第五章固定收益证券

5111)2)3)5.1fixedincomesecurities5.1.1.10010005000Issuer522Maturity1(accumulatedbonds)(bondwithcoupons)E(coupons)2(registeredbond)(unregisteredbond)endorsed(bearerbond)(couponbond)3(mortgagebond)(debenturebond)4Treasurybonds(Treasurybills)Tbills131652()17(TreasuryNotes)5(incomebond)(adjustmentbond)(junkbond)533belowinvestmentgradeconvertiblebond(Serialbond)TBillsTBill26199982697.715100360dFPYFt-=dYtFPdY=4.52%1297.715(1)1004.73%4.52%iid+=⇒=⇒=(2)(2)4.68%4.57%id=⇒=5.1137.5%Tbill1)(1ta-=1dt,0td121/36010,000[1(91/360)(.075)]=9810.425.24001000j40020)1(j+=1000j=.04699.38%(redeem)term(maturitydate)(perpetual)(Britishconsols)(1814)544(callable)(redemptiondate)5.1.2(owner)Creditor(dividend)(debtinstrument)cumulativepreferredstock532()(participatingpreferredstock)(convertiblepreferredstock)5.21231P=5552F=parvaluefaceamount1003C=redemptionvalueC=F124r=couponrate8%4%r=4%5Fr=6g=mortifiedcouponrate1Fr=Cgg=CFrgrgg=rCF7i=yieldrate8n=9K=K=Cnvvi10G=baseamountGi=Fr;G=iFr(5.2.1)i1nominalyield10099%2currentyield19010%3yieldtomaturity5665.2.11P=Frina|+Cnv=Frina|+K(5.2.2)2premium/discountformula()[1()]niniPCFrCiaCgia=+-⋅=+-(5.2.3)3baseamountformulaP=G+(CG)nv(5.2.4)4MakehamP=K+ig(CK)(5.2.5)inP(n,i)=Frina|+Cnv5.2.6|()(1,)0niPFrDanPnii∂=-+∂5.2.7nP∂∂=ln(1)Cii+(gi)nv5.2.812gi5.310008.4%10%1F=1000C=1000r=.042g=r=.042i=.05n=20%5|20a=12.462220)05.1(-=0.3768912020|5%401000(15%)498.488376.89875.378Pa-=++=+=220|5%1000[1(0.040.05)]1000[10.124622]875.378Pa=+-=-=35770.0410008000.05G==20800(1000800)(15%)80075.378875.378P-=+-+=+=4Makeham201000(15%)376.89K-=+=0.04(1000)376.890.8623.11875.3780.05PKK=+-=+×=2ii2.5%3%3.5%4%4.5%5%5.5%6%6.5%7%P(20,i)1233.841148.781071.061000934.9603875.378820.74770.61724.54nnP(n,5%)5885.2.2valuationmarketvaluebookvaluekBVkk||[1()]nkknkinkiBVFraCvCgia---=+=+-5.2.91()(1)kkBViFrBV++=+1(1)kkBViBVFr+=+-0,1,,1kn=-K5.2.100,nBVPBVC==5.2.1115.2.9PC=,0,1,,kBVPCkn===K2PCPCpremiumPCCPdiscount5.11gi=PC=(FrCi)ina|=C(gi)ina|2gi599=CP=(CiFr)ina|=C(ig)ina|1PC=(FrCi)ina|=C(gi)ina|2CP=(CiFr)ina|=C(ig)ina|tBtItPFr0B=PnB=CtItPtBnC=11+pp0|11()niBpgia=+=+-(5.2.12)Fr=Cg=gg1I=i0B=i[1+(gi)ina|](5.2.13)1P=g1I=(gi)(1iina|)=(gi)nv(5.2.14)1B=0B1P=1+(gi)(ina|nv)=1+(gi)ina|1-(5.2.15)0B=P1+tB=(1+i)tBFrt=0,1,…,n1(5.2.16)1+tI=itBt=0,1,…,n1(5.2.17)1+tP=Fr1+tIt=0,1,…,n1(5.2.18)5.1510105.1pp0amortizationofpremiumwritingdownamountforamortizationofpremiump0accumulationofdiscountwritingup5.11nttItPtB01+(gi)ina|1gi[1+(gi)ina|]=g(1nv)+inv(gi)nv1+(gi)ina|1-2gi[1+(gi)ina|1-]=g(11-nv)+i1-nv(gi)1-nv1+(gi)ina|2-tgi[1+(gi)itna|1+-]=g(11+-tnv)+i1+-tnv(gi)1+-tnv1+(gi)itna|-n1gi[1+(gi)ia|2]=g(12v)+i2v(gi)2v1+(gi)ia|1ngi[1+(gi)ia|1]=g(1v)+iv(gi)v1ngng–p(gi)ina|=p5.4100108%6%F=C=100g=4%i=3%gi511118065.1214.885.25.4ttItPtB0114.8774749143.4463240.553675754114.3237991243.4297140.570286027113.7535131343.4126050.587394608113.1661185443.3949840.605016446112.561102543.3768330.623166939111.9379351643.3581380.641861947111.2960731743.3388820.661117806110.6349553843.3190490.68095134109.954004943.298620.70137988109.25262411043.2775790.722421277108.53020281143.2559060.744093915107.78610891243.2335830.766416732107.01969221343.2105910.789409234106.2302831443.1869080.813091511105.41719141543.1625160.837484257104.57970721643.1373910.862608784103.71709841743.1115130.888487048102.82861141843.0848580.915141659101.91346971943.0574040.942595909100.97087382043.0291260.9708737861008065.1225314.87747486512125.5100108%10%F=C=100g=4%i=5%gi5.35.5ttItPtB087.53779144.376889-0.376889587.91468244.395734-0.39573488.31041344.415521-0.415520788.72593444.436297-0.436296789.16223544.458112-0.458111589.62034644.481017-0.481017190.10136744.505068-0.50506890.60643844.530321-0.530321491.13675944.556837-0.556837491.693591044.584679-0.584679392.278271144.613913-0.613913392.892181244.644609-0.644608993.536791344.676839-0.676839494.213631444.710681-0.710681394.924311544.746215-0.746215495.670521644.783526-0.783526296.454051744.822702-0.822702597.276751844.863838-0.863837698.140591944.907029-0.907029599.047622044.952381-0.9523811008092.46221-12.462215131380+12.46=92.4612.463PCjFriPCgiP-=-|()njPCCgiPs-=-|||&11[1()]njnjnijgsPCisCgia+=+=+-(5.2.19)|&[1()],0,1,,knkijBVCgiakn-=+-=K(5.2.20)i=jP=C[1+(gi)ina|]5.2.195.2.201PCp5.4p=14.884tI=.03114.88=3.446443.4464=0.5536i=3%0.553620|.03s=0.553626.8706=14.8756(p=14.88)2PCp5.5p=-12.462210.37688920|.05s=0.37688933.0660=12.46225.6100108%6%5%PPCCg.03P(4.03P)20.025s=P10051414P=20|.02520|.02510041.03ss++=114.46195.440.5665%4tB=P(PC)nt,t=0,1,2,,n(5.2.23)tP=nCP-,t=1,2,,n(5.2.24)tI=FrtP,t=1,2,,n(5.2.25)5.2.3t+k,t=0,1,2,...,n1,10≤≤kktB+t+kkFr(accuredcoupon)settlementdatekFr0Fr=0,1Fr=FrfktB+(flatprice)fullprice.mktB+(marketprice)quotedpricecleanpricefktB+=mktB++kFr,10≤≤k(5.2.20)515151(theoreticalmethod)tfktB+=tBki)1(+(5.2.21)kFr=Friik1)1(-+(5.2.22)mktB+=tBki)1(+Friik1)1(-+(5.2.23)2(practicalmethod)tfktB+=tB(1+ik)(5.2.24)kFr=kFr(5.2.25)mktB+=tB(1+ik)kFr(5.2.26)=(1k)tB+k1+tB(5.2.27)3(semitheoreticalmethod)fktB+=tBki)1(+kFr=kFrmktB+=tBki)1(+kFr(5.2.28)i=g,P=C5.710008%6%44.03401000(