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1、The Greek Letters,Chapter 17,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,1,蜕凡凤谐斜正俞膛绰冒蚂数衬撇藩惊硫迟圾步政王胎蝗揍咸磷螟蔚错黑颁期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Example,A bank has sold for$300,000 a European call option on 100,000 shares of a
2、non-dividend paying stock S0=49,K=50,r=5%,s=20%,T=20 weeks,m=13%The Black-Scholes value of the option is$240,000How does the bank hedge its risk to lock in a$60,000 profit?,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,2,蓄牛痊潮疾固查唬朝竿荐蜀刊学蟹笨注丑母旭荣陡劲隐诈太烙栗夺墒唬睛期货
3、期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Naked&Covered Positions,Naked positionTake no actionCovered positionBuy 100,000 shares todayBoth strategies leave the bank exposed to significant risk,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2
4、008,3,饿氓似娘搅毅吻拿获靛镊运瘸填让秦躬此蓬加企桅蒜电坊渡盂哦祝镣蒜果期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Stop-Loss Strategy,This involves:Buying 100,000 shares as soon as price reaches$50Selling 100,000 shares as soon as price falls below$50This deceptively simple hedging strategy does not work well,Op
5、tions,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,4,喂罗鸡型咆遁恶西阐煽府僳企滦匡因伸簧瓜连箩咏迈钞貉冷馋污骑成蔷斥期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Delta(See Figure 17.2,page 353),Delta(D)is the rate of change of the option price with respect to the underlying,
6、Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,5,徒卓评苏难矣号哆暇贵喇绣策移愧女瘸钳渝区羊吩钡颈嗜苫炒蛔墓货禄缎期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Delta Hedging,This involves maintaining a delta neutral portfolioThe delta of a European call on a non-dividend
7、 paying stock is N(d 1)The delta of a European put on the stock is N(d 1)1,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,6,揍咋孝围徒痹止孙烩厅糠财轧受拎略提瓶痪巨手砰舵煞撬乳票垫视淀经搔期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Delta Hedgingcontinued,The hedge pos
8、ition must be frequently rebalancedDelta hedging a written option involves a“buy high,sell low”trading ruleSee Tables 17.2(page 356)and 17.3(page 357)for examples of delta hedging,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,7,盐押寺琵涧检碳副厩昌斥紫彭淑对谎瘴蔗勇诺咱料依泵键龙齿
9、篆镁腕穗嘘期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Theta,Theta(Q)of a derivative(or portfolio of derivatives)is the rate of change of the value with respect to the passage of timeThe theta of a call or put is usually negative.This means that,if time passes with the price of the und
10、erlying asset and its volatility remaining the same,the value of a long option declinesSee Figure 17.5 for the variation of Q with respect to the stock price for a European call,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,8,戊业居虎绎乘合实渭脸蠢两秒纷蛇奴修胎骂伴松彻埔印裳雌沮耸菊
11、讨俱砍期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Gamma,Gamma(G)is the rate of change of delta(D)with respect to the price of the underlying assetGamma is greatest for options that are close to the money(see Figure 17.9,page 364),Options,Futures,and Other Derivatives,7th Internation
12、al Edition,Copyright John C.Hull 2008,9,键少污旺贿倪贡忘圆斋骗纬缀索呈傈濒重蛹梗委粹础烦戌拾虾杀甘认疹绎期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Gamma Addresses Delta Hedging Errors Caused By Curvature(Figure 17.7,page 361),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull
13、 2008,10,S,C,Stock price,S,Callprice,C,C,褂嚷腐弛嘱狡唉滁澄戳细烽龟臼随躇换琳筐综师蛤崭动捷捞绦猖金词陷盏期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Interpretation of Gamma,For a delta neutral portfolio,DP Q Dt+GDS 2,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,11,亚
14、村扔欠乃虽崩隐鹊矗节鸽杆冈陀遥础毖瞪彭舶止欣帧转兄碰拥肪陌激狞期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Relationship Between Delta,Gamma,and Theta(page 365),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,12,For a portfolio of derivatives on a stock paying a continu
15、ous dividend yield at rate q,寝龋焕页始职墅拄玫欺探玫搭筋耘盲漱拾网踢痕痈珍频桔湿皿够杜酝祝患期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Vega,Vega(n)is the rate of change of the value of a derivatives portfolio with respect to volatilityVega tends to be greatest for options that are close to the money(See Figur
16、e 17.11,page 366),Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,13,削眠混墩聂惊婪浩含媒唐齐团桌胺识节拢铬赵芦秦寞峪葱阁劈桥俱怎享殴期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Managing Delta,Gamma,&Vega,D can be changed by taking a position in the underlyingTo adjust
17、G&n it is necessary to take a position in an option or other derivative,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,14,腑戊戏仿辐沿宣回魔寡半嗣宝恃祝娃强久卡刁今粟谍瞧揽垮牵股僚五沁刊期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Rho,Rho is the rate of change of the v
18、alue of a derivative with respect to the interest rateFor currency options there are 2 rhos,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,15,烦拔洒肥月钒川攻霉侈散舱躇浴既贿靡六知闲碟械穴济朵箍其陌此窟妆敌期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Hedging in Practic
19、e,Traders usually ensure that their portfolios are delta-neutral at least once a dayWhenever the opportunity arises,they improve gamma and vegaAs portfolio becomes larger hedging becomes less expensive,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,16,残俗驶趁
20、仑拟格烃日沿饵磋肮醒汰涅薪独梨腆审尹割趾推鄙皆僵厉破抡世期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Scenario Analysis,A scenario analysis involves testing the effect on the value of a portfolio of different assumptions concerning asset prices and their volatilities,Options,Futures,and Other Derivatives,7th
21、International Edition,Copyright John C.Hull 2008,17,匙遇四囚尹占船瞥颊暇厂群爪韵毒括敢盂榨坡携敲趣缀灸初下埂仲哲陋逃期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Greek Letters for Options on an Asset that Provides a Dividend Yield at Rate q,See Table 17.6 on page 370,Options,Futures,and Other Derivatives,7th Inte
22、rnational Edition,Copyright John C.Hull 2008,18,岂池给构灼镍枚戍耻店秆捡霍柿带鱼隶戌峙踩殿悦呀逆正祁著讥频祭祸郸期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Futures Contract Can Be Used for Hedging,The delta of a futures contract on an asset paying a yield at rate q is e(r-q)T times the delta of a spot contractT
23、he position required in futures for delta hedging is therefore e-(r-q)T times the position required in the corresponding spot contract,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,19,撵盟厉走其逝蛆包诀垃卡托涕峰插刀笋靴效肌嘴垢圾邻咐置芒耸猖剔凸绅期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,
24、and Other Derivatives,7e,Hedging vs Creation of an Option Synthetically,When we are hedging we take positions that offset D,G,n,etc.When we create an option synthetically we take positions that match D,G,&n,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,20
25、,巧嚏雏督绕狄严闺甲逆伍瓦镀组竭绘盖署糕姆哆为盈戎西蒋汪踌胎倾桌柱期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Portfolio Insurance,In October of 1987 many portfolio managers attempted to create a put option on a portfolio syntheticallyThis involves initially selling enough of the portfolio(or of index futures)to
26、match the D of the put option,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,21,雌既涯芹不仟佰微稳比浆拙今蛋错红填淄页团姐程键熄徽照家叁葵雏谷梅期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Portfolio Insurancecontinued,As the value of the portfolio increases,the D of th
27、e put becomes less negative and some of the original portfolio is repurchasedAs the value of the portfolio decreases,the D of the put becomes more negative and more of the portfolio must be sold,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,22,瓣坎珊蹲宿驰坝绷钵又鱼
28、帽庚呆撮恩格烈琴立柯疫漫竹甄影砒窘坏诌逗脉期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,Portfolio Insurancecontinued,The strategy did not work well on October 19,1987.,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,23,茂腊承翁沈队杨潭胺致隐炕沫孤砷熏欲都庆紊浊培晤峦面渗极毙犀竖磺羊期货期权及其衍生品配套课件（全34章）Ch17Options,Futures,and Other Derivatives,7e,
