第八章-利率风险.ppt

InterestRateRisk,Chapter8,RiskManagementandFinancialInstitutions,CopyrightJohnC.Hull,1,8.1ManagementofNetInterestIncome,NetInterestIncome=Interestreceived-InterestpaidConsiderasimplesituationwhereabankoffersconsumersaone-yearandafive-yeardepositrateaswellasaone-yearandfive-yearmortgagerate.TheratesareshowninTable8.1:,RiskManagementandFinancialInstitutions,CopyrightJohnC.Hull,2,Table8.1Exampleofratesofferedbyabanktoitscustomers,Twoquestion:（1）WhatwouldhappenifabankpostedtheratesinTable8.1?（2）Howcanthebankmanageitsrisks?,Assumption:marketparticipantsexpecttheone-yearinterestrateforfuturetimeperiodstoequaltheone-yearratesprevailinginthemarkettoday.Supposeyouhavemoneytodeposit.Wouldyouchoosetodeposityourmoneyforoneyearat3%perannumorforfiveyearat3%perannum?,Ifdepositoneyear:(1+3%)(1+3%)(1+3%)(1+3%)(1+3%)=(1+3%)5Ifdepositfiveyear:(1+3%)5Somostcustomerswouldchooseoneyearbecausethisgivesthemmorefinancialflexibility.Ittiesuptheirfundsforashorterperiodoftime.（流动性偏好）,Nowsupposethatyouwantamortgage.Wouldyouchooseaone-yearmortgageat6%orafive-yearmortgageat6%?One-yearmortgage:(1+6%)(1+6%)(1+6%)(1+6%)(1+6%)=(1+6%)5Five-yearmortgage:(1+6%)5Somostwouldchooseafive-yearmortgagebecauseitfixesyourborrowingrateforthenextfiveyearsandsubjectsyoutolessrefinancingrisk.,由于多数客户会选择1年期存款，5年期贷款，所以，导致银行的资产与负债的不匹配（短借长放现象），从而对净利息收入产生风险冲击。若利率下降，贷款利率6%，存款利率低于3%，利息收入增加。若利率上升，贷款利率6%，存款利率高于3%，利息收入减少。,总结,解决方案：实现资产负债匹配。,表8-2提高5年期利率以达到资产负债的匹配,8.2LIBORRatesandSwapRates,LIBORratesare1-,3-,6-,and12-monthborrowingratesforcompaniesthathaveaAA-ratingSwapRatesarethefixedratesexchangedforfloatinginaninterestrateswapagreement,RiskManagementandFinancialInstitutions,CopyrightJohnC.Hull,9,资料：LIBORratesandSHIBORratesLIBORratesareprovidedbyBritishBankersAssociation(BBA).TheBBAistheleadingtradeassociationfortheUKbankingandfinancialservicessector.Wespeakforover200memberbanksfrom60countriesonthefullrangeofUKandinternationalbankingissues.,UnderstandingBBALIBORLIBORratescloselyreflecttherealratesofinterestbeingusedbytheworldslargestfinancialinstitutions.Whereascentralbanks(suchastheBankofEngland,theUSFederalReserveandtheEuropeanCentralBank)fixofficialbaseratesmonthly,LIBORreflectstheratesatwhichtheseprimebanksborrowmoneyfromeachothereachday,intheworlds10majorcurrenciesandfor15borrowingperiodsrangingfromovernightloansto12month.Oncecalculated,theLIBORfiguresarethenpublishedbyThomsonReuters:theyappearonmorethanonemillionscreensaroundtheworldandarewidelyreportedinthepress,thewireservicesandonline.ThomsonReutersundertakesthisworkfortheBritishBankersAssociation.,Howisitcalculated?Eachdayat11:00hrsLondontimethebankswhichcontributetotheLIBOR-settingprocesssendtheirinterbankborrowingratesconfidentiallytoThomsonReuters.ThomsonReutersdiscardsthehighestandlowestcontributions(thetopandbottomquartiles)andthenusesthemiddletwoquartilestocalculateanaverage.TheAustralianDollar,DanishKrone,NewZealandDollarandSwedishKronepanelshaveeightbanks,TheCanadianDollarandSwissFrancpanelshave12banks.TheSterling,YenandEuropanelshave16membersandtheUSDollarpanelhas19members.Eachfollowsthesameprocedureofdiscardingtheupperandlowerquartilesandaveragingthecentrequartilestocreatearate.,Howdiditbecomesoimportant?LIBORwasfirstdevelopedinthe1980sasdemandgrewforanaccuratemeasureoftherateatwhichbankswouldlendmoneytoeachother.ThisbecameincreasinglyimportantasLondonsstatusgrewasaninternationalfinancialcentre.Morethan20percentofallinternationalbanklendingandmorethan30percentofallforeignexchangetransactionsnowtakeplaceinLondon.LIBORratesarethebasisforarangeoffinancialinstruments:derivativesbasedontheLIBORratesarenowtradedonexchangessuchasLIFFEandtheChicagoMercantileExchange(CME)aswellasover-the-counter.Theratesarealsousedasthebasisformanytypesoflending,fromsyndicatedandcommerciallending,toresidentialmortgages.,SHIBORratesShibor全称是“上海银行间同业拆放利率”（ShanghaiInterbankOfferedRate，SHIBOR），被称为中国的LIBOR（LondonInterbankOfferedRate，伦敦同业拆放利率），自2007年1月4日正式运行。Shibor是由信用等级较高的银行组成报价团自主报出的人民币同业拆出利率计算确定的算术平均利率，是单利、无担保、批发性利率。目前，对社会公布的Shibor品种包括隔夜、1周、2周、1个月、3个月、6个月、9个月及1年。上海首批16家报价行分别为：工商银行，农业银行，中国银行，建设银行，交通银行，兴业银行，浦发银行，北京银行，上海银行，招商银行，光大银行，中信银行，南京商行，德意志上海，汇丰上海，渣打上海。2010年5月，广发银行也成为SHIBOR基准利率互换业务报价行。,WhySwapRatesAreanAverageofLIBORForwardRates,AbankcanLendtoaseriesAA-ratedborrowersfortensuccessivesixmonthperiodsSwaptheLIBORinterestreceivedtothefive-yearswaprateItcanLendtoacertainprincipalforsixmonthstoaAAborrowerandrelenditforninesuccessivesix-monthperiodstoAAborrowers;andEnterintoaswaptoexchangetheLIBORforthefive-yearswaprate.,RiskManagementandFinancialInstitutions,CopyrightJohnC.Hull,15,LIBORVSTreasuryRate,Therisk-freerateisimportantinthepricingoffinancialcontracts.TheusualpracticeamongfinancialinstitutionsistoassumethattheLIBOR/swapyieldcurveprovidestherisk-freerate.TheTreasurycurveisabout50basispointsbelowtheLIBOR/swapzerocurve,RiskManagementandFinancialInstitutions,CopyrightJohnC.Hull,16,Treasuryratesareconsideredtobeartificiallylowforavarietyofregulatoryandtaxreasons,8.3Duration,度量利率风险的常用指标是麦考利（FrederickMacaulay）在1938年提出的久期。假设债券收益率为y，债券价格为B，债券久期的定义为：或等价于：(8-1)式中，y为债券收益率的一个小的变化，B为相应债券价格的变化。,RiskManagementandFinancialInstitutions,CopyrightJohnC.Hull,18,久期的理解：久期就是债券价格相对于利率水平正常变动的敏感度，它可以精确地量化利率变动给债券价格造成的影响。例：如果一只短期债券的久期是2，那么利率每变化1个百分点，该债券价格将上升或下降2%。一只长期债券的久期是12.0，那么利率每变化1个百分点，其价格将上升或下降12%。久期越大，债券价格对利率的变动就越敏感，利率上升所引起的债券价格下降幅度就越大，而利率下降所引起的债券价格上升幅度也越大。久期特征给债券投资提供了参照。当前的利率水平存在上升可能，就可以集中投资于短期品种、缩短债券久期；而当前的利率水平有可能下降，则拉长债券久期、加大长期债券的投资，这就可以帮助我们在债市的上涨中获得更高的溢价。,DurationContinued,债券久期用于检测债券价格对收益率的敏感度。利用微积分的符号，有：(8-2)假定一个债券在t1,t2,tn时刻给债券持有人提供的现金流为c1,c2,cn(现金流包括债息和本金)，债券收益率y是使得债券理论价格等于市场价格的贴现率，如果收益率为连续复利，债券价格与收益率的关系式为：,DurationContinued,求导所以,(8-3),DurationContinued,债券久期：,上式中括号中的项为ti时刻债券支付的现金流的现值与债券价格的比率，债券价格等于未来所有支付的现金本息贴现值的总和，因此久期是付款时间ti的加权平均。即久期是投资者收到所有现金流所要等待的平均时间。,(8-3),CalculationofDurationfora3-yearbondpayingacoupon10%.Bondyield=12%.(Table8.3),RiskManagementandFinancialInstitutions,CopyrightJohnC.Hull,23,例8-1:,由表8-3描述的债券价格为94.213，久期为2.653，根据公式（8-1）：B=-B*D*y=-94.213*2.653y=-249.95y当收益率增加了10个基点（0.1%），即y=0.001，久期公式预计B为：B=-249.95*0.001=-0.25久期公式预期债券价格会下降到94.213-0.25=93.963。为了检验这个预测的准确性，我们计算当收益率增加10个基点到12.1%时的债券价格，其数量为：5e-0.121*0.5+5e-0.121*1+5e-0.121*1.5+5e-0.121*2+5e-0.121*2.5+105e-0.121*3=93.963这一数值同久期公式预计的变化相同。,8.3.1ModifiedDuration,WhentheyieldyisexpressedwithcompoundingmtimesperyearTheexpressionisreferredtoasthe“modifiedduration”,RiskManagementandFinancialInstitutions,CopyrightJohnC.Hull,25,例8-2,由表8-3描述的债券价格为94.213，久期为2.653，每年复利两次的收益率为12.3673%，修正久期为：=2.653/(1+0.123673/2)=2.4985,8.3.2DollarDuration,绝对额久期等于修正久期与债券价格的乘积：采用微分的记号为：,8.4Convexity,对于收益曲线上较小的平移，久期可以检测组合价值的变化。相同久期的债券，导数相同（图8-1）。这意味着当收益率有较小的变动时，两个债券同收益率变化的百分比相同。所引出问题：当利率变化较大时，如何来衡量它们的价值变化呢？,图8-1两个具备同样久期的交易组合,B/B,y,曲率变量用于检验曲线的凸凹变化程度，它可以改善近似式的准确性。债券的曲率被定义为：其中，y对应于债券的收益率。涵义：债券曲率是将来收到现金流的时间平方的平均值。,可得关于债券价格的两阶近似式（附录G）：由此：,（8-4）,注意：和久期公式对比！,例8-3,由表8-3描述的债券价格为94.213，久期为2.653，曲率为：0.05*0.52+0.047*12+0.044*1.52+0.042*22+0.039*2.52+0.779*32=7.57由式（8-4）得出：B/B=-2.653y+0.5*7.57*(y)2假设债券收益率由12%变为14%，久期公式