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

BriefIntroductionTopicweight:StudySession1-2Ethics&ProfessionalStandards10%-15%StudySession3QuantitativeAnalysis5%-10%StudySession4Economics5%-10%StudySession5-6FinancialReportingandAnalysis10%-15%StudySession7-8CorporateFinance5%-10%StudySession9-11EquityValuation10%-15%StudySession12-13FixedIncome10%-15%StudySession14DerivativeInvestment5%-10%StudySession15AlternativeInvestment5%-10%StudySession16-17PortfolioManagement5%T5¾>Weights:100%iefIntroductionContent:SS14:DerivativeInvestments:ValuationandStrategiesReading40:PricingandValuationofForwardCommitmentsReading41:ValuationofContingentClaimsReading42: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.ForwardcommitmentContractsenteredintoatonepointintimethatrequirebothpartiestoengageinatransactionatalaterpointintime(theexpiration)ontermsagreeduponatthestart.Forward,future,andswapContingentclaimDerivativesinwhichtheoutcomeorpayoffisdependentontheoutcomeorpayoffofanunderlyingasset.OptionForwardAnover-the-counterderivativecontractinwhichtwopartiesagreethatoneparty,thebuyer7willpurchaseanunderlyingassetfromtheotherparty,theseller,atalaterdateatafixedprice(forwardprice)theyagreeonwhenthecontractissigned.Inadditiontothe(forward)price,thetwopartiesalsoagreeonseveralothermatters,suchastheidentityandthequantityoftheunderlying.FuturesFuturescontractsarespecializedforwardcontractsthathavebeenstandardizedandtradeonafutureexchange.Futurecontractshavespecificunderlyingassets,timestoexpiration,deliveryandsettlementconditions,andquantities.Theexchangeoffersafacilityintheformofaphysicallocationand/oranelectronicsystemaswellasliquidityprovidedbyauthorizedmarketmakers.SwapAnover-the-counterderivativecontractinwhichtwopartiesagreetoexchangeaseriesofcashflowswherebyonepartypaysavariableseriesthatwillbedeterminedbyanunderlyingassetorrateandtheotherpartypayseither(1)avariableseriesdeterminedbyadifferentunderlyingassetorrateor(2)afixedseries.Aswapisaseriesof(off-market)forwards.PriceofforwardcommitmentThefixedpriceorrateatwhichtheunderlyingwillbepurchasedatalaterdate.Generallymaynotchangeasthe(expected)priceoftheunderlyingassetchanges.ValueofforwardcommitmentThedifferenceofz,withtheposition"from"withouttheposition".Mayincreaseordecreaseasthe(expected)priceoftheunderlyingassetchanges.OptionAderivativecontractinwhichoneparty,thebuyer,paysasumofmoneytotheotherparty,thesellerorwriter,andreceivestherighttoeitherbuyorsellanunderlyingassetatafixedpriceeitheronaspecificexpirationdateoratanytimepriortotheexpirationdate.Anoptionisaright,butnotanobligation.Defaultinoptionsispossibleonlyfromtheshorttothelong.Option(Cont.)Optionpremium(cPP匕paymenttosellerfrombuyer.Calloption:righttobuy.Putoption:righttosell.Exerciseprice/strikeprice(X):thefixedpriceatwhichtheunderlyingassetcanbepurchased.Americanoption:exercisableatorpriortoexpiration.Europeanoption:exercisableonlyatexpiration.ArbitrageArbitrageisatypeOftransactionundertakenwhentwoassetsorportfoliosproduceidenticalresultsbutsellfordifferentprices.1.awofoneprice:Assetsthatproduceidenticalfuturecashflowsregardlessoffutureeventsshouldhavethesameprice;Traderwillexploitthearbitrageopportunityquickly(buylowandsellhigh),thenmakethepricesconverge.ReplicationCreationofanassetorportfoliofromanotherasset,portfolio,and/orderivative.Anassetandahedgingpositionofderivativeontheassetcanbecombinedtoproduceapositionequivalenttoarisk-freeasset.Asset+Derivative=Risk-freeassetAsset-Risk-freeasset=-DerivativeDerivative-Risk-freeasset=-AssetA"-signindicatesashortposition,orborrowingatRf.NoarbitragepricingDeterminethepriceofaderivativebyassumingthattherearenoarbitrageopportunities(noarbitragepricing).Thederivativepricecanthenbeinferredfromthecharacteristicsoftheunderlyingandthederivative,andtherisk-freerate.09-APeaHPricingandValuationofForwardContractTasks:Describehowforwardcontractsispricedandvalued;Calculateandinterprettheno-arbitragevalueofforwardcontract.PricingandValuationofForwardContractPricingofforwardIftheunderlyingassetgeneratesnoperiodiccashflowztheforwardpricecanbecalculatedasfollows: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);Initialinvestmentatinitiation:$0;Atexpiration,settlingtheshortpositiononforwardcontractbydeliveringtheasset.Profitatexpiration:F0(T)-S0(l+r).PricingandValuationofForwardContractCarryarbitragemodelWhenforwardcontractisunderpriced,F«)<SQ+r)rReverseCash-and-CarryArbitrageisavailable:Atinitiation,borrowingandselling(short)thespotasset,investingtheproceedS0atrisk-freerate,andbuying(long)theforwardatFo(T).Initialinvestmentatinitiation:$0;Atexpiration,payingFg)tosettlethelongpositiononforwardcontract,anddeliveringthespotassettoclosetheshortpositiononspotasset.Profitatexpiration:S0(l+r)-F0(T).PricingandValuationofForwardContractPricingofforwardIftheunderlyingassetgeneratesperiodiccashflow,theforwardpricecanbecalculatedas:FO(T)=(SO-V+6)(l+r):benefitofcarryingthespotasset,inpresentvalueform;:costofcarryingthespotasset,inpresentvalueform;-:netcostofcarry.andValuationofForwardContractValuationofforwardInthefinancialworld,wegenerallydefinevalueasthevaluetothelongposition.Atinitiation,theforwardcontracthaszerovalue.Neitherpartytoaforwardtransactionpaystoenterthecontractatinitiation.VO(T)=0PricingandValuationofForwardContractValuationofforward(Cont.)Duringitslife(t<T),thevalueofaforwardcontractis:Vt(T)=(St-Vt+4)-Fo(T)(Nrg):tpresentvalueofthecostofholdinganasset(ttoT);Y:tpresentvalueofthebenefitofholdinganasset(ttoT);Atexpiration,thevalueofaforwardcontractis:VT(T)=SLF0(T)PricingandValuationofForwardContractExampleAssumethatatTime0weenteredintoaone-yearforwardcontractwithpriceF0(T)=105.Ninemonthslater,atTimet=0.75,theobservedpriceofthestockisS075=110andtheinterestrateis5%.Calculatethevalueoftheexistingforwardcontractexpiringinthreemonths.Solution:Vt(T)=St-F0(T)(l+r)-(-t)=110-105(l+5%)'025=6.273Importance:Content:Pricingandvaluationofforwardcontractonunderlyingwith/withoutcashflows.×amtips:是fowardpricingandvaluation的一般形式，对后面的学习非常重要，但考试一般都是靠后面具体的forwardContractotjraIUo3PBMOJAUUSJnOPUBAI5bJo->rol-zl-<olllljdjlu-PUB一n2-O3n-BAPUBo-SloejlcogpBMjoJu113pu3Al三bM0jO-OQ:s*sel三MJSSistt三E3三0uses-sss置'-£andValuationofEquityForwardPricingandvaluationofequityforwardIftheunderlyingisastockandhasdiscretedividends,thenforwardpricecanbecalculatedas:F0(T)=(S0-PVD0)×(l+r)or:Fo(T)=So×(l+r)-FVDPVD:presentvalueofexpecteddividends;FVD:futurevalueofexpecteddividends.Thevalueofequityforwardcanbecalculatedas:Vt(T)=(SrPVDt)-F0(T)(l+r)-(-t)ExampleSupposeNestlestockistradingforCHF70andpaysaCHF2.20dividendinonemonth.Further,assumetheSwissone-monthrisk-freerateis1.0%,quotedonanannualcompoundingbasis.Assumethatthestockgoesex-dividendthesamedaythesinglestockforwardcontractexpires.Thus,thesinglestockforwardcontractexpiresinonemonth.Calculatetheone-monthforwardpriceforNestlestock.Solution:1F0(T)=S0×1+r-FVDr=70x(1+0.01)12-2.2=67.86ExampleSupposeweboughtaone-yearforwardcontractat102andtherearenowthreemonthstoexpiration.Theunderlyingiscurrentlytradingfor110zandinterestratesare5%onanannualcompoundingbasis.Iftherearenoothercarrycashflows,calculatetheforwardvalueoftheexistingcontract.Solution:-T_tVtT=(St-PVDt)-FT1+r°-025=110-102×1+0.05=9.24PricingandvaluationofequityindexforwardForequityindex,theforwardpriceisusuallycalculatedasifthedividendsarepaidcontinuously:F0(T)=S0xe(Rf-cfRc;continuouslycompoundedrisk-freerate;c:continuouslycompoundeddividendyield.Thevalueofequityindexforwardcanbecalculatedas:Vf(T)=St×e-(-t)-F0(T)×e-R-t)andValuationofEquityForwardExampleThecontinuouslycompoundeddividendyieldontheEUROSTOXX50is3%,andthecurrentstockindexlevelis3,500.Thecontinuouslycompoundedannualinterestrateis0.15%.Calculatethethreemonthforwardprice.Solution:F=SoXe(R'C)"350OXe(U5%3%)Xo253475.150PricingandValuationofCurrencyForwardPricingofcurrencyforwardThepriceofcurrencyforwardcanbecalculatedbycoveredinterestrateparity(IRP):L+K、t1.CDCFO(T)=S°>TTLF(7)andS©requotedbydirectquotation:DC/FC;Rcinterestrateofdomesticcurrency;RFUntereStrateofforeigncurrency.Forcontinuouslycompoundedrisk-freerate:F0(T)=S0×(rc-RFcf?IJ嚏×l)2.(I)xSH(I)L:IBPPUnodEO(JOM-F?-H)×LL.g££H吉)XfaABP9n8qu3uP-IBMoJ-O-ro>二一peM£AouxmoOUo4e-三e>三e三u3=n31Ea三su三Sels-SIIllE=IIaHdPricingandValuationofEquityandCurrencyForwardExampleAcorporationsoldEUro()againstBritishpound(£)forwardataforwardrateof£0.8for1atTimeO.ThecurrentspotmarketatTimetissuchthat1isworth£0.75,andtheannuallycompoundedrisk-freeratesare0.80%fortheBritishpoundand0.40%fortheEuro.AssumeatTimettherearethreemonthsuntiltheforwardcontractexpiration.CalculatetheforwardpriceFt(£/,T)atTimetandthevalueofforeignexchangeforwardcontractatTimet.andValuationofEquityandCurrencyForward®Answer: + 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)(i÷Roc)'t0.8(1 0.4%)025 (1 0.8%)0-25= £0.0499Importance:Content:Pricingandvaluationofequityforward;Pricingandvaluationofcurrencyforward.×amtips:常考点：计算题。PricingandValuationofFRATasks:Describehowinterestrateforwardcontractsispricedandvalued;Calculateandinterprettheno-arbitragevalueofinterestrateforwardcontract.PricingandValuationofFRAForwardrateagreement(FRA)AFRAisanover-the-counter(OTC)forwardcontractinwhichtheunderlyingisaninterestrate(e.g.Libor).1.ongpositioncanbeviewedastheobligationtotakealoanatthecontractrate(i.e.,borrowatthefixedrate,floatingreceiver);gainswhenreferencerateincrease;Shortpositioncanbeviewedastheobligationtomakealoanatthecontractrate(i.e.,lendatthefixedrate,fixedreceiver);gainswhenreferenceratedecrease.-ThenotationofFRAThenotationofFRAistypically"a×bFRA":a:thenumberofmonthsuntilthecontractexpires;b:thenumberofmonthsuntiltheunderlyingloanissettled.Example:3×9FRA3×9FRAToday9 months(b)3months(a)PricingandValuationofFRATheusesofFRA1.ocktheinterestrateorhedgetheriskofborrowingorlendingatsomefuturedate.Onepartywillpaytheotherpartythedifference(basedonnotionalvalue)betweentheinterestratespecifiedintheFRAandthemarketinterestrateatcontractsettlement.Ifforwardrate<spotrate,thelongreceivespayment;Ifforwardrate>spotrate,theshortreceivespayment.PricingandValuationofFRAPricingofFRAThe"forwardpricewinFRAisactuallyaforwardrate,itcanbecalculatedfromthespotrates.FRArateisjusttheunbiasedestimateoftheforwardrate;Recalltheforwardratemodelin"FixedIncomeLevel2"Butweusesimpleinterestformoneymarketinstrument.Note:Liborratesareadd-onrateandquotedona30/360daybasisinannualterms.PricingofFRA(Cont.)Forwardratemodelsshowhowforwardratescanbeextrapolatedfromspotrates.1SbxX30b5360IIS30a360xhFRx3°×baI3601o30xbbb3600I1Q30×aS*,360a30xbx1FR360abIPricingandValuationofFRAExampleBasedonmarketquotesonCanadiandollar(C$)Liborzthesix-monthC$Liborandthenine-monthC$Liborarepresentlyat1.5%and1.75%,respectively.Assumea30/360-daycountconvention.Calculatethe6×9FRAfixedrate.Solution:1+(1.5%×180/360)×1+(FRArate×90/360)=1+(1.75%×270/360)So,FRArate二2.22%PricingandValuationofFRAValuationofFRAatexpiration(t=a)Althoughtheinterestontheunderlyingloancomesattheendoftheloan,theFRAissettledattheexpirationofFRA.FOr"a×bFRA，the"interestsavingwduetotheFRApositioncomesat"Timeb",butissettledat"Timea"Sothe"interestsaving"needtobediscountedto"TimeatocalculatethevalueofFRA.NPX(Underlyingrate-Forwardrate)xIfvI360I1Underlyingrate×,I360/-Example:1×4FRASpecificationof1×4FRA:Term=30daysNotionalamount=$1millionUnderlyingrate=90-dayLIBORForwardrate=7%Att=30days,90-dayLIBOR=8%,clarifythepayment(value)ofthisFRA.Solution:1×4FRAUnderlyingfloatingrate>fixedrate,solongpositionreceivespayment.loT30,120I11ForwardExpiryofFRA;Interestsaving:rate:7%90-dayLibor:8%(8%-7%)X90/360X$lm二$2,500Payment=$2,450.98DiscountatLIBORfor90days$2,500/(1+(8%x90/360)PricingandValuationofFRAExampleIn30days,aUKcompanyexpectstomakeabankdepositof£10Mforaperiodof90daysat90-dayLiborset30daysfromtoday.Thecompanyisconcernedaboutadecreaseininterestrates.Itsfinancialadvisersuggeststhatitnegotiatetoday,atTime0,a1×4FRA,aninstrumentthatexpiresin30daysandisbasedon90-dayLibor.Thecompanyentersintoa£10Mnotionalamount1×4receive-fixedFRAthatisadvancedSeLadvancedsettled.PricingandValuationofFRAExample(Cont.)After30days,90-dayLiborinBritishpoundsis0.55%.IftheFRAwasinitiallypricedat0.60%,thepaymentreceivedbytheUKcompanytosettleitwillbeclosestto?Solution:BecausetheUKcompanyreceivesfixedintheFRA7itbenefitsfromadeclineinrates.10M×(0.006-0.0055)×0.25l+0.0055×0.25=£1248.28ValuationofFRApriortoexpiration(t<a)Step1:calculatethenewFRArate(FR);1SbtbtISJtX1FRaL?IdIStep2:calculatethevalueofFRAas:atobDaysfromttobInitiationdateEvaluationdateFRAexpiresUnderlyingmaturesPricingandValuationofFRAExampleWeenteredalong6×9FRAatarateof0.86%,withnotionalamountofC$10M.The6-monthspotC$Liborwas0.628%,and9-monthC$Liborwas0.712%.After90dayshavepassed,the3-monthC$Liboris1.25%andthe6-monthC$Liboris1.35%.Calculatethevalueofthereceivefloating6×9FRA.Answer:Step1:1+(1.25%×90/360)×1+(newFRArateX90/360)=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。IUo<JpBMOJE0P×JJo->l-l-ro<o七dwPUB一nS>PUEP8dS-SLlUOJPBMOJEO0×Mojq'c3Sea:s*selemj23033XH-O0s三>三e置3MdPricingandvaluationoffixedincomeforwardSimilartoequityforward,theforwardpriceoffixedincomeforwardcanbecalculatedas:F0(T)=(S0-PVC0)×(l+r)or:F0(T)=S0X(l÷r)-FVCPVC:presentvalueofexpectedcouponpayment;FVC:futurevalueofexpectedcouponpayment.Thevalueoffixedinco