第七章利率风险

InterestRateRiskChapter7RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull202117.1ManagementofNetInterestIncomeNetInterestIncome=Interestreceived-InterestpaidConsiderasimplesituationwhereabankoffersconsumersaone-yearandafive-yeardepositrateaswellasaone-yearandfive-yearmortgagerate.TheratesareshowninTable7.1:Maturity(yrs)DepositRateMortgageRate13%6%53%6%RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull20212Table7.1ExampleofratesofferedbyabanktoitscustomersTwoquestion:〔1〕WhatwouldhappenifabankpostedtheratesinTable7.1?〔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.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〔短借长放景象〕，从而对净利息收入产生风险冲击。假设利率下降，贷款利率6%，存款利率低于3%，利息收入添加。假设利率上升，贷款利率6%，存款利率高于3%，利息收入减少。★总结处理方案：实现资产负债匹配。Maturity(yrs)DepositRateMortgageRate13%6%54%7%表7-2提高5年期利率以到达资产负债的匹配BadInterestRateRiskManagementHasLedtoBankFailures(BusinessSnapshot7.1,page101)RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull202197.2LIBORRatesandSwapRatesLIBORratesare1-,3-,6-,and12-monthborrowingratesforcompaniesthathaveaAA-ratingSwapRatesarethefixedratesexchangedforfloatinginaninterestrateswapagreementRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull202110LIBORratesareprovidedbyBritishBankersAssociation(BBA).TheBBAistheleadingtradeassociationfortheUKbankingandfinancialservicessector.Wespeakforover200memberbanksfrom60countriesonthefullrangeofUKandinternationalbankingissues.UnderstandingBBALIBORLIBORratescloselyreflecttherealratesofinterestbeingusedbytheworld'slargestfinancialinstitutions.Whereascentralbanks(suchastheBankofEngland,theUSFederalReserveandtheEuropeanCentralBank)fixofficialbaseratesmonthly,LIBORreflectstheratesatwhichtheseprimebanksborrowmoneyfromeachothereachday,intheworld's10majorcurrenciesandfor15borrowingperiodsrangingfromovernightloansto12month.Oncecalculated,theLIBORfiguresarethenpublishedbyThomsonReuters:theyappearonmorethanonemillionscreensaroundtheworldandarewidelyreportedinthepress,thewireservicesandonline.ThomsonReutersundertakesthisworkfortheBritishBankers'Association.Howisitcalculated?Eachdayat11:00hrsLondontimethebankswhichcontributetotheLIBOR-settingprocesssendtheirinterbankborrowingratesconfidentiallytoThomsonReuters.ThomsonReutersdiscardsthehighestandlowestcontributions(thetopandbottomquartiles)andthenusesthemiddletwoquartilestocalculateanaverage.TheAustralianDollar,DanishKrone,NewZealandDollarandSwedishKronepanelshaveeightbanks,TheCanadianDollarandSwissFrancpanelshave12banks.TheSterling,YenandEuropanelshave16membersandtheUSDollarpanelhas19members.Eachfollowsthesameprocedureofdiscardingtheupperandlowerquartilesandaveragingthecentrequartilestocreatearate.Howdiditbecomesoimportant?LIBORwasfirstdevelopedinthe1980sasdemandgrewforanaccuratemeasureoftherateatwhichbankswouldlendmoneytoeachother.ThisbecameincreasinglyimportantasLondon'sstatusgrewasaninternationalfinancialcentre.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日正式运转。Shibor是由信誉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、零售性利率。目前，对社会公布的Shibor种类包括隔夜、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，建立银行，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。2021年5月，广发银行也成为SHIBOR基准利率互换业务报价行。WhySwapRatesAreanAverageofLIBORForwardRatesAbankcanLendtoaseriesAA-ratedborrowersfortensuccessivesixmonthperiodsSwaptheLIBORinterestreceivedtothefive-yearswaprateItcanLendtoacertainprincipalforsixmonthstoaAAborrowerandrelenditforninesuccessivesix-monthperiodstoAAborrowers;andEnterintoaswaptoexchangetheLIBORforthefive-yearswaprate.RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull202116ExtendingtheLIBORCurveAlternative1:CreateatermstructureofinterestratesshowingtherateofinterestatwhichaAA-ratedcompanycanborrowfor1,2,3…yearsAlternative2:UseswapratessothatthetermstructurerepresentsfutureshorttermAAborrowingratesAlternative2istheusualapproach.ItcreatestheLIBOR/swaptermstructureofinterestratesRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull202117LIBORVSTreasuryRateTherisk-freerateisimportantinthepricingoffinancialcontracts.TheusualpracticeamongfinancialinstitutionsistoassumethattheLIBOR/swapyieldcurveprovidestherisk-freerate.TheTreasurycurveisabout50basispointsbelowtheLIBOR/swapzerocurveRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull202118Treasuryratesareconsideredtobeartificiallylowforavarietyofregulatoryandtaxreasons7.3Duration(page102)利率久期用于检验买卖组合对利率曲线的风险暴露。假设债券收益率为y，债券价钱为B，债券久期的定义为： 或等价于：(7-1)式中，△y为债券收益率的一个小的变化，△B为相应债券价钱的变化。 RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull202120DurationContinued债券久期用于检测债券价钱对收益率的敏感度。利用微积分的符号，有：

(7-2)假定一个债券在t1,t2,…,tn时辰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是使得债券实际价钱等于市场价钱的贴现率，假设收益率为延续复利，债券价钱与收益率的关系式为：DurationContinued求导所以(7-3)DurationContinued债券久期：上式中括号中的项为ti时辰债券支付的现金流的现值与债券价钱的比率，债券价钱等于未来一切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一切现金流所要等待的平均时间。(7-3)CalculationofDurationfora3-yearbondpayingacoupon10%.Bondyield=12%.(Table7.3,page103)

RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright©JohnC.Hull202124Time(yrs)CashFlow($)PV($)WeightTime×Weight0.554.7090.0500.0251.054.4350.0470.0471.554.1760.0440.0662.053.9330.0420.0832.553.7040.0390.0983.010573.2560.7782.333Total13094.2131.0002.653例7-1由表7-3描画的债券价钱为94.21