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1、Interest Rates,Chapter 4,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,1,首磷疵怪依酷蹄氯显涎曝仕戏凹兼碾垃豹湿练荡栓精捎脾舅帅厂札象晋公期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Types of Rates,Treasury ratesLIBOR ratesRepo rates,Options,Futures,and Other Derivativ
2、es 7th International Edition,Copyright John C.Hull 2008,2,沿嘿事外从韭载翅任徒茎绰丙丰荚映终归眩掖亨疆体独营吼根烷闽沏鼎恐期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Measuring Interest Rates,The compounding frequency used for an interest rate is the unit of measurementThe difference between quarterly and annual
3、 compounding is analogous to the difference between miles and kilometers,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,3,砂柯娇炎裳扁帖山旭洗互祝型圾炉贝昏挠届子横糕驭惭汉泳罕回访膨宾赐期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Continuous Compounding(Page 77),In the
4、 limit as we compound more and more frequently we obtain continuously compounded interest rates$100 grows to$100eRT when invested at a continuously compounded rate R for time T$100 received at time T discounts to$100e-RT at time zero when the continuously compounded discount rate is R,Options,Future
5、s,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,4,妙历芦帧叶仲鸦佃篱食轰宅闽近涵穆歧抚湿帛减陇羔析龟梁棍搁踊糜锡玩期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Conversion Formulas(Page 77),DefineRc:continuously compounded rateRm:same rate with compounding m times per year,Options,Futu
6、res,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,5,藤报拨纯萄用忽雨凳臀烁摧攀访妊靠朵桔梳巡尸其瘪狞库靠汗蔡门袍溢滩期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Zero Rates,A zero rate(or spot rate),for maturity T is the rate of interest earned on an investment that provides a payoff
7、only at time T,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,6,抵冈呛刺窃姓似柔沾主郸蝉黍祷抖鉴烂峭生楷气豌料惟像蔬侮钵镁愉叼悸期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Example(Table 4.2,page 79),Options,Futures,and Other Derivatives 7th International Edition,Copyr
8、ight John C.Hull 2008,7,刽悼协饼旭境济帘肠募妻遁佳拙侧揍扰抡舅惠嗅痒莉铜毅颧舰献拖盎朵原期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Bond Pricing,To calculate the cash price of a bond we discount each cash flow at the appropriate zero rateIn our example,the theoretical price of a two-year bond providing a 6%coup
9、on semiannually is,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,8,臆迄郁艳像抿蟹甘勿旅缠口酋疡窿锚武搽柬过饮幌砒蜗恢慕河缠胡君颤戈期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Bond Yield,The bond yield is the discount rate that makes the present value of the cash flow
10、s on the bond equal to the market price of the bondSuppose that the market price of the bond in our example equals its theoretical price of 98.39The bond yield(continuously compounded)is given by solving to get y=0.0676 or 6.76%.,Options,Futures,and Other Derivatives 7th International Edition,Copyri
11、ght John C.Hull 2008,9,九穿渡蝶峭锚婶侈道邱貌讯森帕鹿挣托诞燕拣猎剃秉幻意忆柯话膨陇与牧期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Par Yield,The par yield for a certain maturity is the coupon rate that causes the bond price to equal its face value.In our example we solve,Options,Futures,and Other Derivatives 7t
12、h International Edition,Copyright John C.Hull 2008,10,刨浆旺烟板砾莽愤寻描赖门耕曲富蛰泵故劝洒移踢章送岁峰肩湛锄躁襟瑰期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Par Yield continued,In general if m is the number of coupon payments per year,P is the present value of$1 received at maturity and A is the present va
13、lue of an annuity of$1 on each coupon date,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,11,详垣焰编耪浴念埋滑荷车郊丽竭猴讫饵盈轮生脱疯样泻忙亩褥芍邻索磕楞期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Sample Data(Table 4.3,page 80),Options,Futures,and Other Derivative
14、s 7th International Edition,Copyright John C.Hull 2008,12,Bond,Time to,Annual,Bond Cash,Principal,Maturity,Coupon,Price,(dollars),(years),(dollars),(dollars),100,0.25,0,97.5,100,0.50,0,94.9,100,1.00,0,90.0,100,1.50,8,96.0,100,2.00,12,101.6,昨延站楞镁俗弊廖敞冻搅韭娇甜愉泼澄硒郴讲熟图触膨洞丫傅寇畔汾日需期货期权及其衍生品配套课件（全34章）Ch04Optio
15、ns,Futures,and Other Derivatives,7e,The Bootstrap Method,An amount 2.5 can be earned on 97.5 during 3 months.The 3-month rate is 4 times 2.5/97.5 or 10.256%with quarterly compoundingThis is 10.127%with continuous compoundingSimilarly the 6 month and 1 year rates are 10.469%and 10.536%with continuous
16、 compounding,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,13,尉迷醒快妄埔颧辜巷肃痈厄喘口充签坐澎掐草肖频蜀蓖乎验耶友帝吝店踏期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,The Bootstrap Method continued,To calculate the 1.5 year rate we solve to get R=0.10681 or 10.681
17、%Similarly the two-year rate is 10.808%,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,14,捞袍派碗韦茵塌犯歹酱禹革矗竖破氓接写记诊钉帮唬殉啦品料地广男侮姑期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Zero Curve Calculated from the Data(Figure 4.1,page 82),Options,Future
18、s,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,15,Zero Rate(%),Maturity(yrs),10.127,10.469,10.536,10.681,10.808,彭漠谍这盅别信浓诽拍压蕊康仲邮才熊晃尼鄙贵击陆务渡冀厚呕丰硒袄涎期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Forward Rates,The forward rate is the future zero rate implied
19、 by todays term structure of interest rates,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,16,罗北厂切扩碟邹鲸莲绿电爹场豁宅栗抽蚂贺惟异盈套夹监悯永库末畅翔平期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Calculation of Forward Rates Table 4.5,page 83,Options,Futures,and
20、 Other Derivatives 7th International Edition,Copyright John C.Hull 2008,17,n-year,Forward Rate,zero rate,for,n,th Year,Year(,n,),(%per annum),(%per annum),1,3.0,2,4.0,5.0,3,4.6,5.8,4,5.0,6.2,5,5.3,6.5,朔哟拐旭韭壤尹敢岁霉裳版胯槐倪吉关梦霜鸿役乓亭言艺馈航拾弓型惠结期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,For
21、mula for Forward Rates,Suppose that the zero rates for time periods T1 and T2 are R1 and R2 with both rates continuously compounded.The forward rate for the period between times T1 and T2 is,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,18,残春缅胸腻愧治傲枣贱航痒站赫浑
22、么或露照杯晚糜虞风低朴脚犁瞬讲鹿间期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Instantaneous Forward Rate,The instantaneous forward rate for a maturity T is the forward rate that applies for a very short time period starting at T.It is where R is the T-year rate,Options,Futures,and Other Derivativ
23、es 7th International Edition,Copyright John C.Hull 2008,19,捍酮瓣缆税杆屑奔囱领国音龄歧格释瞄会冤吐渤驯饵漳顶阐蜒媒金驶高碉期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Upward vs Downward SlopingYield Curve,For an upward sloping yield curve:Fwd Rate Zero Rate Par YieldFor a downward sloping yield curvePar Yield Z
24、ero Rate Fwd Rate,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,20,溺证傲浚唯庭瘁烫媳前香升积溅了灯猖松蚌眷圣疯鲜愤党磨颤膘贷停袄蔷期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Forward Rate Agreement,A forward rate agreement(FRA)is an agreement that a certain rate will
25、 apply to a certain principal during a certain future time period,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,21,绽撰凹硫想溺聂格相斩炸建煮讥读峡馏惺哩绅屋汗录坏熙估烂掘昨董制趟期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Forward Rate Agreementcontinued,An FRA is eq
26、uivalent to an agreement where interest at a predetermined rate,RK is exchanged for interest at the market rateAn FRA can be valued by assuming that the forward interest rate is certain to be realized,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,22,安卉茶冷报
27、陆楔绒仟还刺渊涅乱匝勇侦汉综叠靡伎应宾恍膨词接坏喘俭涎期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Valuation Formulas(equations 4.9 and 4.10,pages 86-87),Value of FRA where a fixed rate RK will be received on a principal L between times T1 and T2 is L(RKRF)(T2T1)exp(-R2T2)Value of FRA where a fixed rate is
28、paid isL(RFRK)(T2T1)exp(-R2T2)RF is the forward rate for the period and R2 is the zero rate for maturity T2What compounding frequencies are used in these formulas for RK,RF,and R2?,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,23,斧荆辛束纸巫敦匪佑谷帧何落祖泞粟碗搓刷代掩造疏库边
29、归誓懦殷譬爵岿期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Duration(page 87-88),Duration of a bond that provides cash flow ci at time ti iswhere B is its price and y is its yield(continuously compounded)This leads to,Options,Futures,and Other Derivatives 7th International Edition,Copyrig
30、ht John C.Hull 2008,24,劝颐缕误梁锹乘锈浇腕析致棍侦痢鳃庚沸寓篙用侥喜雌搀违笛躲赶丛蔓郎期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Duration Continued,When the yield y is expressed with compounding m times per yearThe expression is referred to as the“modified duration”,Options,Futures,and Other Derivatives 7th I
31、nternational Edition,Copyright John C.Hull 2008,25,售但痪峡唱啄亲痞幸椭涸秀型磺余而睁瘫炳寸橙芝盆弟咋往格东猩混澳疗期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Convexity,The convexity of a bond is defined as,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,26,咋逻遗绊俐蔑氰伐竭嘛斩
32、泰拓聚司弯子刺继握摈哦坷钮垢铝再骡久蘸芭穿期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Theories of the Term StructurePage 91-92,Expectations Theory:forward rates equal expected future zero ratesMarket Segmentation:short,medium and long rates determined independently of each otherLiquidity Preference T
33、heory:forward rates higher than expected future zero rates,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,27,鸿癣射万增息送唐簿臼雅心慈殆盼呸鲜鬃靡烙馁窿兴绑视搞班跪仗缘琼饺期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,Liquidity Preference Theory,Suppose that the outloo
34、k for rates is flat and you have been offered the following choicesWhich would you choose as a depositor?Which for your mortgage?,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,28,粳父锚杂燥辗枕妻蓝箕猴涩藩剩炔蔗海肉圭吭舍喜汀窄愿忻爬对锚才馏藻期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and O
35、ther Derivatives,7e,Liquidity Preference Theory cont,To match the maturities of borrowers and lenders a bank has to increase long rates above expected future short ratesIn our example the bank might offer,Options,Futures,and Other Derivatives 7th International Edition,Copyright John C.Hull 2008,29,痈主夫吝彦咀笔坎队得恐而舀脯烃寸围晃雹栅挟碾肿磨舔铬驮娇长鲍式逐期货期权及其衍生品配套课件（全34章）Ch04Options,Futures,and Other Derivatives,7e,
