cfa二级知识框架图-固定收益金程教育

1、CFA 二级知识框架图Fixede:2-27SS12Valuation ConceptsR34 Term Structure anderest Rates Dynamics R35 The arbitrage-free valuation frameworkSS13Topics in FixedeysisR36 Valuation andysis: Bonds with EmbeddedOptionsR37 Creditysis Ms R38 Credit Default SwapsFramework深化Credit Risk: 定量模型 （一级主要是定性介绍） R37Yield Curve

2、& Yield Curve Risk R34RiskValuation:含权债券的定价 (Binomial Tree) R35、R363-27二级二级三级一级Trading StrategyValuationRiskTypeDefinition(features)Fixede整体框架RR4334remSecuSrittiresu: DcetfiunirngeElaemnedntserest Rates DynamicsFixed -4-27Forward Rate MSpot CurveForward Pricing MNo-arbitrageForward CurveActive Bond

3、Portfolio ManagementPar Curve Bootstrap计算: 己知Par Rate算Spot RateYTM, Spot Rate and Return on Bond:Reflect the credit risk of bsThe Swap Rate CurveNot regulated,more comparable in differentcountriesMany maturities优点(和ernment Bond Yield 比)5-27YTM相当于是spot rate的平均数BenarketCurve Yield curve movementIf fut

4、ure spot rate will be lowern forward rate, forward contract value increase. Riding the yield curveUpward-slocurve: an investor will purchase bonds withmaturities longern his investment horizon.* P*F)*Spot rate Forward rate 计算 * (T* T) * T* *Relationship:1 r(TT)1 r(T )1 f (T , T)Upward-slospot curve

5、upward-slo;Forward curve;When the spot curve is upward slo, the forward curve will above the spot curve.6-27计算性质 (spread反映的风险Swap spreadSwap rate -Treasury yield Note: Treasury bond一same maturity, on-the-runDefault risk有些期限，swap的liquidity可能更好I-spreadYieldsubject bond Swap rateNotes: same maturityCre

6、dit riskLiquidity riskZ-spread试错法PCrinmarket(1 S Z )1(1 S Z )2(1 S Z )3123Credit riskLiquidity riskOption risk对含权债券和不含权债券的比较不合适TED spreadLibor -T-bill rateNote: same maturity，常见3个月Default riskhe bing systemLibor-OIS spreadLibor - OIS rateNote: OIS rate 相当于间隔夜借贷成本, Credit Risk 最小High: concerns abored

7、itworthinessLow: high liquiditySpreadSpread =yieldsubject bond - yieldbenark7-27Description (性质)解释yield curve形状Pure (Unbiased ) Expecions Theory Forward rates are solely a function of expectedfuture spot rates Investor should earn the same return over a giveninvestment horizon Risk neutrality Upward

8、 slope: rise Downward slope: fall Flat yield: remainLocal ExpecionTheory 类似Unbiased Expecions Theory Only for short periods: risk-neutrality Longeriods: risk premiums existTerm Structure oferest Rates目的: 解释yield curve形状8-27Description (性质)解释yield curve形状LiquidityPreference Theory Forward rates: bias

9、ed estimates of expecion offuture rates Include a liquidity premium Liquidity premium: larger during periods of greatereconomic uncertayUpward slope: Future rates rise Rates remain constant, butthe addition of the liquiditypremiumSegmented MarketTheoryYield at eaaturity is determined independently o

10、fthe yields at other maturitiesDetermined by thepreferenof borrowers andlendersPreferred HabiTheory Forward rates: expected future spot rates +premium Premium is not related to maturity Premium (incentive): 使投资者 shift from preferredhabisTerm Structure oferest Rates目的:解释yield curve形状9-27公式性质Equllibri

11、umMsCox一Ingersoll一 Ross M(CIR)dr = a (b - r)dt +rdzDrift term &random termMean-reverting (b), a是reverting speedVolatility increases with rVasicek Mdr = a (b - r)dt +dzDifference from CIR: volatility不随r而上升Disadvantage: r may benegativeArbitrage Free ModeHo-Lee Mdrt = t dt +dztAdvantage: match current

12、 market price and current yield curveModern Term Structure Ms定量描述 r基本不会考计算注意三个模型之间的辨析10-27Yield Curve Factor M概念、辨析、计算Yield curvefactorDescription重要程度LevelUpward/Downward shift(同上同下)77%SteepnessLong-term rate和short-term rate变动幅度不同17%CurvatureLong-term & short-term rate 和 middle-term rate 变动幅度不同3%Man

13、aging yield curve risk: P D X D X D rPLLSSCCYield curve riskEffective duration: parallel shiftKey rate duration: non-parallel shift (sharisk)Yield curvevolatilityImportant for securities with embedded optionsShort-termerest rates are generally more volatilen are long-term rates.The arbitrage-free va

14、luation framework11-27RR443512-27Arbitrage OpportunityValue additivity DominanceStripReconstitutionroduction ofArbitrage freeValuation (spot curve)PCrinmarket(1 S )1(1 S )2(1 S )3123BinomialerestRate Tree求二叉树Equal probabilityMiddle forward rate (f): 1 r(T *T )(T*T ) 1 r(T*)T*1 f (T*,T )Ti ie2 i ie2

15、i ie41,H1,L2,HL2,LL2,HH2,HHOption-free bond valuationPathwise valuationn period, 2n-1 paths一求算数平均Monte Carlo SimulationBinomial tree: backward induction 适用于callable,putabondCash flow of MBS: path dependencyAdvantage of MCS: 解决path dependency 适用MBS13-27总结：Bond定价方法NCFiP0 (1 r)iiiOption-free bondBond w

16、ith EmbeddedOptionCF时间、金额确定不确定(取决于将来 r的变化)rSingle yield(YTM): bond price CPN1 CPN 2 CPN N Par(1 YTM )(1 YTM )2(1 YTM )NArbitrage-free: no arbitrage price CPN1 CPN 2 CPN N Par(1 S )(1 S )2(1 S )N12NBinomial tree: backward induction (考虑将来 r变化)一callable, putableMonte Carlo Simulation: 解决path dependency

17、 一MBSValuation andysis: Bonds with Embedded Options14-27RR453615-27Simple OptionsCallabondPutabondExtendibond (可以看成是Putabond): 比如2年可以扩展成3年，相当于3年期Putable ，2年可执行Complex OptionsEse Put: Contingent Put OptionSinking Fund Bonds (Sinkers)16-27Valuation of Callable and PutabondsValue计算Binomial TreeV callab

18、le: 高过Strike price的价格只能取Strike PriceVputable: 低过Strike price的价格只能取Strike Price计算 VoptionVcallable=Vnoncallable VcallVputable=Vnonputable +VputVolatility对 Value 的影响会影响 Binomial Tree: Spread outVolatility 一 Vcall 一 Vcallable Volatility 一 Vput Vputable OAS计算Binomial Tree (试错法)Volatility的影响Callable:Vola

19、tility 一 OAScall Putable:Volatility 一 OASput OAS:可以对比不含权债券和含权债券17-27Yield Curve RiskEffect of yield curve changesLevelr Vcallable Vputable Vcall optionVcall option will be lower for upward sloyield curvePutr Vput optionVput option will be lower as an upward-sloyield curve flattens18-27含权债券duration性质

20、计算EDCallable, Putable ED putabler 一ED callableBV BVED yy 2 BV0 yECCallable:r一Negative convexityPutable:r一More convexityEC BVy BVy - 2 BV0BV y20One-side DurationCallable: lower one-sided down-durationn one-sided up-durationPutable: larger one-sided down-durationn one-sided up-duration不要求Key Rate Dura

21、tionCallable/putable: 在exercise date 和maturity date 最大 其他性质了解不要求19-27Capped& Floor Floater计算 (Binomial Tree)Option-free floater: price = par Cap: couponcap, 只能取cap Floor: couponfloor, 只能取floor注意 : 折现率还是用原来的利率计算Value of cap/floorValue of capped floater= Value of straight bond - Value of embedded capV

22、alue of floored floater= Value of straight bond +Value of embedded floorRatchetBondsCapped floater:extreme protectioncap = current coupon rate20-27Convertible Bond计算Converprice & market converpriceConvervalue, straight value, minimum valueMarket converpremium, premium overstraight value性质e equivalen

23、t(busted convertible)Market stock price ConverpriceHybrid securityRR4367Creditysis Ms21-2722-27Arbitrage-free valuation分类Valuing risky fixed-rate bonds 计算Valuing risky floating-rate bonds 计算CVA公式：FV= VND -CVA计算的三步法 理解衡量Credit Risk的指标Probability of defaultLoss given default公式：LGD(%)=100-Recovery rate

24、Actual LGD Vs. Risk-neutral LGDExpected loss公式：EL=PD*LGDExpected exureCredit spread23-27reting Changes in CreditSpreadPD推导过程 理解itively correlated with credit spreadRecoveryrate推导过程 理解itively correlated with credit spread四大模型重点掌握Credit Scoring优缺点Credit Ratings优缺点Notching& Credit transition matrixStructure MOptionogystock value = Max(0, A-K)dealue = Min(A,K)假设&优缺点 (对比Reduced Form M)Reduced Form M假设&优缺点