利率风险实用PPT课件PPT课件

1、8.1 Management of Net Interest Income Net Interest Income=Interest received-Interest paid Consider a simple situation where a bank offers consumers a one-year and a five-year deposit rate as well as a one-year and five-year mortgage rate. The rates are shown in Table 8.1:Maturity (yrs)Deposit RateMo

2、rtgage Rate13%6%53%6%Risk Management and Financial Institutions, Copyright John C. Hull 1Table 8.1 Example of rates offered by a bank to its customers第1页/共36页 Two question:（1）What would happen if a bank posted the rates in Table 8.1?（2）How can the bank manage its risks?第2页/共36页 Assumption: market pa

3、rticipants expect the one-year interest rate for future time periods to equal the one-year rates prevailing in the market today. Suppose you have money to deposit. Would you choose to deposit your money for one year at 3% per annum or for five year at 3% per annum?第3页/共36页 If deposit one year: (1+3%

4、)(1+3%)(1+3%)(1+3%)(1+3%)=(1+3%)5 If deposit five year:(1+3%)5 So most customers would choose one year because this gives them more financial flexibility. It ties up their funds for a shorter period of time.（流动性偏好）第4页/共36页 Now suppose that you want a mortgage. Would you choose a one-year mortgage at

5、 6% or a five-year mortgage at 6%? One-year mortgage:(1+6%)(1+6%)(1+6%)(1+6%)(1+6%)=(1+6%)5 Five-year mortgage:(1+6%)5 So most would choose a five-year mortgage because it fixes your borrowing rate for the next five years and subjects you to less refinancing risk.第5页/共36页 由于多数客户会选择1年期存款，5年期贷款，所以，导致银

6、行的资产与负债的不匹配（短借长放现象短借长放现象），从而对净利息收入产生风险冲击。 若利率下降若利率下降，贷款利率6%，存款利率低于3%，利息收入增加利息收入增加。 若利率上升若利率上升，贷款利率6%，存款利率高于3%，利息收入减少利息收入减少。总结第6页/共36页解决方案：实现资产负债匹配。Maturity (yrs)Deposit RateMortgage Rate13%6%54%7%表8-2 提高5年期利率以达到资产负债的匹配第7页/共36页8.2 LIBOR Rates and Swap Rates LIBOR rates are 1-, 3-, 6-, and 12-month bo

7、rrowing rates for companies that have a AA-rating Swap Rates are the fixed rates exchanged for floating in an interest rate swap agreementRisk Management and Financial Institutions, Copyright John C. Hull 8第8页/共36页资料：资料： LIBOR rates and SHIBOR rateslLIBOR rates are provided by British Bankers Associ

8、ation (BBA).lThe BBA is the leading trade association for the UK banking and financial services sector. We speak for over 200 member banks from 60 countries on the full range of UK and international banking issues.第9页/共36页Understanding BBA LIBORlLIBOR rates closely reflect the real rates of interest

9、 being used by the worlds largest financial institutions. lWhereas central banks (such as the Bank of England, the US Federal Reserve and the European Central Bank) fix official base rates monthly, LIBOR reflects the rates at which these prime banks borrow money from each other each day, in the worl

10、ds 10 major currencies and for 15 borrowing periods ranging from overnight loans to 12 month. lOnce calculated, the LIBOR figures are then published by Thomson Reuters: they appear on more than one million screens around the world and are widely reported in the press, the wire services and online. l

11、Thomson Reuters undertakes this work for the British Bankers Association.第10页/共36页 How is it calculated? lEach day at 11:00 hrs London time the banks which contribute to the LIBOR-setting process send their interbank borrowing rates confidentially to Thomson Reuters. lThomson Reuters discards the hi

12、ghest and lowest contributions (the top and bottom quartiles) and then uses the middle two quartiles to calculate an average. lThe Australian Dollar, Danish Krone, New Zealand Dollar and Swedish Krone panels have eight banks, The Canadian Dollar and Swiss Franc panels have 12 banks. The Sterling, Ye

13、n and Euro panels have 16 members and the US Dollar panel has 19 members. Each follows the same procedure of discarding the upper and lower quartiles and averaging the centre quartiles to create a rate.第11页/共36页 How did it become so important? lLIBOR was first developed in the 1980s as demand grew f

14、or an accurate measure of the rate at which banks would lend money to each other. This became increasingly important as Londons status grew as an international financial centre. More than 20 per cent of all international bank lending and more than 30 per cent of all foreign exchange transactions now

15、 take place in London. lLIBOR rates are the basis for a range of financial instruments: derivatives based on the LIBOR rates are now traded on exchanges such as LIFFE and the Chicago Mercantile Exchange (CME) as well as over-the-counter. The rates are also used as the basis for many types of lending

16、, from syndicated and commercial lending, to residential mortgages. 第12页/共36页 SHIBOR rates lShibor全称是“上海银行间同业拆放利率”（Shanghai Interbank Offered Rate，SHIBOR），被称为中国的LIBOR（London Interbank Offered Rate，伦敦同业拆放利率），自2007年1月4日正式运行。 lShibor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Shibo

17、r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。 l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。 第13页/共36页Why Swap Rates Are an Average of LIBOR Forward Rates A bank can Lend to a series AA-rated borrowers for ten successive six mo

18、nth periods Swap the LIBOR interest received to the five-year swap rate It can Lend to a certain principal for six months to a AA borrower and relend it for nine successive six-month periods to AA borrowers; and Enter into a swap to exchange the LIBOR for the exchange the LIBOR for the five-year swa

19、p ratefive-year swap rate.Risk Management and Financial Institutions, Copyright John C. Hull 14第14页/共36页LIBOR VS Treasury Rate The risk-free rate is important in the pricing of financial contracts. The usual practice among financial institutions is to assume that the LIBOR/swap LIBOR/swap yield curv

20、e provides the risk-free rateyield curve provides the risk-free rate. . The Treasury curve is about 50 basis points below the Treasury curve is about 50 basis points below the LIBOR/swap zero curveLIBOR/swap zero curveRisk Management and Financial Institutions, Copyright John C. Hull 15第15页/共36页 Tre

21、asury rates are considered to be artificially low for a variety of regulatory and tax reasons第16页/共36页8.3 Duration 8.3 Duration 度量利率风险的常用指标是麦考利（Frederick Macaulay）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。Risk Management and Financial Institutions, Copyright

22、John C. Hull 17yDBBBDBy 第17页/共36页 久期的理解：久期的理解： l久期就是债券价格债券价格相对于利率水平利率水平正常变动的敏感度，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%。l久期越大，债券价格对利率的变动就越敏感，利率上升利率上升所引起的债券价格下降幅度债券价格下降幅度就越大越大，而利率下降利率下降所引起的债券价格上升幅度债券价格上升幅度也越大越大。l久

23、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。第18页/共36页Duration Continued 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：1d BDBd y 1nytiiiBc e 第19

24、页/共36页Duration Continued 求导 所以1nytiiiBc e 1/()nytiiiidB dycet11()iyniiitdBDB dyBc et (8-3)第20页/共36页Duration Continued 债券久期：11()iyniiitdBDB dyBc et 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)第21页/共36页Calculation of Duration for a 3-year bond

25、 paying a coupon 10%. Bond yield=12%. (Table 8.3) Risk Management and Financial Institutions, Copyright John C. Hull 22Time (yrs)Cash Flow ($)PV ($)WeightTime Weight0.554.7090.0500.0251.054.4350.0470.0471.554.1760.0440.0662.053.9330.0420.0832.553.7040.0390.0983.010573.2560.7782.333Total13094.2131.00

26、02.653第22页/共36页例例8-1:8-1: 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

27、+105e-0.121*3=93.963 这一数值同久期公式预计的变化相同。第23页/共36页8.3.1 Modified Duration When the yield y is expressed with compounding m times per year The expression is referred to as the “modified duration”Risk Management and Financial Institutions, Copyright John C. Hull 24myyBDB1Dy m1 第24页/共36页例例8-28-2 由表8-3描述的债

28、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) =2.49851DDy m第25页/共36页8.3.2 Dollar Duration8.3.2 Dollar Duration 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：$BDy $dBDdy 第26页/共36页8.4 Convexity 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

29、它们的价值变化呢？第27页/共36页图8-1 两个具备同样久期的交易组合B/By第28页/共36页 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。22211/inyiid BtCBiB dyec t 第29页/共36页 可得关于债券价格的两阶近似式（附录G ）： 由此： 2221()2dBdBByydydy21()2BDyCyB （8-4）注意：和久期公式对比！第30页/共36页例例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%，久期公式预期债券价值变化将是： -94.213*2.653*0.02=-4.999， 曲率关系式预计变化为： -94.213*2