期货期权及其衍生品配套课件全34章Ch13.ppt

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1、The Black-Scholes-Merton Model,Chapter 13,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,1,驳穆买劈轧墒总据骆附屯冰能儿篱靠秧饥任越翱吼疥渔脓蛊异套分扬藤漂期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Stock Price Assumption,Consider a stock whose price is SIn a shor

2、t period of time of length Dt,the return on the stock is normally distributed:where m is expected return and s is volatility,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,2,强缺嚼饼仰蝗覆儒腿览毗拢虫靴骚瞧潍孩躲坎惫弃募峻肢郴范蓉邑弛凝介期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other D

3、erivatives,7e,The Lognormal Property(Equations 13.2 and 13.3,page 278),It follows from this assumption that Since the logarithm of ST is normal,ST is lognormally distributed,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,3,减湿兆皮倍缓列撵撅骋志敢棉蹲申衰造哨裙材纽果章读埠惯皂晓睡然俐栏期

4、货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Lognormal Distribution,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,4,鸥杰姻帆镶昨补黔庙穆牛但稗胀赎终漱泪坝冒抄哟洋杖仆腺忙萄炊鹊揍隆期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Continuously Compound

5、ed Return(Equations 13.6 and 13.7),page 279),If x is the continuously compounded return,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,5,蜕骇仰蝶搅喝跌滑绦员琢藏祸情院仿鼠闷锐寝筋寒匣颈招猛谢懊具削铰钵期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Expected Return,The

6、 expected value of the stock price is S0emTThe expected return on the stock is m s2/2 not mThis is because are not the same,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,6,饿凸卖尿怨驯厨小徘亚香牌耀柄尺件纬煮弄苔棕圃嘛喝议亏妮惶韭苛言细期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other De

7、rivatives,7e,m and ms2/2,Suppose we have daily data for a period of several monthsm is the average of the returns in each day=E(DS/S)ms2/2 is the expected return over the whole period covered by the data measured with continuous compounding(or daily compounding,which is almost the same),Options,Futu

8、res,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,7,疹栗著率碎蜡叠眨掩辰磺颅孕牟棠杆呀熔撩馒践哥弓济烂亩廖忠竞兹篮涂期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Mutual Fund Returns(See Business Snapshot 13.1 on page 281),Suppose that returns in successive years are 15%,20%,30%,-20%an

9、d 25%The arithmetic mean of the returns is 14%The returned that would actually be earned over the five years(the geometric mean)is 12.4%,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,8,汽拣烤峭侗卓蜂娱矾狭尹傲僵喊劲膜铬泛型砖危郴密杰康汗媚伦贮募采喘期货期权及其衍生品配套课件（全34章）Ch13Options,Futures

10、,and Other Derivatives,7e,The Volatility,The volatility is the standard deviation of the continuously compounded rate of return in 1 yearThe standard deviation of the return in time Dt is If a stock price is$50 and its volatility is 25%per year what is the standard deviation of the price change in o

11、ne day?,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,9,竖醇嫩咒夺起渝毅诬席胃棚邻拣肘绷怔仍磨寸河踌汹硕错湃生厩阑仰棘瓮期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Estimating Volatility from Historical Data(page 282-84),Take observations S0,S1,.,Sn at intervals of t

12、yearsCalculate the continuously compounded return in each interval as:Calculate the standard deviation,s,of the uisThe historical volatility estimate is:,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,10,实扎淳枫膜佣舵憋诈童囤听拼档赋镰污敦随挫阮再碑恨骸状口激镍旷饵木期货期权及其衍生品配套课件（全34章）C

13、h13Options,Futures,and Other Derivatives,7e,Nature of Volatility,Volatility is usually much greater when the market is open(i.e.the asset is trading)than when it is closedFor this reason time is usually measured in“trading days”not calendar days when options are valued,Options,Futures,and Other Deri

14、vatives,7th International Edition,Copyright John C.Hull 2008,11,氰乱鞘挡著爬酞杖瘴殖付委棘茶径奢截凹隋差异禾滁饺苞粥敖绰凹竿久焰期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Concepts Underlying Black-Scholes,The option price and the stock price depend on the same underlying source of uncertaintyWe can form a

15、portfolio consisting of the stock and the option which eliminates this source of uncertaintyThe portfolio is instantaneously riskless and must instantaneously earn the risk-free rateThis leads to the Black-Scholes differential equation,Options,Futures,and Other Derivatives,7th International Edition,

16、Copyright John C.Hull 2008,12,货矮齿偷拉饺缀陈限吻蝴龋眠黄刨孪中恫执矫告后轴夸格算热吕糊扇纠祟期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Derivation of the Black-Scholes Differential Equation,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,13,孙镣歹孔计酚替察徽粪早诱憋渣趋棒鄙翻滚蔷陋看

17、锅梢疹惦耽曾蒸粱灼啄期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Derivation of the Black-Scholes Differential Equation continued,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,14,拷煤坯颇烛疙距将改辫洗停藕仿镁讥逮绪撩住烘押些呛瓶糙痉炔铺秃统赞期货期权及其衍生品配套课件（全34章）Ch13Options,F

18、utures,and Other Derivatives,7e,The Derivation of the Black-Scholes Differential Equation continued,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,15,虐堂仪署骏氓客股索携广梭扣军茹酣驯蛙看喇啥箍驼楔咕穷跨里蔑锥扁膏期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Differ

19、ential Equation,Any security whose price is dependent on the stock price satisfies the differential equationThe particular security being valued is determined by the boundary conditions of the differential equationIn a forward contract the boundary condition is=S K when t=T The solution to the equat

20、ion is=S K er(T t),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,16,锨赋拓蓖倪摹寐搭谢途邓拴昔嫡贡代霸爬节捷韩煎蛊经贪羚瞩评态榴镣豪期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Black-Scholes Formulas(See pages 291-293),Options,Futures,and Other Derivatives,7th Int

21、ernational Edition,Copyright John C.Hull 2008,17,普左嘘鲁诈雹蝶衙泞咬吐转按榷肺鸽尹夺郎槛朔序矣疯户缴炔浅启再陡疤期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The N(x)Function,N(x)is the probability that a normally distributed variable with a mean of zero and a standard deviation of 1 is less than xSee tables at

22、the end of the book,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,18,痈动席蜘所啃片和榜宅蛾多奎葱匿褪估字兢脂撤歪些伤伤蔷剪极澄雾彼驱期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Properties of Black-Scholes Formula,As S0 becomes very large c tends to S0 Ke-rT and p ten

23、ds to zeroAs S0 becomes very small c tends to zero and p tends to Ke-rT S0,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,19,幅坏递滁宇蚌参壹竭姚瓷盗彬鹏喊齿淑抿腥件沮廖仪藏韧履茄诣续泛创啼期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Risk-Neutral Valuation,The variable

24、 m does not appearin the Black-Scholes equationThe equation is independent of all variables affected by risk preferenceThe solution to the differential equation is therefore the same in a risk-free world as it is in the real worldThis leads to the principle of risk-neutral valuation,Options,Futures,

25、and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,20,湍菇座明掘绦宗蜜轩弘蒜帛渔搀工赢凿拖剁芹滓般新委轮卤征饱缉栏召丝期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Applying Risk-Neutral Valuation(See appendix at the end of Chapter 13),1.Assume that the expected return from the stock price

26、is the risk-free rate2.Calculate the expected payoff from the option3.Discount at the risk-free rate,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,21,滓群札娄杰檄柿接昨擂倾俘蒜法搅伺意谈挝固磁丫歹葵昔虎罚图沮谴心威期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Valuing a

27、 Forward Contract with Risk-Neutral Valuation,Payoff is ST KExpected payoff in a risk-neutral world is S0erT KPresent value of expected payoff is e-rTS0erT K=S0 Ke-rT,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,22,涨狐嫂衔墅挪殷译即绞侧革稚赢预淑曙俱善竭措镜谜牢碗淤被展干俺份芹期货期权及其衍

28、生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Implied Volatility,The implied volatility of an option is the volatility for which the Black-Scholes price equals the market priceThere is a one-to-one correspondence between prices and implied volatilitiesTraders and brokers often quote impli

29、ed volatilities rather than dollar prices,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,23,茧模寞恩疫交箭脚捌揩单四垣某慨绿稿糟迸渍牲团辙盏耻冯雇酶钞雌庶佩期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The VIX S&P500 Volatility Index,Chapter 24 explains how the index is

30、 calculated,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,24,敷池曹聚另冒季凉痘崇粥逛惯弱蛔辙窿阀坡短徽旧准贞笋姑译窝陕角八金期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,An Issue of Warrants&Executive Stock Options,When a regular call option is exercised the stock tha

31、t is delivered must be purchased in the open marketWhen a warrant or executive stock option is exercised new Treasury stock is issued by the companyIf little or no benefits are foreseen by the market the stock price will reduce at the time the issue of is announced.There is no further dilution(See B

32、usiness Snapshot 13.3.),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,25,语涂疵遂递缕茧网惋啡秸陷膏赖扮令秆虐琴士妒狗寄葛汕时瑚木博此胀吓期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,The Impact of Dilution,After the options have been issued it is not necessary to take

33、account of dilution when they are valuedBefore they are issued we can calculate the cost of each option as N/(N+M)times the price of a regular option with the same terms where N is the number of existing shares and M is the number of new shares that will be created if exercise takes place,Options,Fu

34、tures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,26,份冯赫经夫乎皆捡轮勤埠萍岸聪么酷署编啡千苍酌授孜胃茁影鉴臭希埋牲期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,Dividends,European options on dividend-paying stocks are valued by substituting the stock price less the present value o

35、f dividends into Black-ScholesOnly dividends with ex-dividend dates during life of option should be included The“dividend”should be the expected reduction in the stock price expected,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,27,谜刮妮圣孜埔徊扰官透浮舷墨蔷芍瘸寓荧拘矮蛆滥入

36、甚浩橡磁挝午峙擦榔期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,American Calls,An American call on a non-dividend-paying stock should never be exercised earlyAn American call on a dividend-paying stock should only ever be exercised immediately prior to an ex-dividend dateSuppose dividend da

37、tes are at times t1,t2,tn.Early exercise is sometimes optimal at time ti if the dividend at that time is greater than,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,28,悦裙谎版熔驶热渝骡倍祥骋呵桔炮哺毗梅放如骏瓜屯勇叶樟疾拳花绑杜庚期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivat

38、ives,7e,Blacks Approximation for Dealing withDividends in American Call Options,Set the American price equal to the maximum of two European prices:1.The 1st European price is for an option maturing at the same time as the American option2.The 2nd European price is for an option maturing just before the final ex-dividend date,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,29,魄挖辙浓臣焰咆详琵谓虽樟苛知垮驱压湛秃莱损孩襟肉欢讲弱拣虑肛趟寺期货期权及其衍生品配套课件（全34章）Ch13Options,Futures,and Other Derivatives,7e,