CFA二级-复习冲刺-衍生：Derivative Instruments.docx

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1、BriefIntroductionTopicweight:StudySession1-2Ethics&ProfessionalStandards10%-15%StudySession3QuantitativeAnalysis5%-10%StudySession4Economics5%-10%StudySession5-6FinancialReportingandAnalysis10%-15%StudySession7-8CorporateFinance5%-10%StudySession9-11EquityValuation10%-15%StudySession12-13FixedIncome

2、10%-15%StudySession14DerivativeInvestment5%-10%StudySession15AlternativeInvestment5%-10%StudySession16-17PortfolioManagement5%T5Weights:100%iefIntroductionContent:SS14:DerivativeInvestments:ValuationandStrategiesReading40:PricingandValuationofForwardCommitmentsReading41:ValuationofContingentClaimsRe

3、ading42:DerivativesStrategiesBriefIntroduction学习建议：本门课程难度比较大，计算公式很多，一定要着重理解和总结；知识点之间的类比关系比较强，建议把第一部分学透后,在继续学后面的知识点；可以适当多做一些题，熟悉解题步骤，提高做题速度；最重要的，认真、仔细的听课。ReviewofDerivativesinLevel1Tasks:Reviewthebasicsofderivativeinstrument;Reviewthefundamentalofderivativepricing.ForwardcommitmentContractsenteredint

4、oatonepointintimethatrequirebothpartiestoengageinatransactionatalaterpointintime(theexpiration)ontermsagreeduponatthestart.Forward,future,andswapContingentclaimDerivativesinwhichtheoutcomeorpayoffisdependentontheoutcomeorpayoffofanunderlyingasset.OptionForwardAnover-the-counterderivativecontractinwh

5、ichtwopartiesagreethatoneparty,thebuyer7willpurchaseanunderlyingassetfromtheotherparty,theseller,atalaterdateatafixedprice(forwardprice)theyagreeonwhenthecontractissigned.Inadditiontothe(forward)price,thetwopartiesalsoagreeonseveralothermatters,suchastheidentityandthequantityoftheunderlying.FuturesF

6、uturescontractsarespecializedforwardcontractsthathavebeenstandardizedandtradeonafutureexchange.Futurecontractshavespecificunderlyingassets,timestoexpiration,deliveryandsettlementconditions,andquantities.Theexchangeoffersafacilityintheformofaphysicallocationand/oranelectronicsystemaswellasliquiditypr

7、ovidedbyauthorizedmarketmakers.SwapAnover-the-counterderivativecontractinwhichtwopartiesagreetoexchangeaseriesofcashflowswherebyonepartypaysavariableseriesthatwillbedeterminedbyanunderlyingassetorrateandtheotherpartypayseither(1)avariableseriesdeterminedbyadifferentunderlyingassetorrateor(2)afixedse

8、ries.Aswapisaseriesof(off-market)forwards.PriceofforwardcommitmentThefixedpriceorrateatwhichtheunderlyingwillbepurchasedatalaterdate.Generallymaynotchangeasthe(expected)priceoftheunderlyingassetchanges.ValueofforwardcommitmentThedifferenceofz,withthepositionfromwithouttheposition.Mayincreaseordecrea

9、seasthe(expected)priceoftheunderlyingassetchanges.OptionAderivativecontractinwhichoneparty,thebuyer,paysasumofmoneytotheotherparty,thesellerorwriter,andreceivestherighttoeitherbuyorsellanunderlyingassetatafixedpriceeitheronaspecificexpirationdateoratanytimepriortotheexpirationdate.Anoptionisaright,b

10、utnotanobligation.Defaultinoptionsispossibleonlyfromtheshorttothelong.Option(Cont.)Optionpremium(cPP匕paymenttosellerfrombuyer.Calloption:righttobuy.Putoption:righttosell.Exerciseprice/strikeprice(X):thefixedpriceatwhichtheunderlyingassetcanbepurchased.Americanoption:exercisableatorpriortoexpiration.

11、Europeanoption:exercisableonlyatexpiration.ArbitrageArbitrageisatypeOftransactionundertakenwhentwoassetsorportfoliosproduceidenticalresultsbutsellfordifferentprices.1.awofoneprice:Assetsthatproduceidenticalfuturecashflowsregardlessoffutureeventsshouldhavethesameprice;Traderwillexploitthearbitrageopp

12、ortunityquickly(buylowandsellhigh),thenmakethepricesconverge.ReplicationCreationofanassetorportfoliofromanotherasset,portfolio,and/orderivative.Anassetandahedgingpositionofderivativeontheassetcanbecombinedtoproduceapositionequivalenttoarisk-freeasset.Asset+Derivative=Risk-freeassetAsset-Risk-freeass

13、et=-DerivativeDerivative-Risk-freeasset=-AssetA-signindicatesashortposition,orborrowingatRf.NoarbitragepricingDeterminethepriceofaderivativebyassumingthattherearenoarbitrageopportunities(noarbitragepricing).Thederivativepricecanthenbeinferredfromthecharacteristicsoftheunderlyingandthederivative,andt

14、herisk-freerate.09-APeaHPricingandValuationofForwardContractTasks:Describehowforwardcontractsispricedandvalued;Calculateandinterprettheno-arbitragevalueofforwardcontract.PricingandValuationofForwardContractPricingofforwardIftheunderlyingassetgeneratesnoperiodiccashflowztheforwardpricecanbecalculated

15、asfollows:F0(T)=S0(l+r)Sspotprice;r:riskfreerate.PricingandValuationofForwardContractCarryarbitragemodelWhentheforwardcontractisoverpriced,F(J)Sy.+r)T,Cash-and-CarryArbitrageisavailable:Atinitiation,borrowingmoneyS前risk-freerate,buying(long)thespotasset,andselling(short)theforwardatF0(T);Initialinve

16、stmentatinitiation:$0;Atexpiration,settlingtheshortpositiononforwardcontractbydeliveringtheasset.Profitatexpiration:F0(T)-S0(l+r).PricingandValuationofForwardContractCarryarbitragemodelWhenforwardcontractisunderpriced,F)SQ+r)rReverseCash-and-CarryArbitrageisavailable:Atinitiation,borrowingandselling

17、(short)thespotasset,investingtheproceedS0atrisk-freerate,andbuying(long)theforwardatFo(T).Initialinvestmentatinitiation:$0;Atexpiration,payingFg)tosettlethelongpositiononforwardcontract,anddeliveringthespotassettoclosetheshortpositiononspotasset.Profitatexpiration:S0(l+r)-F0(T).PricingandValuationof

18、ForwardContractPricingofforwardIftheunderlyingassetgeneratesperiodiccashflow,theforwardpricecanbecalculatedas:FO(T)=(SO-V+6)(l+r):benefitofcarryingthespotasset,inpresentvalueform;:costofcarryingthespotasset,inpresentvalueform;-:netcostofcarry.andValuationofForwardContractValuationofforwardInthefinan

19、cialworld,wegenerallydefinevalueasthevaluetothelongposition.Atinitiation,theforwardcontracthaszerovalue.Neitherpartytoaforwardtransactionpaystoenterthecontractatinitiation.VO(T)=0PricingandValuationofForwardContractValuationofforward(Cont.)Duringitslife(trol-zl-TTLF(7)andSrequotedbydirectquotation:D

20、C/FC;Rcinterestrateofdomesticcurrency;RFUntereStrateofforeigncurrency.Forcontinuouslycompoundedrisk-freerate:F0(T)=S0(rc-RFcf?IJ嚏l)2.(I)xSH(I)L:IBPPUnodEO(JOM-F?-H)LL.gH吉)XfaABP9n8qu3uP-IBMoJ-O-ro二一peMAouxmoOUo4e-三e三e三u3=n31Ea三su三Sels-SIIllE=IIaHdPricingandValuationofEquityandCurrencyForwardExampleA

21、corporationsoldEUro()againstBritishpound()forwardataforwardrateof0.8for1atTimeO.ThecurrentspotmarketatTimetissuchthat1isworth0.75,andtheannuallycompoundedrisk-freeratesare0.80%fortheBritishpoundand0.40%fortheEuro.AssumeatTimettherearethreemonthsuntiltheforwardcontractexpiration.Calculatetheforwardpr

22、iceFt(/,T)atTimetandthevalueofforeignexchangeforwardcontractatTimet.andValuationofEquityandCurrencyForwardAnswer: + Ft(T) = StX :I /0.75 II 1 + 0.8 l.Il + 0.4% /0.7507TheforwardpriceF(fgT)atTimet:ThevalueofforeignexchangeforwardcontractatTimet:V (T)=-tt(1+Rjt0.75Fo(T)(iRoc)t0.8(1 0.4%)025 (1 0.8%)0-

23、25= 0.0499Importance:Content:Pricingandvaluationofequityforward;Pricingandvaluationofcurrencyforward.amtips:常考点：计算题。PricingandValuationofFRATasks:Describehowinterestrateforwardcontractsispricedandvalued;Calculateandinterprettheno-arbitragevalueofinterestrateforwardcontract.PricingandValuationofFRAFo

24、rwardrateagreement(FRA)AFRAisanover-the-counter(OTC)forwardcontractinwhichtheunderlyingisaninterestrate(e.g.Libor).1.ongpositioncanbeviewedastheobligationtotakealoanatthecontractrate(i.e.,borrowatthefixedrate,floatingreceiver);gainswhenreferencerateincrease;Shortpositioncanbeviewedastheobligationtom

25、akealoanatthecontractrate(i.e.,lendatthefixedrate,fixedreceiver);gainswhenreferenceratedecrease.-ThenotationofFRAThenotationofFRAistypicallyabFRA:a:thenumberofmonthsuntilthecontractexpires;b:thenumberofmonthsuntiltheunderlyingloanissettled.Example:39FRA39FRAToday9 months(b)3months(a)PricingandValuat

26、ionofFRATheusesofFRA1.ocktheinterestrateorhedgetheriskofborrowingorlendingatsomefuturedate.Onepartywillpaytheotherpartythedifference(basedonnotionalvalue)betweentheinterestratespecifiedintheFRAandthemarketinterestrateatcontractsettlement.Ifforwardratespotrate,theshortreceivespayment.PricingandValuat

27、ionofFRAPricingofFRATheforwardpricewinFRAisactuallyaforwardrate,itcanbecalculatedfromthespotrates.FRArateisjusttheunbiasedestimateoftheforwardrate;RecalltheforwardratemodelinFixedIncomeLevel2;Butweusesimpleinterestformoneymarketinstrument.Note:Liborratesareadd-onrateandquotedona30/360daybasisinannua

28、lterms.PricingofFRA(Cont.)Forwardratemodelsshowhowforwardratescanbeextrapolatedfromspotrates.1SbxX30b5360IIS30a360xhFRx3baI3601o30xbbb3600I1Q30aS*,360a30xbx1FR360abIPricingandValuationofFRAExampleBasedonmarketquotesonCanadiandollar(C$)Liborzthesix-monthC$Liborandthenine-monthC$Liborarepresentlyat1.5

29、%and1.75%,respectively.Assumea30/360-daycountconvention.Calculatethe69FRAfixedrate.Solution:1+(1.5%180/360)1+(FRArate90/360)=1+(1.75%270/360)So,FRArate二2.22%PricingandValuationofFRAValuationofFRAatexpiration(t=a)Althoughtheinterestontheunderlyingloancomesattheendoftheloan,theFRAissettledattheexpirat

30、ionofFRA.FOrabFRA，theinterestsavingwduetotheFRApositioncomesatTimeb,butissettledatTimea;SotheinterestsavingneedtobediscountedtoTimeatocalculatethevalueofFRA.NPX(Underlyingrate-Forwardrate)xIfvI360I1Underlyingrate,I360/-Example:14FRASpecificationof14FRA:Term=30daysNotionalamount=$1millionUnderlyingra

31、te=90-dayLIBORForwardrate=7%Att=30days,90-dayLIBOR=8%,clarifythepayment(value)ofthisFRA.Solution:14FRAUnderlyingfloatingratefixedrate,solongpositionreceivespayment.loT30,120I11ForwardExpiryofFRA;Interestsaving:rate:7%90-dayLibor:8%(8%-7%)X90/360X$lm二$2,500Payment=$2,450.98DiscountatLIBORfor90days$2,

32、500/(1+(8%x90/360)PricingandValuationofFRAExampleIn30days,aUKcompanyexpectstomakeabankdepositof10Mforaperiodof90daysat90-dayLiborset30daysfromtoday.Thecompanyisconcernedaboutadecreaseininterestrates.Itsfinancialadvisersuggeststhatitnegotiatetoday,atTime0,a14FRA,aninstrumentthatexpiresin30daysandisba

33、sedon90-dayLibor.Thecompanyentersintoa10Mnotionalamount14receive-fixedFRAthatisadvancedSeLadvancedsettled.PricingandValuationofFRAExample(Cont.)After30days,90-dayLiborinBritishpoundsis0.55%.IftheFRAwasinitiallypricedat0.60%,thepaymentreceivedbytheUKcompanytosettleitwillbeclosestto?Solution:Becauseth

34、eUKcompanyreceivesfixedintheFRA7itbenefitsfromadeclineinrates.10M(0.006-0.0055)0.25l+0.00550.25=1248.28ValuationofFRApriortoexpiration(ta)Step1:calculatethenewFRArate(FR);1SbtbtISJtX1FRaL?IdIStep2:calculatethevalueofFRAas:atobDaysfromttobInitiationdateEvaluationdateFRAexpiresUnderlyingmaturesPricing

35、andValuationofFRAExampleWeenteredalong69FRAatarateof0.86%,withnotionalamountofC$10M.The6-monthspotC$Liborwas0.628%,and9-monthC$Liborwas0.712%.After90dayshavepassed,the3-monthC$Liboris1.25%andthe6-monthC$Liboris1.35%.Calculatethevalueofthereceivefloating69FRA.Answer:Step1:1+(1.25%90/360)1+(newFRArate

36、X90/360)=1+(1.35%180/360)So,newFRArate=1.46%Step2:Vt=IOM(1.46%-0.86%)0.25/(1+1.35%180/360)=14900Importance:Content:PricingandvaluationofFRA.Examtips:常考点：FRAVaIUe的计算。I。IUol-l-roPUEP8dS-SLlUOJPBMOJEO0Mojqc3Sea:s*selemj23033XH-O0s三三e置3MdPricingandvaluationoffixedincomeforwardSimilartoequityforward,theforwardpriceoffixedincomeforwardcanbecalculatedas:F0(T)=(S0-PVC0)(l+r)or:F0(T)=S0X(lr)-FVCPVC:presentvalueofexpectedcouponpayment;FVC:futurevalueofexpectedcouponpayment.Thevalueoffixedinco