期权 期货以及其他衍生品(3)

Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.1InterestRateMarketsChapter5Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.2TypesofRates•Treasuryrates•LIBORrates•ReporatesOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.3ZeroRatesAzerorate(orspotrate),formaturityTistherateofinterestearnedonaninvestmentthatprovidesapayoffonlyattimeTOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.4Example(Table5.1,page95)Maturity(years)ZeroRate(%contcomp)0.55.01.05.81.56.42.06.8Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.5BondPricing•Tocalculatethecashpriceofabondwediscounteachcashflowattheappropriatezerorate•Inourexample,thetheoreticalpriceofatwo-yearbondprovidinga6%couponsemiannuallyis333103983900505005810006415006820eeee.........Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.6BondYield•Thebondyieldisthediscountratethatmakesthepresentvalueofthecashflowsonthebondequaltothemarketpriceofthebond•Supposethatthemarketpriceofthebondinourexampleequalsitstheoreticalpriceof98.39•Thebondyieldisgivenbysolvingtogety=0.0676or6.76%.333103983905101520eeeeyyyy.....Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.7ParYield•Theparyieldforacertainmaturityisthecouponratethatcausesthebondpricetoequalitsfacevalue.•Inourexamplewesolveg)compoundins.a.(with876getto10021002220.2068.05.1064.00.1058.05.005.0.c=ececececOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.8ParYieldcontinuedIngeneralifmisthenumberofcouponpaymentsperyear,disthepresentvalueof$1receivedatmaturityandAisthepresentvalueofanannuityof$1oneachcoupondateAmdc)100100(Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.9SampleDataforDeterminingtheZeroCurve(Table5.2,page97)BondTimetoAnnualBondPrincipalMaturityCouponPrice(dollars)(years)(dollars)(dollars)1000.25097.51000.50094.91001.00090.01001.50896.01002.0012101.6Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.10TheBootstrappingtheZeroCurve•Anamount2.5canbeearnedon97.5during3months.•The3-monthrateis4times2.5/97.5or10.256%withquarterlycompounding•Thisis10.127%withcontinuouscompounding•Similarlythe6monthand1yearratesare10.469%and10.536%withcontinuouscompoundingOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.11TheBootstrapMethodcontinued•Tocalculatethe1.5yearratewesolvetogetR=0.10681or10.681%•Similarlythetwo-yearrateis10.808%96104445.10.110536.05.010469.0ReeeOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.12ZeroCurveCalculatedfromtheData(Figure5.1,page98)910111200.511.522.5ZeroRate(%)Maturity(yrs)10.12710.46910.53610.68110.808Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.13ForwardRatesTheforwardrateisthefuturezerorateimpliedbytoday’stermstructureofinterestratesOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.14CalculationofForwardRatesTable5.4,page98ZeroRateforForwardRateann-yearInvestmentfornthYearYear(n)(%perannum)(%perannum)110.0210.511.0310.811.4411.011.6511.111.5Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.15FormulaforForwardRates•SupposethatthezeroratesformaturitiesT1andT2areR1andR2withbothratescontinuouslycompounded.•TheforwardratefortheperiodbetweentimesT1andT2isRTRTTT221121Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.16InstantaneousForwardRate•TheinstantaneousforwardrateforamaturityTistheforwardratethatappliesforaveryshorttimeperiodstartingatT.ItiswhereRistheT-yearrateRTRTOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.17UpwardvsDownwardSlopingYieldCurve•Foranupwardslopingyieldcurve:FwdRateZeroRateParYield•ForadownwardslopingyieldcurveParYieldZeroRateFwdRateOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.18ForwardRateAgreement•Aforwardrateagreement(FRA)isanagreementthatacertainratewillapplytoacertainprincipalduringacertainfuturetimeperiodOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.19ForwardRateAgreementcontinued(Page100)•AnFRAisequivalenttoanagreementwhereinterestatapredeterminedrate,RKisexchangedforinterestatthemarketrate•AnFRAcanbevaluedbyassumingthattheforwardinterestrateiscertaintoberealizedOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.20TheoriesoftheTermStructurePages102•ExpectationsTheory:forwardratesequalexpectedfuturezerorates•MarketSegmentation:short,mediumandlongratesdeterminedindependentlyofeachother•LiquidityPreferenceTheory:forwardrateshigherthanexpectedfuturezeroratesOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.21DayCountConventionsintheU.S.(Pages102-103)TreasuryBonds:CorporateBonds:MoneyMarketInstruments:Actual/Actual(inperiod)30/360Actual/360Options,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.22TreasuryBondPriceQuotesintheU.SCashprice=Quotedprice+AccruedInterestOptions,Futures,andOtherDerivatives,5thedition©2002byJohnC.Hull5.23TreasuryBillQuoteintheU.S.IfYisthecashpriceofaTreas