CFA二级-复习冲刺-固收-2019：Fixed income

FixedIncomeLevel2--2019Instructor:IntroductionStudySession1-2StudySession3&10-15%5-10%5-10%StudySession4StudySession5-6StudySession7-8StudySession9-11StudySession12-13StudySession14StudySession15StudySession16-17FinancialandAnalysis10-15%FinanceIncome5-10%10-15%10-15%5-10%5-10%5-15%100%Introduction➢StudySession12:Concepts✓34:TheStructureandDynamics✓35:TheIntroduction➢StudySession13:inIncomeAnalysis✓36:andAnalysis:BondswithEmbeddedOptions✓37:AnalysisModels✓38:Introduction:➢与2018年相比，年的考纲变化不大。✓37中，“oflossloss,andofthelossanddescribetheimportanceofeachthecreditspectrum”微调为“thelosstheprobabilityofandthe”；Introduction:✓37中，新增“theofabondanditsassumptionsabouttherisk”。Introduction:➢本门课程难度比较大，要着重理解和总结；➢逻辑递进关系比较强，要把每个知识点学懂了再继续学；➢听课与做题相结合，但并不建议“刷题”；➢最重要的，认真、仔细的听课。ForwardModels&ForwardPricingModels➢Describeamongspotandandtheshapeoftheyieldcurve;➢Describethepricingandmodels,andandspotpricesandusingthosemodels.ForwardRateModels&ForwardPricingModelsSpot➢Theofonasecurityasingleaintime(a.k.aort=0t=jt=j+kS(j)$1[1+S(j)]j✓S(j):spottimej.➢Spotcurve:theofspottheofthespotForwardRateModels&ForwardPricingModels➢istheofasingle-securitybeissuedafuturet=0t=jt=j+kf(j,k)$1[1+f(j,k)]k✓f(j,k):k-yeartimej.➢curve:theoftheoftheForwardRateModels&ForwardPricingModelsmodels➢modelscanbespotj+k()jk+(+)=++()1Sjk1S1fj,kj[1+S(j+k)]j+kt=0t=jt=j+k[1+S(j)]j[1+f(j,kForwardRateModels&ForwardPricingModels➢Thespotbondswithmaturitiesofone,and9%,10%and11%.theaone-yearissuedAnswer:(1+0.11)3=(1+0.10)×[1+f(2,1)]f(2,1)=13.03%ForwardRateModels&ForwardPricingModelsSpotcurvevs.curve➢Ifyieldcurvessloping,curvesliethespotcurve.✓Thetheinitiationthehigherthecurve.curvesJul.31,2013ForwardRateModels&ForwardPricingModelsSpotcurvevs.curve➢Ifyieldcurvessloping,curvesliebelowthespotcurve.✓Thetheinitiationthethecurves.curvesDec.31,2006ForwardRateModels&ForwardPricingModels➢Thepriceofasingle-unittimej:1P()=jj1+S()jt=0P(j)t=j$1t=j+kS(j)ForwardRateModels&ForwardPricingModelsprice➢Thepricetimejabondwithj+kandunitprincipal.1F(j,k)=k1+f(j,k)t=0t=jt=j+k$1f(j,k)F(j,k)ForwardRateModels&ForwardPricingModelspricingmodels➢Thepricingmodeldescribestheof()Pj+k()()Pj+k=PFj,k()Fj,k=jPjP(j+k)t=0t=jt=j+kP(j)F(j,k)ForwardRateModels&ForwardPricingModels➢Considera2-yearloanbeginningin1The1-yearspotis7%andthe3-yearspotis9%.thepriceofa2-yearbondbeissuedin1F(1,2)=0.7722÷0.9346=0.8262.Summary➢Importance:☆☆☆➢•Spot&•Spotcurveandcurve;•models&pricingmodels.➢tips:•常考点：两个模型的运用，计算题;•常考点：curve和forwardcurve的相对位置，概念题。Yieldand➢DescribeamongYTM,andonbonds;➢Describe➢Explaincurveandspread;➢DescribeZ-spread,TEDandLibor–OISspreads.YieldandSpread(YTM)➢Theofonthecashofabond.PMTFnP=+t(1+YTM)t(1+YTM)nt=1✓isthesameasthespotbonds;✓couponbonds,ifthespotcurveisnottheYTMwillnotbethesameasthespot✓issomeofspotYieldandSpread➢criticalassumptionsYTM:✓Theholdthebondmaturity;✓Theissuerfullandtimelycouponandprincipal•Thebondisoption-freeandisnorisk.✓TheisablecouponYTM.YieldandSpread➢Expectedtheabondholderearn.✓TheYTMistheonlyifallthecriticalassumptions➢istheactualonthebondduringthetimeanholdsthebond.✓Itisbasedonactualandtheyieldcurvetheendoftheholdingperiod.YieldandSpread➢Usingtheoutputofoneastheinputof✓Spotbetheparcurve.•istheYTMofabondpar;•curveistheofpartheofparYieldandSpread➢IftheYTMsannualbondsparwithmaturityof12and31%,1.25%,and1.5%theand3-spotYieldandSpread➢1:S=1%;1➢2:the2-yearbondusingspot100=1.25/(1+1%)+101.25/(1+S)22=>S=1.252%;2➢3:the3-yearbondusingspot100=1.5/(1+1%)+1.5/(1+1.252%)+101.5/(1+S)33=>S=1.51%.3YieldandSpreadcurve➢thethelegofan➢curvecurve):theyieldcurveofYieldandSpreadcurve➢thecurvethanspotcurveinbondbecause:✓theriskofthan✓Thenotbywhichincountries✓Thecurvetypicallyhasyieldquotesmaturities.YieldandSpread➢Theamountwhichthetheofthe-the-run”securitywiththesame✓=-security✓Liborcurveisthewidelyusedyieldcurvebecauseittheriskofcommercialbanks.YieldandSpread➢Theneedbeaddedtheimpliedspotcurvesothecashofabondequalitsprice.CFCFCFnPrice=+++121+S+Z1+S+Z)(++)n21SZ12nYieldandSpreadTED➢TheofLibortheyieldonaT-billwith✓TEDisanofcreditriskinthe•Anincrease/decreaseintheTEDisasigntheriskofonloansisincreasing/decreasing.YieldandSpread➢TheofLiborthe(OIS)✓AnOISisanwhichtheperiodicfloatingisequalthegeometricofanoftheperiod.✓Consideredanoftheriskandliquidityofmoneysecurities.Summary➢Importance:☆☆➢•YTM,and••curveand•Z-spread,TEDandLibor–OISspreads.➢tips:•常考点：spreads的定义，概念题。➢Explaintraditionaltheoriesoftheof➢Describetheimplicationsofeachtheoryandtheshapeoftheyieldcurve.StructureTheoriesof➢theunderlyingeconomictheshapeoftheyieldcurve.✓theory✓LocalExpectationsTheory✓Liquiditytheory✓theory✓theoryStructureTheories➢Thistheorysuggeststheisanunbiasedofthespot✓Underlyingassumption:risk•Thisassumptionisasignificantshortcoming.✓UnderthisbondsofmaturityoneStructureTheories➢Undertheunbiasedtheory:✓Ifyieldcurveissloping,short-termrise;✓Ifyieldcurveissloping,short-term✓Ifyieldcurveisshort-termStructureTheories➢Thistheoryassumerisk-neutralityonlyintheshortwhileuncertaintyinthelong✓Underthisthebondshorttimeperiodsthesame.•Butitobservedshort-holding-periodonbondsdothoseonbonds.StructureTheories➢Thistheoryassertsliquiditytheaddedrisktheywhenlendinglong✓=spot+liquidity•Liquiditypremiumincreasewith✓anofunchangingshort-termspotthistheorypredictsanupward-slopingyieldcurve.StructureTheories➢Underthiseachmaturitycanbethoughtofasainwhichyieldbysupplyofanddemandloan,andindependenttheyieldsothersegments.✓withaasset/liabilitymanagement✓notaofspotorliquidityStructureTheories➢Similarthebutiftheisenough,willtheirmaturitiesor✓isnotdirectlymaturity;✓BasedonthenotionwillacceptadditionalriskinadditionalSummary➢Importance:☆☆☆➢•5theories.➢tips:•常考点：五种理论的辨识和比较，概念题。termstructuremodels➢Describemodernmodelsandtheyused.ModernStructureModels➢precisedescriptionsof✓Equilibriummodels•Themodel•TheModel✓models•TheHo-LeeModelModernStructureModels➢Describethedynamicsoftheusingfundamentaleconomicassumed✓Canbeormodels.ModernStructureModels➢Inthemodelingimposedtheofequilibriumpricesbondsandoptions.✓thespecificationofadriftandtheassumptionofafunctional.ModernStructureModels(CIR)➢CIRmodelisbasedontheideaindividualshis/heroptimalbetweenconsumptionandandconsumingatime.✓Higher→→supply→andvice✓willaequilibriumwhichnooneneedsorlend.ModernStructureModelsCIR➢theCIRmodelisas()dr=ab-rdt+σrdzWhere:✓dr:asmallchangeinshort-term✓dt:asmallincreaseintime;✓dz:ansmallinaModernStructureModelsCIRmodel✓b:long-runoftheshort-term✓r:theshort-term✓a:aspeedofmeanandthethe✓σ:ModernStructureModelsCIR➢TheCIRmodelof()✓Driftab-rdt;whichmeanstheislong(b)withspeed(a),alsonamed✓σrdz;alsonamedr•inthe(r)be,andhigherwillleadhigher.ModernStructureModels➢SimilartheCIRmodel,themodelmean()dr=ab-rdt+σdz✓ofmodel:•Doesnotbe•remainstheperiodanalysis.ModernStructureModels➢Thismodelsassumebondsinthepriced➢Themodelingdeterminesthesuchthebondstheirprices.ModernStructureModels➢Themodelassumestheyieldcurveinaiswithano-arbitragecondition.dr=θdt+σdzttt✓θ:atime-dependentdriftSummary➢Importance:☆➢•3modernmodels.➢tips:•不是考试重点。Portfolio➢Describetheofridingtheyieldcurve;➢Explaintheofyieldcurverisk;➢ExplainthematurityofyieldandtheironpriceActiveBondPortfolioManagement➢Ifspotactuallyasimpliedthecurve,theofbondsofvaryingasameperiodthesame.j()jk+1+Sj+k()1+S=j()k1+fj,k✓Ifspotisf(j,k),Sisthesame.jActiveBondPortfolioManagement➢Assumeone-yearspot(S)is9%and1spot(S)is10%,thentheimpliedf(1,1)2is11.01%.+2110%f1,)==11.01%+19%➢Theofone-yearbondtheone-holdingperiodis9%.ActiveBondPortfolioManagement➢Thepriceofabond(P)is:01001+10%P=0=82.642)➢Ifactualone-yearspotoneisf(1,1),thepriceofthebondone(P)is:1100(+.%)11101P=1=90.08ActiveBondPortfolioManagement➢theofbondtheone-yearholdingperiodisalso9%.()−=90.0882.6419%ActiveBondPortfolioManagement➢Ifspotturnoutbeimpliedtheofbondsofvaryingasameperiod✓Ifspotbethebondbeundervalued/overvalued.➢AnmanageroutperformtheifthemanagerpredicthowspotwilltheimpliedActiveBondPortfolioManagementRidingyieldcurve➢Whenayieldcurveisslopingandthetheyieldcurvewillnotchangeitsandshape,thenbuyingbondswithamaturitylongerthantheathantheonamaturity-matching✓Thebondissuccessivelyyieldsandhigherprices,andthensoldahigherActiveBondPortfolioManagement➢Theayieldcurveandthepricesofa3%annual-paycouponbondwith$100parandmaturities.31005152530488.8871.8163.6755.5ActiveBondPortfolioManagement➢Assuminganwithof5purchasethebondwithmaturityof5(maturity-✓Annualcoupon3%;✓Capitalnone.➢Ifthepurchasethebondwithmaturityof30andsellit5(ridingtheyieldcurve):✓Annualcoupon3%;✓Capital$71.81-$63.67=$8.14.ActiveBondPortfolioManagementSummary➢(pricesensitivityYTM)•••Nowell-definedIRR(YTM)•Modified•Money✓➢Curve(pricesensitivitybenchmarkyieldcurve)••shift➢(sensitivityyieldspecificmaturity)ActiveBondPortfolioManagementManagingyieldcurverisk➢curverisk:riskarisingchangesintheyieldcurve.➢Measurementofyieldcurverisk✓✓✓andActiveBondPortfolioManagement➢Measuresthebondpricesensitivityasmallshiftinabenchmarkyieldcurve(△Curve).P-P2(ΔCurve)PEffDur=-+0ActiveBondPortfolioManagement➢Measuresthebondpricesensitivityasmallchangeinabenchmarkyieldcurveaspecificsegment.✓Shapingrisk:bondpricesensitivitychangesintheshapeofthebenchmarkyieldcurve.ActiveBondPortfolioManagementand➢Theyieldcurvecanbedecomposed(ΔX),(ΔX),LSand(ΔX).CActiveBondPortfolioManagementand➢Theproportionalchangeinyieldcurvecanbemodeledas:ΔPP≈-DΔX-DΔX-DΔXCLLSSC✓D,D,andDasthesensitivitiesofLSCsmallchangesintheandActiveBondPortfolioManagementofyield➢Aoftheyieldofabondmaturityof✓short-termthanlong-•Short-termisuncertaintypolicy;•Long-termisuncertaintytheandSummary➢Importance:☆☆➢•spotandofridingtheyieldcurve;•ofyieldcurverisk;•Maturityofyield➢tips:•常考点：Ridingtheyieldcurve策略，概念题。Arbitrage-FreeValuation➢Explainofa➢theofanoption-free,couponbond.Arbitrage-FreeValuationTheofprice➢goodssellthesamepriceintheabsenceof✓Otherwise,buyingtheandsellingthehigherwillearnarisklessandtheprices➢earnrisklesswithoutofArbitrage-FreeValuation➢typesofopportunities:✓additivity:theofthewholeequalsthesumoftheoftheparts.•Stripping:theindividualcashandthemassecurities;•Reconstitution:recombinetheindividualcouponsecuritiesandtheunderlyingbond.✓Dominance:afinancialwitharisk-freeinthefutureapriceArbitrage-FreeValuation➢AnsecuritydeterminessecuritywiththeabsenceofanArbitrage-FreeValuation➢Viewingbondasaofbonds;➢Usingspotcorrespondthematuritiesofthebondsthebondprice.PMTFnP=+t(1+Z)t(1+Z)nt=1tnZ:spotperiodn.n✓Ifpriceiswiththeprice,isanopportunityofadditivityArbitrage-FreeValuation➢Supposetheone-yearspotis2%,thespotis3%,andthethree-yearspotis4%.Then,thepriceofabonda5%annualcouponis:55105()1.04P=++=102.96()1.021()1.0323Summary➢Importance:☆☆➢•opportunitiesand➢tips:•常考点：用rates给债券定价。Binomialinteresttree➢Describeabinomial➢DescribetheofabinomialaspecificBinomialInterestRateBinomial➢Theofbondwithspotisnotbondswithembeddedoption,andneedawithbinomial.✓bondswithembeddedoptions,changesinimpactthetheoptionwillbeandinsodoingimpactthecashBinomialInterestRateBinomial➢Amodelassumesoftime(node)anequalprobabilityofoneofpossibleintheperiod,anupper(U)anda(L).✓Theeachnodeone-periodcorrespondingthenodalperiod.BinomialInterestRateBinomial➢E.g.:inode2thewilloccurifinitialinode0the0node1,andthentheuppernode2.i=ie2σi=ie2σi=ie4σ2,UU✓2,UU•σ:of0BinomialInterestRateBinomial➢Thebinomialisalognormal(lognormalappealing✓of✓higherhigherBinomialInterestRateBinomial➢Whenabinomialrulesbelow:✓Choosetheyieldcurvesothemodelthebenchmarkbonds;✓Adjacentthesameperiod)apart.Summary➢Importance:☆☆➢•andofbinomial➢tips:•一般不直接出题，但是后面重要知识点的基础。ValuingOption-FreeBonds➢Describetheinductionandtheofabond;➢Describeandtheofabond.ValuingOption-freeBonds➢bondperiodtime➢Bondnode:✓ofpossibleperiod;✓Discountistheone-periodnode.ValuingOption-freeBonds➢Usingthetheaannual-paybondwithacouponof7%.018%3%5%ValuingOption-freeBonds➢1:thebondup-node1:1100+7100+7V=+=99.071,U21.081.08012$100$7$99.07$78%$100$73%5%$100$7ValuingOption-freeBonds➢2:thebonddown-node1:1100+7100+7V=+=101.9021.051.05012$100$7$99.07$78%$100$73%$101.9$75%$100$7ValuingOption-freeBonds➢3:thebond0:199.07+7101.90+7V=+=104.35021.031.03012$100$7$99.07$78%$104.353%$100$7$101.9$75%$100$7ValuingOption-freeBonds➢theofabondeachpossibleandtheofthese✓abinomialwithnperiods,willbe2uniquepaths.ValuingOption-freeBonds➢Usingthetheaannual-paybondwithacouponof3%.01210.738%5.778%3.88%7.198%4.825%3%ValuingOption-freeBonds➢1:findalltheaccordingthe13%25.778%5.778%3.88%310.738%7.198%7.198%4.825%12343%3%3%3.88%ValuingOption-freeBonds➢2:thebondeachandtheofthese33✓=++=113%25.778%5.778%3.88%310.738%7.198%7.198%4.825%91.0393.8595.5297.5594.4912343%3%3%3.88%Summary➢Importance:☆☆➢•induction•➢tips:•一般不直接出题，但是后面重要知识点的基础。BondswithEmbedded➢Describesecuritieswithembeddedoptions;➢Explainandshapeoftheyieldcurvetheofcallableorputablebond.BondswithEmbeddedOptionBasicsof➢Embeddedoptionscontingencyinthe✓Callablebonds:theissuerbenefitthebondissueearly;✓Putablebonds:thebondholderbenefithigherputtingbackthebondstheissuer•Extendiblebond:thebondholderthebondanumberofBondswithEmbeddedOptionBasicsof✓put:theofanputthebondbacktheissuerupontheofthe✓Sinkingfundbonds:theissuerasidefundsperiodicallythebond.BondswithEmbeddedOptionBasicsof➢acallablebond,theislongthebondbutshortthecalloptiononthebond.✓=–BondswithEmbeddedOption➢aputablebond,thehasalongpositioninboththebondandtheputoptiononthebond.✓=+BondswithEmbeddedOption➢Theofembeddedoption,ofthetypeofoption,increaseswithThus:✓Asincreases,theofthecallablebonddecreases;•=–✓Asincreases,theoftheputablebondincreases.•=+BondswithEmbeddedOptionofyieldcurvevs.callablebond➢Asdecline,theofthecallablebondriseslessthantheofthebond,limitingtheupsidethe✓Calloptionincreasesasdecline,theriseofthebondispartiallybytheincreaseintheofthecalloption;•theprice-yieldcurveofcallablebond.BondswithEmbeddedOptionofyieldcurvevs.➢Asrise,theoftheputablebondlessthantheofthebond.✓Putoptionincreasesasrise,thedeclineofthebondispartiallybytheincreaseintheoftheputoption;•theprice-yieldcurveofputablebond.BondswithEmbeddedOptionShapeofyieldcurvevs.callablebond➢Astheyieldcurvebeingsloping,sloping,theofthecalloptionincreases,andtheofthecallablebonddecreases.✓Theone-periodbecomeandtheopportunitiescallincrease.BondswithEmbeddedOptionShapeofyieldcurvevs.➢Astheyieldcurvebeingsloping,sloping,theoftheputoptiondecreases,andtheoftheputablebonddecreases.✓Theone-periodbecomeandtheopportunitiesputdeclines.Summary➢Importance:☆☆☆➢•Basictypesofbondswithembeddedoption;•Componentsoftheofbondswithembeddedoption;•onbondwithembeddedoption.➢tips:•常考点：影响含权债券价值的因素，概念题。ValuingBondswithEmbedded➢Describethecanbeusedabondwithembeddedoptions;➢theofacallableorputablebondanValuingBondswithEmbeddedOptionembedded➢Thebasicabondwithembeddedoptionissimilartheofbond;➢the✓Onlybinomialmodelisapplicable,withspotisValuingBondswithEmbeddedOptionembedded✓Needcheckeachnodewhethertheembeddedoptionwillbeornot.•Callrule:theofcallablebondistheofthecallpriceandthepriceifthebondisnotcalled;•Putrule:theofputablebondisthehigheroftheputpriceandthepriceifthebondisnotput.ValuingBondswithEmbeddedOptionof➢Usingthethea7%annual-paybond,whichhasaparof$100andcallable$100theendof1.018%3%5%ValuingBondswithEmbeddedOption➢1:thebondup-node1:✓Callablebond=Min(100,99.07)=$99.07012$100$7$99.07$100$7$100$78%3%5%$100$7ValuingBondswithEmbeddedOption➢2:thebonddown-node1:✓Callablebond=Min(100,101.9)=$100012$100$7$99.07$78%$100$73%$101.9$100$7$100$75%ValuingBondswithEmbeddedOption➢3:thebond0:✓Callablebond=$103.43012$100$7$99.07$78%$103.433%$100$7$100$75%$100$7ValuingBondswithEmbeddedOptionof➢Usingthethea7%annual-paybond,whichhasaparof$100andputable$100theendof1.018%3%5%ValuingBondswithEmbeddedOption➢1:thebondup-node1:✓Putablebond=Max(100,99.07)=$100012$100$7$99.07$100$7$100$78%3%5%$100$7ValuingBondswithEmbeddedOption➢2:thebonddown-node1:✓Putablebond=Min(100,101.9)=$101.9012$100$7$100$78%$100$73%$101.9$100$7$100$75%ValuingBondswithEmbeddedOption➢3:thebond0:✓Putablebond=$104.8012$100$7$100$78%$104.83%$100$7$101.9$75%$100$7Summary➢Importance:☆☆☆➢•Calculationofacallableorputablebondan➢tips:•常考点：利用interestratetree给含权债券定价，概念题或计算题都有可能考到。ValuingBondswithEmbeddedOption➢Explainthecalculationanduseofoption-adjustedspreads;➢Explainoption-spreads.ValuingBondswithEmbeddedOptionrisky➢Z-spreadandoption-adjusted(OAS):✓Z-spread:ayieldaddedspotcurveofbondequalprice.CCC+Par(1+S+Z)nPMarket=++.....+(1+S+Z)(1+S+Z)12n12✓yieldtheinfluenceofembeddedoption.•=-Option(%)ValuingBondswithEmbeddedOptionrisky➢ofZ-spreadand:RatesCorporateBondYieldsZ-spreadOptioncostOASBenchmarkSpotRateCurveMaturityValuingBondswithEmbeddedOptionrisky➢Whenriskybondwiththespotcurve,themodeldoesnotprice(typicallyhigherthanprice).➢Option-adjusted(OAS):thewhenaddedalltheone-periodonthethemodelpriceofthebondequalitsprice.ValuingBondswithEmbeddedOption➢Ifthepriceofcallablebondinthepreviousis$102.71,thewillbe50bps.012$98.62$100$7$100$78%+0.5%$100$7$102.713%+0.5%$101.42$100$75%+0.5%$100$7ValuingBondswithEmbeddedOptionrisky➢isusedasaofthebenchmark.✓Anthanabondthebondis.✓Anthanabondthebondisunderpriced.✓Ancloseabondthebondispriced.ValuingBondswithEmbeddedOption➢Asincreases,calloptionincreases,sothethecallablebonddecreases,andvice✓–calloption=➢Asincreases,putoptionincreases,sothetheputablebondincreases,andvice✓+putoption=➢Z-spreadisValuingBondswithEmbeddedOptionCarlo➢dependency:beinaparticularperioddependsontheitsasasthe✓E.g.:ofMBSisdependent.✓Binomialinductionassumescashnotdependent,itcannotthesecuritieswithsuchcashValuingBondswithEmbeddedOptionCarlo➢Carlosimulationanumberofpaths.✓AoftheCarlomethodistheunderlyingcashcanbedependent.Summary➢Importance:☆☆➢•Calculationandapplicationof••Carlosimulation.➢tips:•常考点：OAS的基本概念与应用，概念题。InterestRiskofBondswithEmbeddedOption➢andofacallableorputablebond;➢Describeone-sidedand➢ofcallable,putable,andbonds.InterestRateRiskofBondswithEmbeddedOption➢Thesensitivityofthepricea100bpsshiftofthebenchmarkyieldcurve,typicallytheparcurve,assumingnochangeinthespread.PV-PV2CurvePV0=-+EffectivedurationInterestRateRiskofBondswithEmbeddedOption➢Thetheand:-+✓1:theimpliedthebenchmarkyieldcurveaccordingtheprice);0✓2:shiftthebenchmarkyieldcurvedown(△Curve),anewandthentheusingthein1;-InterestRateRiskofBondswithEmbeddedOption✓3:shiftbenchmarkyieldcurveup(△Curve),andthewithsimilarmethod;+✓4:theusingtheInterestRateRiskofBondswithEmbeddedOption➢Bothcallandputoptionwillpotentiallythesotheofbothcallableandputablebondwillbelessorequalofbond.InterestRateRiskofBondswithEmbeddedOption➢Theimpactonofbond,butmuchinfluenceonofcallableandputablebonds.✓Decreaseofwilldecreasetheofcallablebond;✓Increaseofwilldecreasetheofputablebond.•theprice-yieldcurves.InterestRateRiskofBondswithEmbeddedOption➢Thebemisleadingwhenitthechangesshiftingthebenchmarkyieldcurveupanddownthesameamount.✓Thepricesensitivityofbondswithembeddedoptionsisnotwhentheembeddedoptionisinthe•Thecallablebondpricehasupside•TheputablebondpricehasdownsideInterestRateRiskofBondswithEmbeddedOptionOne-side➢Thewhenupordown.✓One-side:applyonlywhenrise.✓One-side:applyonlywhen.InterestRateRiskofBondswithEmbeddedOption➢Thesensitivityofthepricechangesinspecificmaturitiesonthebenchmarkyieldcurve.✓Helpidentifytherisk”bonds.•Shapingrisk:thesensitivityofpricechangesintheshapeoftheyieldcurve(e.g.,andInterestRateRiskofBondswithEmbeddedOption➢ThesensitivityofchangesinPV+PV−2PV=-+0Effectiveconvexity2(Curve)PV0➢bond:➢Callablebond:✓Whenhigh,callableandbondsimilar✓Whenthecalloptionisinthemoney,theofthecallablebondturns.InterestRateRiskofBondswithEmbeddedOption➢Putablebond:✓✓Whentheputoptionisinthemoney,theoftheputablebondishigherthanbond.•theprice-yieldcurves.Summary➢Importance:☆☆➢•one-side•➢tips:•常考点：effectiveduration的计算与比较，计算题或概念题。ValuingCappedorFlooredFloating-Bonds➢theofacappedorbond.ValuingFlooredFloating-rateBonds➢ThecouponisansuchLIBOR.Coupon=+quoted✓typically✓isusually✓Couponin:basedonValuingFlooredFloating-rateBonds➢Cappedbonds:thecouponnotthespecified(cap).✓Acappedtheissuerrisingandisthusanissueroption.✓Theislongthebondbutshorttheembeddedoption,so:ofcappedbond=ofa–oftheembeddedcapValuingFlooredFloating-rateBonds➢Flooredbonds:couponnotbelowthespecifiedminimum(floor).✓Athedecliningandisthusanoption.✓Theislongboththebondandtheembedded“floor”option,so:ofbond=ofa+oftheembeddedfloorValuingFlooredFloating-rateBonds➢cappedandcanbeusingtheinductionmethodinabinomial✓checkwhetherthecaporfloorapplieseachnode.✓Ifitdoes,thecashisValuingFlooredFloating-rateBonds➢Usingthethea$100whosecouponisalsothe✓Q1:theofanoption-freebond.✓Q2:theofacappedwithcapof7%andtheofthecap.✓Q3:theofawithfloorof4%andtheoftheValuingFlooredFloating-rateBonds018%3%5%ValuingFlooredFloating-rateBonds➢Q1:anoption-freebondwithitscouponequaltheparSotheofanoption-bondfloater”)is$100.ValuingFlooredFloating-rateBonds➢Q2:thebondas012$99.07$38%$100$8$7$99.553%$100$3$100$55%ValuingFlooredFloating-rateBonds➢Question2:thebondas100+7✓푉===1,푈1+8%100+51+5%✓푉=1,퐿99.07+3+(100+3)/21+3%✓푉==0✓ofcap=offloater”–ofcapped=100-99.55=$0.45ValuingFlooredFloating-rateBonds➢Q3:thebondas012$100$3$4$100$8$100.978%3%$100$3$100$5$45%ValuingFlooredFloating-rateBonds➢Q3:thebondas✓NeitherVnorVbelow4%,sotheofbothVandV$100.100+4+(100+4)1+3%✓푉==0✓offloor=of–offloater”=100.97-100=$0.97Summary➢Importance:☆☆☆➢•ofcappedorbonds.➢tips:•常考点：计算题。ConvertibleBonds➢Describedefiningofabond;➢andthecomponentsofa➢ofabondwithbondandcommonConvertibleBondsof➢bond:asecuritybondholdersthetheirdebtequityduringaperiod(period)aprice(price).✓option:acalloptionontheissuercommonConvertibleBondsof➢:thenumberofcommonthebondholderthebonds✓=Issueprice✓price=Issue•bondsissuedparConvertibleBonds➢:theofthebondifitcommon✓=price×✓butthepriceisfloating,sotheisfloating.➢:theofthebondifitnot✓Theofthecash➢Minimumvalue:ConvertibleBonds➢price:thepricetheunderlyingcommoniftheybuythebondandthenit✓price=bond✓premiumper=price-price✓premium=premiumperpriceConvertibleBonds➢AbondofA,issued$900withof$1000andcouponof5be10commonwhichis$80perthebondis$850.theprice,price,perConvertibleBonds➢price=$900/10=$90;➢=$80*10=$800;➢price=$850/10=$85;➢per=$85-$80=$5;➢=$5/$80=6.25%;ConvertibleBondsrisk➢canbeusedasabenchmarkofthedownsideriskofabond.✓=bondprice/Straightprice)-1➢DependsprimarilyontheoftheunderlyingcommonConvertibleBonds➢Thebondcanbeastheequivalenceofitscomponentcombination:✓bond=bond+Calloptionon✓Callablebond=bond+Calloptionon-Calloptiononbond✓Putablebond=bond+calloptionon+putoptiononbondConvertibleBondsof➢Whentheunderlyingpriceisbelowtheprice,thebondbond✓actsasadownsidelimit.➢Whentheunderlyingpriceistheprice,thebond➢InthesethebondaSummary➢Importance:☆☆➢•Definingofabond;•Componentsofa•Comparisonofbondwithbondandcommon➢tips:•常考点：概念题。MeasuresCreditRisk➢Explainthelosstheprobabilityofandthe➢theofabondanditsassumptionsabouttherisk➢theanalysisdebtthecreditanalysisofdebt.MeasuresRiskofrisk