赫尔《期权、期货及其他衍生产品》（第8版）复习笔记及课后习题详解 (87).docx

EXTRAPROBLEMSNewto8thEdition1. InJuly,asmallchocolatefactoryreceivesalargeorderforchocolatebarstobedeliveredinNovember.ThespotpriceforCocoais$2,400permetricton.Itwillneed10metrictonsofCocoainSeptembertofillthisorder.Becauseoflimitedstoragecapacityandvolatilityintheworldcocoaprices,thecompanydecidesthebeststrategyistobuy10calloptionsfor$53eachwithstrikepriceof$2,400(equaltothecurrentprice)withamaturitydateofSeptember2012.WhentheoptionsexpireinSeptember,howmuchwillthecompanypay(includingthecostoftheoptions)forcocoaifthespotpriceinSeptemberprovestobe:a)$2,300,andb)$2,600?($23,530,$24,530)2. AtraderinvestsinFacebookbybuying1000sharesinJunefor$27pershare.Shealsobuys1000putoptionsfor$5eachasinsuranceincasethestockdropssharply.Theputoptionshaveastrikepriceof$27andamaturitydateofDecember.WhatisthegainorlossifthespotpriceonDecemberis:a)$20,b)$27,c)$32andd)$37?($5,000loss,$5,000loss,$0,$5,000gain)3. ThespotpriceforGooglestockis$578onJune6.Atraderconsiderstwoalternatives:buy100sharesofthestock,orbuy100EuropeancalloptionsonGooglefor$38eachwithastrikepriceof$575andmaturitydateofSeptember2012.Foreachalternative,whatis:a)theupfrontcost?b)thetotalgainifthestockpriceatmaturityis$650?c)thetotallossifthestockpriceis$500atmaturity?($57,800and$3,800;$7,200and$3,700;-S7,800and-$3,800)4. Atradertakesthelongpositionandahedgefundtakesashortpositiononten1-monthS&P500futurescontractsat1300.AsingleS&P500futurescontractequals($250)x(IndexValue).Theinitialmarginis$325,000andthemaintenancemarginis$245,000forbothaccounts.Tentradingdayslater,thefuturespriceoftheindexdropsto1,260triggeringamargincallforthetrader.Whatisthechangemarginaccountbalance(indicategainorloss)for:a)thetraderandb)thehedgefund?Whatisthemargincallforthetrader?(trader:$100,000loss,hedgefund:$100,000gain,margincall:$100,000)5. AspeculatorsellsaJuly2013wheatfuturescontractat721centsperbushel.Eachfuturescontractisfor5,000bushels.Thefuturespricedropsto676onDecember31,2012andrisesto712inMay2013whensheclosesthecontract.Whatisthegainorlossforaccountingpurposesin2013?($180,000loss)6. InDecember2011,acompanyexpectstobuy100,000MMBtuofnaturalgasbeforetheendofMarch2012,butdoesnotknowexactlywhen.Tohedgeagainstvolatilegasprices,itimplementsarollingforwardhedgebytakingalongpositionon10twomonthnaturalgasfutures(onlyheldfor1month).Onefuturescontractisfor10,000MMBtuandisquotedin$perMMBtu.ThecommodityispurchasedinMarch2012.Whatistotaldollargain/lossfromtherollinghedge?Assumeahedgeratioof0.8.($84,000loss)DateDec2011Jan2012Feb2012Mar2012Feb2012FuturesPrice3.653.00-Mar2012FuturesPrice-2.952.70-Apr2012FuturesPrice-2.652.50SpotPrice3.672.507. Atraderowns55,000troyOZofsilveranddecidestohedgewith6-monthsilverfuturescontracts.Eachfuturescontractison5,000troyoz.Thestandarddeviationofthechangeinthespotpriceofsilveris0.43.Thestandarddeviationofthechangeinsilverfuturespricesis0.40.Thecoefficientofcorrelationbetweenthetwois0.95.a. Whatistheminimumvariancehedgeratio?b. Whatistheoptimalnumberoffuturescontractswithouttailingthehedge?c. Whatistheoptimalnumberoffuturescontractswithtailingthehedge?(1.02J1.23,12.08)8. Foraninterestratecompoundedannuallyof7%,whatistheequivalentinterestratecompounded:(6.88%,6.82%,6.78%,6.77%,6.77%)a. Semi-annuallyb. Quarterlyc. Monthlyd. Weeklye. Daily9. Giventhezeroratesandcashflowsforabond(seetablebelow):a.Whatisthetheoreticalprice?($986.23)b.Whatisthebondyield?(3.19%)Maturity(Years)TreasuryZeroRates(%)CouponPaymentsPrincipal0.52.0%$10-1.02.3%$15-1.52.7%$10-2.03.2%$15$100010. Astockprovidesadividendyieldof5.0%paidsemi-annually(equivalentto4.94%continuouslycompounded).Thespotpriceofthestockiscurrently$500,andtherisk-freerateis7.5%withcontinuouscompounding.a. Whatisthetwo-yearforwardpriceforastock?($526.27)b. Whatisthecontinuouslycompoundedcostofcarryforthestock?(2.56%)11. AUSinvestorseesanarbitrageopportunityinthecurrencymarkets.ThespotexchangeratebetweentheSwissFrancandUSDollaris1.0404($perCHF).AssumethecontinuouslycompoundedinterestratesintheUSandSwitzerlandare0.25%and0%,respectively.The3-monthcurrencyforwardpriceis1.0300($perCHF).Whatisthetheoreticallycorrectforwardprice.Whatistheinvestor,stotalprofit(inCHF),assumingshebeginsbyborrowing1,000CHF?(1.04105,10.73)12. ContinuouslycompoundedLIBORratesperannumfor6,12,and18-monthsaregiveninthetablebelow.The2-yearswaprateis3%perannumwithpaymentsmadesemi-annually.Whatisthe2-yearLIBOR/swapzeroratefor2years?UseLIBORdiscounting(2.99%)Maturity(Years)LIBOR/SwapZeroRates(%)0.52.0%1.02.4%1.52.6%2.0?13. Consideracurrencyswapwith3yearsremaining.Afinancialinstitutionreceives3.0%perannuminsterling(GBP)andpays1.5%perannumindollarsonceayear.TheLIBOR/swapinterestratewithcontinuouscompoundingisflatinbothcountries.TheBritishrateis2.5%perannumandtheUSrateis2.0%perannum.Theprincipalamountsare£10millionpoundsand$15milliondollars,andthecurrentexchangerateis$1.5=£1.Byvaluingthecurrencyswapasfixed-ratebonds,whatis:a. Thevalueofthedollarbondin$?($14.78Million)b. Thevalueofthesterlingbondin£?(£10.13Million)c. Thevalueofthecurrencyswapin$?($0.4255Million)a. GiventheABS&ABSCDOshown,whatistheminimumlossontheportfolioofunderlyingassetswhenb. 1.owertwoABStrancheshavea100%lossofprincipal?(30%)c. SeniorABStranchea50%haslossofprincipal?(65%)d. EquityABSCDOtranchehasa100%lossofprincipal?(6.25%)e. MezzanineABSCDOtranchehasa100%lossofprincipal?(12.5%)f. SeniorABSCDOtranchehasa50%lossofprincipal?(21.25%)g. SeniorABSCDOtranchehasa100%lossofprincipal?(30%)14. Aninvestorbuys5calloptioncontracts,eachon100shareswithastrikeof60.Thereisa6-for-5stocksplit.Givethefollowing:a. Thenewstrikeprice(50)b. Thenewnumberofsharesunderlyingthe5contracts(600)15. ThepriceofaEuropeancallandputonastockare$2and$5,respectively.Bothhaveastrikepriceof$45andanexpirationdateof6months.Thecurrentpriceoftheunderlyingnon-dividend-payingstockis$40?Whatistheimpliedrisk-freeinterestrate?(9.09%)16. Aninvestorcreatesabutterflyspreadbytrading9-monthcalloptionswithstrikepricesof$115,$125,and$135.Thepricesoftheoptionsare$20.50,$14.50,and$9.50,respectively.(Note:Totalpayoffdoesnotincludeinitialinvestment)a. Whatistheinitialinvestment?($1paidout)b. Whatisthetotalpayoffwhenthestockpricein9monthsis110?($0)c. Whatisthetotalpayoffwhenthestockpricein9monthsis120?($5)d. Whatisthetotalpayoffwhenthestockpricein9monthsis125?($10)e. Whatisthetotalpayoffwhenthestockpricein9monthsis128?($7)f. Whatisthetotalpayoffwhenthestockpricein9monthsis140?($0)17. A1-yearoptionisofferedonanon-dividend-payingstock.Thestockpriceis$85.Theexercisepriceoftheoptionis$90andthevolatilityis18%perannum.Thecontinuouslycompoundedrisk-freerateis6%perannum.WhentheBlack-Scholes-Mertonmodelisuseda. Whatisthevalueofdi?(0.106)b. Whatisthevalueofd2?(-0.074)c. Whatisthepriceofacalloption,c?($6.21)d. Whatisthepriceofaputoption,p?($5.97)Now,assumethatthestockpaysadividendafter3-monthsand9-monthsof$1.50.e. Whatisthepresentvalueofthedividends?($2.91)f. Whatisthenewvalueofdwithdividends(-0.088)g. Whatisthenewvalueofchwithdividends(-0.268)h. Whatisthevalueofacalloption?($4.74)18. Discusstheprosandconsofexecutivestockoptionsversuspayingexecutivesdirectlywithstock.19. Atwo-stepbinomialtreeisusedtovalueanoptionontheAustraliandollar.Thestrikepriceis1.00USDperAUDandtheexpirationdateisin6months.Eachstepis3months.ThecurrentpriceofoneAUDis1.04USD.TheUSriskfreerateis2.0%,andtheAUDrisk-freerateis2.5%.Theexchangeratehasavolatilityof6%perannum.a. Whatistheproportionalupmovement,u,forthecurrency(1.0305)b. Whatistheprobabilityofanupmovement,p?(0.4717)c. WhatisthepriceofanAmericancalloptiononthecurrency?($0.0427)20. Thespotpriceofanindexis250.Thedividendyieldontheindexis3%perannum.Theriskfreerateis4%.Ifpriceofa3-monthEuropeancalloptionis$16whenthestrikepriceis240,whatistheimpliedvolatilityperannum?(20.4%)21. UseBlack,smodeltovalueaEuropeanputoptiononthespotpriceofacommoditywhenthestrikepriceis$30andtheexpirationisin12months.Thecurrentfuturespriceofcommodityforacontractlasting12monthsis$35.Theriskfreerateis5%perannumandthevolatilityis25%.($1.26)22. Atraderdecidestohedgeherportfolioagainstlargemarketmovesbytakingpositionsintheunderlyingassetandtwooptions(seetablebelow).a. Howmanyunitsofoptions1and2,respectively,areneededtomaketheportfoliogammaandveganeutral?(300,-25)b. Howmanyunitsoftheunderlyingassetareneededtomakethehedgedportfoliodeltaneutral(indicatelong/shortposition)?(11long)DeltaGammaVegaPortfolio0.50-1000-500Option1-0.03102.5Option20.10801023. Atraderdecidestoprotectherportfoliowithaputoption.Theportfolioisworth$150millionandtherequiredputoptionhasastrikepriceof$145millionwithamaturityof24weeks.Thevolatilityoftheportfoliois15%andthedividendyieldontheportfoliois3%perannum.Therisk-freerateis4%.Becausetheoptionisnotavailableonexchanges,thetraderdecidestocreateanoptionbymaintainingapositionintheunderlyingportfoliowiththerequireddelta.Whatpercentageoftheoriginalportfolioshouldbesoldandinvestedattherisk-freerate:a. Initiallyattimezero?(sell32.9%)b. Afteroneweek,whenvalueis$145million?(sellanadditional12.7%)c. Aftertwoweekswhenvalueis$148million?(buyback7.99%)24. ACox-Ross-RubinsteinbinomialtreeisusedtovalueanoptionontheDowJonesIndustrialAverage(DJIA)index.Thedividendyieldis3%perannum,theindexvolatilityis14%perannum,thetimestepis2months,andtherisk-freeinterestrateis5%perannum.Whatistheprobabilityofanupmove?(0.5149)