfuturedateswhenforeignexchangetransactionswilloccur.Thus,theyaregenerallyclosedoutinareversingtrade.Infact,thecommissionthatbuyersandsellerspaytotransactinthefuturesmarketisasingleamountthatcoverstheround-triptransactionsofinitiatingandclosingouttheposition.

4.HowcantheFXfuturesmarketbeusedforpricediscovery?

Answer:

TotheextentthatFXforwardpricesareanunbiasedpredictoroffuturespotexchangerates,themarketanticipateswhetheronecurrencywillappreciateordepreciateversusanother.BecauseFXfuturescontractstradeinanexpirationcycle,differentcontractsexpireatdifferentperiodicdatesintothefuture.Thepatternofthepricesofthesecontractsprovidesinformationastothemarket’scurrentbeliefabouttherelativefuturevalueofonecurrencyversusanotheratthescheduledexpirationdatesofthecontracts.Onewillgenerallyseeasteadilyappreciatingordepreciatingpattern;however,itmaybemixedattimes.Thus,thefuturesmarketisusefulforpricediscovery,i.e.,obtainingthemarket’sforecastofthespotexchangerateatdifferentfuturedates.

5.Whatisthemajordifferenceintheobligationofonewithalongpositioninafutures（orforward）contractincomparisontoanoptionscontract?

Answer:

Afutures（orforward）contractisavehicleforbuyingorsellingastatedamountofforeignexchangeatastatedpriceperunitataspecifiedtimeinthefuture.Ifthelongholdsthecontracttothedeliverydate,hepaystheeffectivecontractualfutures（orforward）price,regardlessofwhetheritisanadvantageouspriceincomparisontothespotpriceatthedeliverydate.Bycontrast,anoptionisacontractgivingthelongtherighttobuyorsellagivenquantityofanassetataspecifiedpriceatsometimeinthefuture,butnotenforcinganyobligationonhimifthespotpriceismorefavorablethantheexerciseprice.Becausetheoptionownerdoesnothavetoexercisetheoptionifitistohisdisadvantage,theoptionhasaprice,orpremium,whereasnopriceispaidatinceptiontoenterintoafutures（orforward）contract.

6.Whatismeantbytheterminologythatanoptionisin-,at-,orout-of-the-money?

Answer:

Acall（put）optionwithSt>E（E>St）isreferredtoastradingin-the-money.IfStEtheoptionistradingat-the-money.IfSt

7.Listthearguments（variables）ofwhichanFXcallorputoptionmodelpriceisafunction.Howdoesthecallandputpremiumchangewithrespecttoachangeinthearguments?

Answer:

Bothcallandputoptionsarefunctionsofonlysixvariables:

St,E,ri,r$,Tand.Whenallelseremainsthesame,thepriceofaEuropeanFXcall（put）optionwillincrease:

1.thelarger（smaller）isS,

2.thesmaller（larger）isE,

3.thesmaller（larger）isri,

4.thelarger（smaller）isr$,

5.thelarger（smaller）r$isrelativetori,and

6.thegreateris.

Whenr$andriarenottoomuchdifferentinsize,aEuropeanFXcallandputwillincreaseinpricewhentheoptionterm-to-maturityincreases.However,whenr$isverymuchlargerthanri,aEuropeanFXcallwillincreaseinprice,buttheputpremiumwilldecrease,whentheoptionterm-to-maturityincreases.Theoppositeistruewhenriisverymuchgreaterthanr$.ForAmericanFXoptionstheanalysisislesscomplicated.SincealongertermAmericanoptioncanbeexercisedonanydatethatashortertermoptioncanbeexercised,orasomelaterdate,itfollowsthattheallelseremainingthesame,thelongertermAmericanoptionwillsellatapriceatleastaslargeastheshortertermoption.

PROBLEMS

1.Assumetoday’ssettlementpriceonaCMEEURfuturescontractis$0.9716/EUR.Youhaveashortpositioninonecontract.Yourmarginaccountcurrentlyhasabalanceof$1,700.Thenextthreedays’settlementpricesare$0.9702,$0.9709,and$0.9625.Calculatethechangesinthemarginaccountfromdailymarking-to-marketandthebalanceofthemarginaccountafterthethirdday.

Solution:

$1,700+[（$0.9716-$0.9702）+（$0.9702-$0.9709）

+（$0.9709-$0.9625）]xEUR125,000=$2,837.50,

whereEUR125,000isthecontractualsizeofoneEURcontract.

2.Doproblem1againassumingyouhavealongpositioninthefuturescontract.

Solution:

$1,700+[（$0.9702-$0.9716）+（$0.9709-$0.9702）+（$0.9625-$0.9709）]xEUR125,000=$562.50,

whereEUR125,000isthecontractualsizeofoneEURcontract.

Withonly$562.50inyourmarginaccount,youwouldexperienceamargincallrequestingthatadditionalcashbeaddedtothemarginaccounttobringitbackuptotheinitialmarginlevel.

3.UsingthequotationsinExhibit9.3,calculatethefacevalueoftheopeninterestintheDecember2002Swissfrancfuturescontract.

Solution:

984contractsxSF125,000=SF123,000,000.

whereSF125,000isthecontractualsizeofoneSFcontract.

4.UsingthequotationsinExhibit9.3,notethattheDecember2002Mexicanpesofuturescontracthasapriceof$0.10068.YoubelievethespotpriceinDecemberwillbe$0.11000.Whatspeculativepositionwouldyouenterintotoattempttoprofitfromyourbeliefs?

Calculateyouranticipatedprofits,assumingyoutakeapositioninthreecontracts.Whatisthesizeofyourprofit（loss）ifthefuturespriceisindeedanunbiasedpredictorofthefuturespotpriceandthispricematerializes?

Solution:

IfyouexpecttheMexicanpesotorisefrom$0.10068to$0.11000,youwouldtakealongpositioninfuturessincethefuturespriceof$0.10068islessthanyourexpectedspotprice.

Youranticipatedprofitfromalongpositioninthreecontractsis:

3x（$0.11000-$0.10068）xMP500,000=$13,980.00,whereMP500,000isthecontractualsizeofoneMPcontract.

Ifthefuturespriceisanunbiasedpredictoroftheexpectedspotprice,theexpectedspotpriceisthefuturespriceof$0.10068/MP.Ifthisspotpricematerializes,youwillnothaveanyprofitsorlossesfromyourshortpositioninthreefuturescontracts:

3x（$0.10068-$0.10068）xMP500,000=0.

5.Doproblem4againassumingyoubelievetheDecember2002spotpricewillbe$0.08500.

Solution:

IfyouexpecttheMexicanpesotodepreciatefrom$0.10068to$0.08500,youwouldtakeashortpositioninfuturessincethefuturespriceof$0.10068isgreaterthanyourexpectedspotprice.

Youranticipatedprofitfromashortpositioninthreecontractsis:

3x（$0.10068-$0.08500）xMP500,000=$23,520.00.

Ifthefuturespriceisanunbiasedpredictorofthefuturespotpriceandthispricematerializes,youwillnotprofitorlosefromyourlongfuturesposition.

6.Recalltheforwardrateagreement（FRA）exampleinChapter6.ShowhowthebankcanalternativelyuseapositioninEurodollarfuturescontractstohedgetheinterestrateriskcreatedbythematuritymismatchithaswiththe$3,000,000six-monthEurodollardepositandrolloverEurocreditpositionindexedtothree-monthLIBOR.AssumethebankcantakeapositioninEurodollarfuturescontractsmaturinginthreemonths’timethathaveafuturespriceof94.00.

Solution:

Tohedgetheinterestrateriskcreatedbythematuritymismatch,thebankwouldneedtobuy（golong）threeEurodollarfuturescontracts.Ifonthelastdayoftrading,three-monthLIBORis51/8%,thebankwillearnaprofitof$6,562.50fromitsfuturesposition.Thisiscalculatedas:

[94.875-94.00]x100bpx$25x3contracts=$6,562.50.

Notethatthissumdiffersslightlyfromthe$6,550.59profitthatthebankwillearnfromthe