第四章-JOHN-HULL-期权与期货市场基本原理第七版

FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 InterestRates Chapter4 1 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 TypesofRates TreasuryratesLIBORratesReporates 2 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 MeasuringInterestRates ThecompoundingfrequencyusedforaninterestrateistheunitofmeasurementThedifferencebetweenquarterlyandannualcompoundingisanalogoustothedifferencebetweenmilesandkilometers 3 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ContinuousCompounding Page83 Inthelimitaswecompoundmoreandmorefrequentlyweobtaincontinuouslycompoundedinterestrates 100growsto 100eRTwheninvestedatacontinuouslycompoundedrateRfortimeT 100receivedattimeTdiscountsto 100e RTattimezerowhenthecontinuouslycompoundeddiscountrateisR 4 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ConversionFormulas Page83 DefineRc continuouslycompoundedrateRm sameratewithcompoundingmtimesperyear 5 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ZeroRates Azerorate orspotrate formaturityTistherateofinterestearnedonaninvestmentthatprovidesapayoffonlyattimeT 6 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 Example Table4 2 page85 7 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 BondPricing TocalculatethecashpriceofabondwediscounteachcashflowattheappropriatezerorateInourexample thetheoreticalpriceofatwo yearbondprovidinga6 couponsemiannuallyis 8 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 BondYield ThebondyieldisthediscountratethatmakesthepresentvalueofthecashflowsonthebondequaltothemarketpriceofthebondSupposethatthemarketpriceofthebondinourexampleequalsitstheoreticalpriceof98 39Thebondyieldisgivenbysolvingtogety 0 0676or6 76 p 9 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ParYield Theparyieldforacertainmaturityisthecouponratethatcausesthebondpricetoequalitsfacevalue Inourexamplewesolve 10 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ParYieldcontinued Ingeneralifmisthenumberofcouponpaymentsperyear Pisthepresentvalueof 1receivedatmaturityandAisthepresentvalueofanannuityof 1oneachcoupondate 11 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 SampleData Table4 3 page86 Bond Timeto Annual Bond Principal Maturity Coupon Price dollars years dollars dollars 100 0 25 0 97 5 100 0 50 0 94 9 100 1 00 0 90 0 100 1 50 8 96 0 100 2 00 12 101 6 12 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 TheBootstrapMethod Anamount2 5canbeearnedon97 5during3months The3 monthrateis4times2 5 97 5or10 256 withquarterlycompoundingThisis10 127 withcontinuouscompoundingSimilarlythe6monthand1yearratesare10 469 and10 536 withcontinuouscompounding 13 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 TheBootstrapMethodcontinued Tocalculatethe1 5yearratewesolvetogetR 0 10681or10 681 Similarlythetwo yearrateis10 808 14 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ZeroCurveCalculatedfromtheData Figure4 1 page88 ZeroRate Maturity yrs 10 127 10 469 10 536 10 681 10 808 15 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ForwardRates Theforwardrateisthefuturezerorateimpliedbytoday stermstructureofinterestrates 16 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 CalculationofForwardRatesTable4 5 page89 ZeroRatefor ForwardRate an n yearInvestment for n thYear Year n perannum perannum 1 3 0 2 4 0 5 0 3 4 6 5 8 4 5 0 6 2 5 5 3 6 5 17 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 FormulaforForwardRates SupposethatthezeroratesfortimeperiodsT1andT2areR1andR2withbothratescontinuouslycompounded TheforwardratefortheperiodbetweentimesT1andT2is 18 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 UpwardvsDownwardSlopingYieldCurve Foranupwardslopingyieldcurve FwdRate ZeroRate ParYieldForadownwardslopingyieldcurveParYield ZeroRate FwdRate 19 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ForwardRateAgreement Aforwardrateagreement FRA isanagreementthatacertainratewillapplytoacertainprincipalduringacertainfuturetimeperiod 20 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 ForwardRateAgreementcontinued AnFRAisequivalenttoanagreementwhereinterestatapredeterminedrate RKisexchangedforinterestatthemarketrateAnFRAcanbevaluedbyassumingthattheforwardinterestrateiscertaintoberealized 21 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 FRAExample Acompanyhasagreedthatitwillreceive4 on 100millionfor3monthsstartingin3yearsTheforwardratefortheperiodbetween3and3 25yearsis3 Thevalueofthecontracttothecompanyis 250 000discountedfromtime3 25yearstotimezero 22 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 FRAExampleContinued Supposerateprovestobe4 5 withquarterlycompoundingThepayoffis 125 000atthe3 25yearpointThisisequivalenttoapayoffof 123 609atthe3 yearpoint 23 FundamentalsofFuturesandOptionsMarkets 7thEd Ch4 Copyright JohnC Hull2010 TheoriesoftheTermStructurePage93 ExpectationsTheory forwardratesequalexpectedfuturezeroratesMarketSegmentation short mediumandlongratesdeterminedindependentlyofeachotherLiquidityPreferenceTheory forwardrateshigherthanexpectedfuture