固收

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固收1

• R32 the term structure and interest rate dynamics
  • 1.benchmark curve
    • spot rate S
      • discount factor:P()
      • 对于国债，Zero-coupon bond,YTM=Spot rate(zero coupon rate,zero rate)
      • spot rate&YTM关系
        • zero-coupon
          • YTM=S
        • coupon-paying
          • YTM&S1,S2，YTM shoule be weighted average of spot rate ，更接近现金流多的或到期时间点的spot rate
    • forward rate f
      • discount factor:F( , )
      • forward rate model
        • 计算：s & f 的转换
        • s & f关系：spot curve is upward(downward) sloping,the forward curve will lie above(below) the spot curve;f(1,1)<f(1,2)
      • forward pricing model
        • 无套利前提下，forward contract price=F(X,Y)=P(X+Y)/P(X)
      • active management（return+）
        • Forward:比较s*与f，未来long/short
          • s*<f,long;>,short
        • riding the yield curve
          • assumption:收益率曲线向上倾斜等价于forward curve is always above the current spot curve;stable,no reversal
          • strategy:buying bonds with a maturity longer than the investment horizon
    • par rate
      • the par curve represents the YTM on coupon-paying gov bond priced at par,over a range of maturities
      • CR= YTM = par rate
        • 计算：par rate 求 spot rate（bootstrapping：forward substitution）
    • YTM
      • 3 assumption
    • swap rate
      • the interest rate for the fixed-rate leg of an interest rate swap
      • 计算(用衍生品求法)
        • 优点
          • liquidity；default risk(benchmark yield);unregulated
  • 2.yield spread(yi-yb)
    • swap spread
      • swap rate - treasury yield
        • 风险补偿：default;market liquidity
    • I-spread
      • bond rate - swap rate
        • credit;liquidity
    • Z-spread
      • Sc - St
        • credit;liquidity
          • 衡量公司债更准确
      • 计算：试错法
    • TED-spread
      • libor - T-bill rate
        • a measure of counterparty risk(credit risk)
          • 衡量银行体系风险
    • M一致
    • libor-OIS spread
      • libor - OIS (注：OIS:一天的swap rate)
        • 衡量money market secutities
    • 注：题目中未特殊说明的yield curve，一般指的是benchmark的yb
  • 3.term structure theory (定性：r短 r长解释收益率曲线形状
    • pure expectation theory
      • description:forward rate is an unbiased predictor of the future spot rate
      • assumption:risk neutral
        • shape:3
      • local expectation theory:pure expectation theory短期可，长期不适用
    • liquidity preference theory
      • description:短期 + liquidity premium
      • shape:5
    • segmented market theory
      • description:利率由资金市场供需关系决定；长期与短期资金市场完全独立
      • shape:2
    • preferred habitat theory
      • description:if the ecpected additional returns to be gained become large enough,institutions will be willing to deviate from their preferred maturities or habitats
      • shape:2
  • 4.modern term structure theory(定量)
    • equilibrium structure model
      • CIR
        • two parts:deterministic part;stochastic(random) part
        • mean reversion均值复归特征
        • volatility to increase with the level of interest rate
      • Vasicek model
        • 前两项同CIR，volatility remains constant
        • disadvantage:r可能<0
    • arbitrage-free model
      • H0-Lee model
        • match current market price.(time varying parameters)
  • 5.yield curve risk
    • factor
      • parallel shift
        • level(most);
      • non-parallel
        • steepness（r短，r长）;curvature曲度（r短，r中，r长）
    • key rate duration
      • （for non-paralleled shifts）含义：eg KRD5=3 五年期的收益率变动1%，其他点的收益率保持不变，如果五年期收益率的KRD等于3，代表整个组合的变动未3%
      • 计算
        • KRDi=Wi*Di
          • Dp=KRDi加总
            • 非平行移动时，计算价格变动百分比
        • △P/P=-D*△y=-[KRD1*△y1+。。]
    • r volatilitiy
      • short term rates are more volatile than long-term rates
      • 平方根转换
• R33 arbitrage-free valuation framework
  • 1.arbitrage opportunity
    • type
      • value additivity
        • 未来可化为相等
      • dominance
        • 现在可化为相等
    • fixed-income security
      • stripping；reconstitution
  • 2.interest rate trrees
    • 每列时间点相互独立。i1H=i1L*e2个volatilitiy
    • volatilitiy估计
      • historical interest rate volatilitiy(data:recent past)
      • implied volatilitiy:observed market price of interest rate derivatives
    • middle forward rate
      • 通过spot rate求出
        • middle forward rate可求出i1H,i1L。注意指数几个volatilitiy
    • volatilitiy +，spread out
  • 3.Monte Carlo method
    • MBS对于现金流或利率由路径依赖特征
    • MBS不能用二叉树估值，Monte Carlo method可以

固收2

• R34valuation and analysis of bonds with embedded option
  • 1.callable and putable bonds
    • 相关概念
      • Vcallable=Vpure - Vcall;Vputable=Vpure + Vput
    • 计算（二叉树）
      • Vcallable Vputable
        • Vpure
      • Vcall Vput
        • 先计算Vpure,V含权
      • call：P>X,X;put:P<X.X
    • interest rate volatility变动
      • volatility+,Vcallable-;volatility+,Vputable+(不影响option-free bond)
    • OAS(option-adjusted spread)
      • 计算：试错法
        • Pmkt=CF/(1+r+OAS)+..
      • 结论
        • 含权bond,OAS更准确（OAS是行权后的spread，Z-spread是不行权的spread,衡量不含权bond。对于不含权bond，Z-spread=OAS）
        • OAS lower,r-,P+(overprice);反之推导
      • interest rate volatility变动
        • volatility+,OAS(callable)-;OAS(putable)+
    • interest rate risk
      • effect of interest rate change
        • callable and putable bond
          • call option and put option
      • effective duration(not symmetrical)
        • zreo-coupon
        • fixed-rate(coupon-paying)
        • floator
        • callable& putable
      • one-side duration
        • callable bond:one side down duration利率风险小<one side up duration利率风险大
        • putable bond:one side down duration利率风险大>one side up duration利率风险小
    • key rate duration
      • 含义：shifting any par rate has an effect on the value of the bond
        • PR影响spot rate继而影响p
      • 哪个时间点利率的变动对债券价格影响大；5类型
        • option-free
          • trading at par
            • maturity matched rate is the only rate that the bond value,其他时间D=0
          • not trading at par
            • maturity matched rate has the greatest effect
        • callable
          • low CR,maturity matched rate;high CR,ecercise-date rate
        • putable
          • low CR,ecercise-date rate;high CR,maturity matched rate
        • zero-coupon
          • 到期日影响最大，其他时间KRD为负数
  • 2.floater with cap or floor
    • 相关概念
      • Vfloater with cap=Vpure - Vcap;Vfloater with floor=Vpure+ Vfloor
    • valuation
      • 计算（二叉树）
        • VVfloater with cap; Vfloater with floor
          • Vpure
        • Vcap Vfloor
          • 先计算Vpure,V含权
        • call：CR>cap，cap:
          • put：CR<floor,floor
    • Ratchet bond
      • 浮动债券，cap=CR,CR单边下降，对issuer有好处，支付的coupon越来越少
      • 改进：开始的coupon高；设置或有put
  • 3.convertiable bonds
    • 基本术语
      • conversion ratio；conversion price（issue price/conversion ratio）；market conversion price（bond market price/conversion ratio）； conversion value（market price of stock*conversion ratio)
      • Vconvertible bond=Vpure+Vcall on stock
    • stock price volatility
      • volatility+,Vcall on stock+,Vconvertible bond+
    • risk-return characteristivs of the bond
      • Ps(underlying share price)<X（the conversion price）
        • bond"busted convertible"受r影响大
      • Ps(underlying share price)>X（the conversion price）
        • stock"common stock equity"受p影响大
    • 计算：
      • market conversion premium per share=market coversion price-market price
      • min value=max(straight value=the price of a straight bond,convision value)
• R35 Credit analysis models
  • 1.valuing risk bonds
    • 相关概念
      • expected exposure
        • probability of default POD
          • recovery rate
            • loss given default LGD
      • Expected loss=POD*LGD
        • credit valuation adjustment CVA(预期损失现值之和，衡量信用风险)
      • Fair value of corporate bond=VND-CVA
    • flat yield curve 同一r
      • zero coupon corporate bond
        • fair value
        • rate of return
          • default:IRR
          • no default:YTM
        • credit spread
      • coupon-paying corporate bond
        • fair value
          • rate of return
            • credit spread
    • aebitrage-free valuation
      • fixed-rate corporate bond
      • floating-rate corporate bond
  • 2.credit risk model
    • 定性
      • credit scoring
        • F1 score影响因素
          • payment history;debt burden;length of history;types of credit used;recent rearches for credit
      • credit rating
        • 计算：评级改变算return的变化，△%p=△p/p
    • 定量
      • structural model
        • 对对错；internal；Why
      • reduced model
        • 错错对；exteral；when
          • 回归分析
      • B/S;Asset-traded;经济周期；info；credit risk
  • 3.credit spread
    • 参数影响
      • POD（相比RR,影响更多=大）+,risk+,spread+
        • RR+,risk-，spread-
    • 影响因素
      • credit quality;
        • financial condition宏观经济
          • market supply and demand dynamics
            • company-value model
  • 4.credit analysis for securitized debt
    • ABS credit risk影响因素
      • 数量，颗粒度granularity；资产之间的相似度；相关服务机构质量；structure（破产隔离，信用增级）
    • covered bond
      • 缺钱银行以及旗下bond的dual recourse
• R36credit default swap
  • 1.structure
    • the issuer of reference obligation is called reference entity(C)
      • OTC交易，unofficial ISDA regualted
    • default swap premium is also called CDS spread
      • notinal amount保额
    • 支付方式：upfront or over a period of time
    • standardization:fixed coupon.the difference is paid upfront 在期初
    • credit protection buyer is short(债券价格下降，gain) and credit protection is long
    • settle
      • physical；cash(payout amount;payout ratio)
    • credit event:C bankruptcy,failure to pay；restructure(not considered a credit event)
    • bond creadit risk+,buy protection(short,价格下降获利)
  • 2.types
    • single-name CDS
      • any debt obligation issued by the owner that is pari passu(ranked equivalently in priority of claims)or higher relative to the reference obligation is covered
      • in the same seniority,cheapest-to-deliver
    • index CDS(CDX)
      • 相当于bond portfolio投保CDS,保额平均分配；correlation+，risk+
  • 3.valuation of CDS
    • factors influence CDS spread
      • POD+,spread+；LGD+,spread+
    • upfront premium=(credit spread- fixed coupon)*Duration
  • 4.application of CDS
    • naked CDS；long/short trade；synthetic CDO
    • curve trade
      • credit curve flattening:buy ST CDS(short）,sell LT CDS(long)
      • credit curve steepening:buy LT CDS(short）,sell ST CDS(long)
    • basis trade:bond spread CDS spread不同套利