利率風(fēng)險(xiǎn)課件

InterestRateRiskChapter7RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull20091

InterestRateRiskChapter77.1ManagementofNetInterestIncome

NetInterestIncome=Interestreceived-InterestpaidConsiderasimplesituationwhereabankoffersconsumersaone-yearandafive-yeardepositrateaswellasaone-yearandfive-yearmortgagerate.TheratesareshowninTable7.1:Maturity(yrs)DepositRateMortgageRate13%6%53%6%RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull20092Table7.1Exampleofratesofferedbyabanktoitscustomers7.1ManagementofNetInterestTwoquestion:（1）WhatwouldhappenifabankpostedtheratesinTable7.1?（2）Howcanthebankmanageitsrisks?Twoquestion:3Assumption:

marketparticipantsexpecttheone-yearinterestrateforfuturetimeperiodstoequaltheone-yearratesprevailinginthemarkettoday.Supposeyouhavemoneytodeposit.Wouldyouchoosetodeposityourmoneyforoneyearat3%perannumorforfiveyearat3%perannum?Assumption:marketparticipant4Ifdepositoneyear:(1+3%)(1+3%)(1+3%)(1+3%)(1+3%)=(1+3%)5Ifdepositfiveyear:(1+3%)5Somostcustomerswouldchooseoneyearbecausethisgivesthemmorefinancialflexibility.Ittiesuptheirfundsforashorterperiodoftime.Ifdepositoneyear:5Nowsupposethatyouwantamortgage.Wouldyouchooseaone-yearmortgageat6%orafive-yearmortgageat6%?One-yearmortgage:(1+6%)(1+6%)(1+6%)(1+6%)(1+6%)=(1+6%)5Five-yearmortgage:(1+6%)5Somostwouldchooseafive-yearmortgagebecauseitfixesyourborrowingrateforthenextfiveyearsandsubjectsyoutolessrefinancingrisk.Nowsupposethatyouwantamo6由于多數(shù)客戶會選擇1年期存款，5年期貸款，所以，導(dǎo)致銀行的資產(chǎn)與負(fù)債的不匹配（短借長放現(xiàn)象），從而對凈利息收入產(chǎn)生風(fēng)險(xiǎn)沖擊。若利率下降，貸款利率6%，存款利率低于3%，利息收入增加。若利率上升，貸款利率6%，存款利率高于3%，利息收入減少?！锟偨Y(jié)由于多數(shù)客戶會選擇1年期存款，5年期貸款，所以，導(dǎo)致銀行的資7解決方案：實(shí)現(xiàn)資產(chǎn)負(fù)債匹配。Maturity(yrs)DepositRateMortgageRate13%6%54%7%表7-2提高5年期利率以達(dá)到資產(chǎn)負(fù)債的匹配解決方案：實(shí)現(xiàn)資產(chǎn)負(fù)債匹配。Maturity(yrs)De8BadInterestRateRiskManagementHasLedtoBankFailures

(BusinessSnapshot7.1,page101)RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull20099BadInterestRateRiskManagem7.2LIBORRatesandSwapRatesLIBORratesare1-,3-,6-,and12-monthborrowingratesforcompaniesthathaveaAA-ratingSwapRatesarethefixedratesexchangedforfloatinginaninterestrateswapagreementRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull2009107.2LIBORRatesandSwapRatesLIBORratesareprovidedbyBritishBankersAssociation(BBA).TheBBAistheleadingtradeassociationfortheUKbankingandfinancialservicessector.Wespeakforover200memberbanksfrom60countriesonthefullrangeofUKandinternationalbankingissues.LIBORratesareprovidedbyBrUnderstandingBBALIBORLIBORratescloselyreflecttherealratesofinterestbeingusedbytheworld'slargestfinancialinstitutions.Whereascentralbanks(suchastheBankofEngland,theUSFederalReserveandtheEuropeanCentralBank)fixofficialbaseratesmonthly,LIBORreflectstheratesatwhichtheseprimebanksborrowmoneyfromeachothereachday,intheworld's10majorcurrenciesandfor15borrowingperiodsrangingfromovernightloansto12month.Oncecalculated,theLIBORfiguresarethenpublishedbyThomsonReuters:theyappearonmorethanonemillionscreensaroundtheworldandarewidelyreportedinthepress,thewireservicesandonline.ThomsonReutersundertakesthisworkfortheBritishBankers'Association.UnderstandingBBALIBORLIBORHowisitcalculated?Eachdayat11:00hrsLondontimethebankswhichcontributetotheLIBOR-settingprocesssendtheirinterbankborrowingratesconfidentiallytoThomsonReuters.ThomsonReutersdiscardsthehighestandlowestcontributions(thetopandbottomquartiles)andthenusesthemiddletwoquartilestocalculateanaverage.TheAustralianDollar,DanishKrone,NewZealandDollarandSwedishKronepanelshaveeightbanks,TheCanadianDollarandSwissFrancpanelshave12banks.TheSterling,YenandEuropanelshave16membersandtheUSDollarpanelhas19members.Eachfollowsthesameprocedureofdiscardingtheupperandlowerquartilesandaveragingthecentrequartilestocreatearate.Howisitcalculated?EachdayHowdiditbecomesoimportant?LIBORwasfirstdevelopedinthe1980sasdemandgrewforanaccuratemeasureoftherateatwhichbankswouldlendmoneytoeachother.ThisbecameincreasinglyimportantasLondon'sstatusgrewasaninternationalfinancialcentre.Morethan20percentofallinternationalbanklendingandmorethan30percentofallforeignexchangetransactionsnowtakeplaceinLondon.LIBORratesarethebasisforarangeoffinancialinstruments:derivativesbasedontheLIBORratesarenowtradedonexchangessuchasLIFFEandtheChicagoMercantileExchange(CME)aswellasover-the-counter.Theratesarealsousedasthebasisformanytypesoflending,fromsyndicatedandcommerciallending,toresidentialmortgages.HowdiditbecomesoimportantSHIBORratesShibor全稱是“上海銀行間同業(yè)拆放利率”（ShanghaiInterbankOfferedRate，SHIBOR），被稱為中國的LIBOR（LondonInterbankOfferedRate，倫敦同業(yè)拆放利率），自2007年1月4日正式運(yùn)行。Shibor是由信用等級較高的銀行組成報(bào)價團(tuán)自主報(bào)出的人民幣同業(yè)拆出利率計(jì)算確定的算術(shù)平均利率，是單利、無擔(dān)保、批發(fā)性利率。目前，對社會公布的Shibor品種包括隔夜、1周、2周、1個月、3個月、6個月、9個月及1年。上海首批16家報(bào)價行分別為：工商銀行，農(nóng)業(yè)銀行，中國銀行，建設(shè)銀行，交通銀行，興業(yè)銀行，浦發(fā)銀行，北京銀行，上海銀行，招商銀行，光大銀行，中信銀行，南京商行，德意志上海，匯豐上海，渣打上海。

2010年5月，廣發(fā)銀行也成為SHIBOR基準(zhǔn)利率互換業(yè)務(wù)報(bào)價行。

SHIBORratesShibor全稱是“上海銀行間同業(yè)拆WhySwapRatesAreanAverageofLIBORForwardRatesAbankcanLendtoaseriesAA-ratedborrowersfortensuccessivesixmonthperiodsSwaptheLIBORinterestreceivedtothefive-yearswaprateItcanLendtoacertainprincipalforsixmonthstoaAAborrowerandrelenditforninesuccessivesix-monthperiodstoAAborrowers;andEnterintoaswaptoexchangetheLIBORforthefive-yearswaprate.RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200916WhySwapRatesAreanAverageExtendingtheLIBORCurveAlternative1:CreateatermstructureofinterestratesshowingtherateofinterestatwhichaAA-ratedcompanycanborrowfor1,2,3…yearsAlternative2:UseswapratessothatthetermstructurerepresentsfutureshorttermAAborrowingratesAlternative2istheusualapproach.ItcreatestheLIBOR/swaptermstructureofinterestratesRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200917ExtendingtheLIBORCurveAlterLIBORVSTreasuryRateTherisk-freerateisimportantinthepricingoffinancialcontracts.TheusualpracticeamongfinancialinstitutionsistoassumethattheLIBOR/swapyieldcurveprovidestherisk-freerate.TheTreasurycurveisabout50basispointsbelowtheLIBOR/swapzerocurveRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200918LIBORVSTreasuryRateTheriskTreasuryratesareconsideredtobeartificiallylowforavarietyofregulatoryandtaxreasonsTreasuryratesareconsidered7.3Duration(page102)利率久期用于檢驗(yàn)交易組合對利率曲線的風(fēng)險(xiǎn)暴露。假設(shè)債券收益率為y，債券價格為B，債券久期的定義為：

或等價于：

(7-1)式中，△y為債券收益率的一個小的變化，△B為相應(yīng)債券價格的變化。 RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull2009207.3Duration(page102)利率久期用于檢DurationContinued債券久期用于檢測債券價格對收益率的敏感度。利用微積分的符號，有：

(7-2)假定一個債券在t1,t2,…,tn時刻給債券持有人提供的現(xiàn)金流為c1,c2,…,cn(現(xiàn)金流包括債息和本金)，債券收益率y是使得債券理論價格等于市場價格的貼現(xiàn)率，如果收益率為連續(xù)復(fù)利，債券價格與收益率的關(guān)系式為：DurationContinued債券久期用于檢測債券價格DurationContinued求導(dǎo)所以(7-3)DurationContinued求導(dǎo)(7-3)22DurationContinued債券久期：

上式中括號中的項(xiàng)為ti時刻債券支付的現(xiàn)金流的現(xiàn)值與債券價格的比率，債券價格等于未來所有支付的現(xiàn)金本息貼現(xiàn)值的總和，因此久期是付款時間ti的加權(quán)平均。即久期是投資者收到所有現(xiàn)金流所要等待的平均時間。(7-3)DurationContinued債券久期：23CalculationofDurationfora3-yearbondpayingacoupon10%.Bondyield=12%.(Table7.3,page103)

RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200924Time(yrs)CashFlow($)PV($)WeightTime×Weight0.554.7090.0500.0251.054.4350.0470.0471.554.1760.0440.0662.053.9330.0420.0832.553.7040.0390.0983.010573.2560.7782.333Total13094.2131.0002.653CalculationofDurationfora例7-1

由表7-3描述的債券價格為94.213，久期為2.653，根據(jù)公式（7-1）：△B=-B*D*△y=-94.213*2.653△y=-249.95△y當(dāng)收益率增加了10個基點(diǎn)（0.1%），即△y=0.001，久期公式預(yù)計(jì)△B為：△B=-249.95*0.001=-0.25久期公式預(yù)期債券價格會下降到94.213-0.25=93.963。為了檢驗(yàn)這個預(yù)測的準(zhǔn)確性，我們計(jì)算當(dāng)收益率增加10個基點(diǎn)到12.1%時的債券價格，其數(shù)量為：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

這一數(shù)值同久期公式預(yù)計(jì)的變化相同。例7-1由表7-3描述的債券價格為947.3.1ModifiedDurationWhentheyieldyisexpressedwithcompoundingmtimesperyear

()Theexpression

isreferredtoasthe“modifiedduration”RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull2009267.3.1ModifiedDurationWhent例7-2由表7-3描述的債券價格為94.213，久期為2.653，每年復(fù)利兩次的收益率為12.3673%，修正久期為：

=2.653/(1+0.123673/2)

=2.4985例7-2由表7-3描述的債券價格為94.213，久期為2277.3.2絕對額久期絕對額久期等于修正久期與債券價格的乘積：采用微分的記號為：7.3.2絕對額久期絕對額久期等于修正久期與債券價格的乘積28TheendTheend演講完畢，謝謝觀看！演講完畢，謝謝觀看！

InterestRateRiskChapter7RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200931

InterestRateRiskChapter77.1ManagementofNetInterestIncome

NetInterestIncome=Interestreceived-InterestpaidConsiderasimplesituationwhereabankoffersconsumersaone-yearandafive-yeardepositrateaswellasaone-yearandfive-yearmortgagerate.TheratesareshowninTable7.1:Maturity(yrs)DepositRateMortgageRate13%6%53%6%RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200932Table7.1Exampleofratesofferedbyabanktoitscustomers7.1ManagementofNetInterestTwoquestion:（1）WhatwouldhappenifabankpostedtheratesinTable7.1?（2）Howcanthebankmanageitsrisks?Twoquestion:33Assumption:

marketparticipantsexpecttheone-yearinterestrateforfuturetimeperiodstoequaltheone-yearratesprevailinginthemarkettoday.Supposeyouhavemoneytodeposit.Wouldyouchoosetodeposityourmoneyforoneyearat3%perannumorforfiveyearat3%perannum?Assumption:marketparticipant34Ifdepositoneyear:(1+3%)(1+3%)(1+3%)(1+3%)(1+3%)=(1+3%)5Ifdepositfiveyear:(1+3%)5Somostcustomerswouldchooseoneyearbecausethisgivesthemmorefinancialflexibility.Ittiesuptheirfundsforashorterperiodoftime.Ifdepositoneyear:35Nowsupposethatyouwantamortgage.Wouldyouchooseaone-yearmortgageat6%orafive-yearmortgageat6%?One-yearmortgage:(1+6%)(1+6%)(1+6%)(1+6%)(1+6%)=(1+6%)5Five-yearmortgage:(1+6%)5Somostwouldchooseafive-yearmortgagebecauseitfixesyourborrowingrateforthenextfiveyearsandsubjectsyoutolessrefinancingrisk.Nowsupposethatyouwantamo36由于多數(shù)客戶會選擇1年期存款，5年期貸款，所以，導(dǎo)致銀行的資產(chǎn)與負(fù)債的不匹配（短借長放現(xiàn)象），從而對凈利息收入產(chǎn)生風(fēng)險(xiǎn)沖擊。若利率下降，貸款利率6%，存款利率低于3%，利息收入增加。若利率上升，貸款利率6%，存款利率高于3%，利息收入減少?！锟偨Y(jié)由于多數(shù)客戶會選擇1年期存款，5年期貸款，所以，導(dǎo)致銀行的資37解決方案：實(shí)現(xiàn)資產(chǎn)負(fù)債匹配。Maturity(yrs)DepositRateMortgageRate13%6%54%7%表7-2提高5年期利率以達(dá)到資產(chǎn)負(fù)債的匹配解決方案：實(shí)現(xiàn)資產(chǎn)負(fù)債匹配。Maturity(yrs)De38BadInterestRateRiskManagementHasLedtoBankFailures

(BusinessSnapshot7.1,page101)RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200939BadInterestRateRiskManagem7.2LIBORRatesandSwapRatesLIBORratesare1-,3-,6-,and12-monthborrowingratesforcompaniesthathaveaAA-ratingSwapRatesarethefixedratesexchangedforfloatinginaninterestrateswapagreementRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull2009407.2LIBORRatesandSwapRatesLIBORratesareprovidedbyBritishBankersAssociation(BBA).TheBBAistheleadingtradeassociationfortheUKbankingandfinancialservicessector.Wespeakforover200memberbanksfrom60countriesonthefullrangeofUKandinternationalbankingissues.LIBORratesareprovidedbyBrUnderstandingBBALIBORLIBORratescloselyreflecttherealratesofinterestbeingusedbytheworld'slargestfinancialinstitutions.Whereascentralbanks(suchastheBankofEngland,theUSFederalReserveandtheEuropeanCentralBank)fixofficialbaseratesmonthly,LIBORreflectstheratesatwhichtheseprimebanksborrowmoneyfromeachothereachday,intheworld's10majorcurrenciesandfor15borrowingperiodsrangingfromovernightloansto12month.Oncecalculated,theLIBORfiguresarethenpublishedbyThomsonReuters:theyappearonmorethanonemillionscreensaroundtheworldandarewidelyreportedinthepress,thewireservicesandonline.ThomsonReutersundertakesthisworkfortheBritishBankers'Association.UnderstandingBBALIBORLIBORHowisitcalculated?Eachdayat11:00hrsLondontimethebankswhichcontributetotheLIBOR-settingprocesssendtheirinterbankborrowingratesconfidentiallytoThomsonReuters.ThomsonReutersdiscardsthehighestandlowestcontributions(thetopandbottomquartiles)andthenusesthemiddletwoquartilestocalculateanaverage.TheAustralianDollar,DanishKrone,NewZealandDollarandSwedishKronepanelshaveeightbanks,TheCanadianDollarandSwissFrancpanelshave12banks.TheSterling,YenandEuropanelshave16membersandtheUSDollarpanelhas19members.Eachfollowsthesameprocedureofdiscardingtheupperandlowerquartilesandaveragingthecentrequartilestocreatearate.Howisitcalculated?EachdayHowdiditbecomesoimportant?LIBORwasfirstdevelopedinthe1980sasdemandgrewforanaccuratemeasureoftherateatwhichbankswouldlendmoneytoeachother.ThisbecameincreasinglyimportantasLondon'sstatusgrewasaninternationalfinancialcentre.Morethan20percentofallinternationalbanklendingandmorethan30percentofallforeignexchangetransactionsnowtakeplaceinLondon.LIBORratesarethebasisforarangeoffinancialinstruments:derivativesbasedontheLIBORratesarenowtradedonexchangessuchasLIFFEandtheChicagoMercantileExchange(CME)aswellasover-the-counter.Theratesarealsousedasthebasisformanytypesoflending,fromsyndicatedandcommerciallending,toresidentialmortgages.HowdiditbecomesoimportantSHIBORratesShibor全稱是“上海銀行間同業(yè)拆放利率”（ShanghaiInterbankOfferedRate，SHIBOR），被稱為中國的LIBOR（LondonInterbankOfferedRate，倫敦同業(yè)拆放利率），自2007年1月4日正式運(yùn)行。Shibor是由信用等級較高的銀行組成報(bào)價團(tuán)自主報(bào)出的人民幣同業(yè)拆出利率計(jì)算確定的算術(shù)平均利率，是單利、無擔(dān)保、批發(fā)性利率。目前，對社會公布的Shibor品種包括隔夜、1周、2周、1個月、3個月、6個月、9個月及1年。上海首批16家報(bào)價行分別為：工商銀行，農(nóng)業(yè)銀行，中國銀行，建設(shè)銀行，交通銀行，興業(yè)銀行，浦發(fā)銀行，北京銀行，上海銀行，招商銀行，光大銀行，中信銀行，南京商行，德意志上海，匯豐上海，渣打上海。

2010年5月，廣發(fā)銀行也成為SHIBOR基準(zhǔn)利率互換業(yè)務(wù)報(bào)價行。

SHIBORratesShibor全稱是“上海銀行間同業(yè)拆WhySwapRatesAreanAverageofLIBORForwardRatesAbankcanLendtoaseriesAA-ratedborrowersfortensuccessivesixmonthperiodsSwaptheLIBORinterestreceivedtothefive-yearswaprateItcanLendtoacertainprincipalforsixmonthstoaAAborrowerandrelenditforninesuccessivesix-monthperiodstoAAborrowers;andEnterintoaswaptoexchangetheLIBORforthefive-yearswaprate.RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200946WhySwapRatesAreanAverageExtendingtheLIBORCurveAlternative1:CreateatermstructureofinterestratesshowingtherateofinterestatwhichaAA-ratedcompanycanborrowfor1,2,3…yearsAlternative2:UseswapratessothatthetermstructurerepresentsfutureshorttermAAborrowingratesAlternative2istheusualapproach.ItcreatestheLIBOR/swaptermstructureofinterestratesRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200947ExtendingtheLIBORCurveAlterLIBORVSTreasuryRateTherisk-freerateisimportantinthepricingoffinancialcontracts.TheusualpracticeamongfinancialinstitutionsistoassumethattheLIBOR/swapyieldcurveprovidestherisk-freerate.TheTreasurycurveisabout50basispointsbelowtheLIBOR/swapzerocurveRiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull200948LIBORVSTreasuryRateTheriskTreasuryratesareconsideredtobeartificiallylowforavarietyofregulatoryandtaxreasonsTreasuryratesareconsidered7.3Duration(page102)利率久期用于檢驗(yàn)交易組合對利率曲線的風(fēng)險(xiǎn)暴露。假設(shè)債券收益率為y，債券價格為B，債券久期的定義為：

或等價于：

(7-1)式中，△y為債券收益率的一個小的變化，△B為相應(yīng)債券價格的變化。 RiskManagementandFinancialInstitutions,2e,Chapter7,Copyright?JohnC.Hull2009507.3Duration(page102)利率久期用于檢DurationContinued債券久期用于檢測債券價格對收益率的敏感度。利用微積分的符號，有：

(7-2)假定一個債券在t1,t2,