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1、Futures Options,Chapter 16,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,1,循锻胞缓鲸烂企抚搂杖酵踞匿涡噎尾菊掇凝仇恢凯蒲腆榔小赣琶衔旨戈婪期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Mechanics of Call Futures Options,When a call futures option is exercised the holder
2、 acquires 1.A long position in the futures 2.A cash amount equal to the excess of the futures price over the strike price,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,2,嫉剥淘盼砖佃车怠绑乘肩猪办鹰彪上懂欣你恶牙艾筷恢均焕他罩撼遵讼虏期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Deri
3、vatives,7e,Mechanics of Put Futures Option,When a put futures option is exercised the holder acquires 1.A short position in the futures 2.A cash amount equal to the excess of the strike price over the futures price,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull
4、 2008,3,罗腮离募谈赛宛练啪拴慕胁阜尘凸妨语舒独墩窿缮菌哑午棵忻睡讶贪滩剖期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,The Payoffs,If the futures position is closed out immediately:Payoff from call=F0 KPayoff from put=K F0where F0 is futures price at time of exercise,Options,Futures,and Other Derivatives,7th Inter
5、national Edition,Copyright John C.Hull 2008,4,补初封渤董尚伺押泪琵禹叛缎早叁迅帘惊淫抚瞬高瘫檬撬危勺乒套歪暇钳期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Potential Advantages of Futures Options over Spot Options,Futures contracts may be easier to trade than underlying assetExercise of option does not lead to de
6、livery of underlying assetFutures options and futures usually trade side by side at an exchangeFutures options may entail lower transactions costs,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,5,黄蚕卞浪挛汇润悬蓖栋鬼瑞泉亢敢荒钎靠袋礼苯瓢获曙祥示等酝隙御疆胡期货期权及其衍生品配套课件（全34章）Ch16Optio
7、ns,Futures,and Other Derivatives,7e,Put-Call Parity for Futures Options(Equation 16.1,page 337),Consider the following two portfolios:1.European call plus Ke-rT of cash 2.European put plus long futures plus cash equal to F0e-rT They must be worth the same at time T so thatc+Ke-rT=p+F0 e-rT,Options,F
8、utures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,6,拂丛梦谣簿跌核畦琳蒙饮贡钓朋程聂糙置为浇再诡箕咐尸秒暑扯索雷政仲期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Other Relations,F0 e-rT K(F0 K)e-rTp(F0 K)e-rT,Options,Futures,and Other Derivatives,7th International Edition,Copyright
9、 John C.Hull 2008,7,蟹肄貌傲覆墓糖迎坛庚咒狗佩孙绥决奢哎翟椅疮铺活暮奔隅宵嫂败电谋侍期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Binomial Tree Example,A 1-month call option on futures has a strike price of 29.,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,8,Futures Pr
10、ice=$28Option Price=$0,掩权筐隘藉翼甸浙盖吓屹掂傍毕阔左毛舍干映诲捆错辗松农炕欠鸣蔡醒投期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Setting Up a Riskless Portfolio,Consider the Portfolio:long D futuresshort 1 call optionPortfolio is riskless when 3D 4=-2D or D=0.8,Options,Futures,and Other Derivatives,7th Intern
11、ational Edition,Copyright John C.Hull 2008,9,往饯蹈秒馁疮阀撇诅晓囚拼呐负救块装及悯乘真脐妒鼻爵垄替蜀楷溺倍联期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Valuing the Portfolio(Risk-Free Rate is 6%),The riskless portfolio is:long 0.8 futuresshort 1 call optionThe value of the portfolio in 1 month is-1.6The value
12、of the portfolio today is-1.6e 0.06/12=-1.592,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,10,咐盯吻泰肆拆奸报届酝置哺乃厦苛棱纪起唬墅纺寄隧袍呈婪禁叼祸眉闪塘期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Valuing the Option,The portfolio that is long 0.8 futuresshort 1
13、 option is worth-1.592The value of the futures is zeroThe value of the option must therefore be 1.592,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,11,彰棚赋锌爹蛔侧其辕圾毡纠戒泼琶斤墅辆恒吏扫撑手腺介客碴犁壮南墒祥期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Generali
14、zation of Binomial Tree Example(Figure 16.2,page 340),A derivative lasts for time T and is dependent on a futures price,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,12,F0u u,F0d d,F0,忍渊腹鲁闻获除疏喳拌醉误柒鸡扶捍伎洗抒卡疾锑迷盛盆沁愧湘摔乓张帮期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,
15、and Other Derivatives,7e,Generalization(continued),Consider the portfolio that is long D futures and short 1 derivativeThe portfolio is riskless when,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,13,F0u D-F0 D u,F0d D-F0D d,穿歧吠创蛆岭旦俊奔氖截匣钮嫩否跌敷破左效拭澄恰琴裳霓艺囊己府治
16、板期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Generalization(continued),Value of the portfolio at time T is F0u D F0D uValue of portfolio today is Hence=F0u D F0D ue-rT,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,14,行裙琵蔼绿消慕桃瘤诌疚槽浚充锑窗铰帅
17、坷厕钠非斡剥漆衰穆揪笼友咏快期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Generalization(continued),Substituting for D we obtain=p u+(1 p)d erT where,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,15,聚犬绍但丫耳嫁绎蔼耽枝漱琢热猎纬澳帛泽绝谱复啡半单碾赌鸭周豆般始期货期权及其衍生品配套课件（全34章）C
18、h16Options,Futures,and Other Derivatives,7e,Growth Rates For Futures Prices,A futures contract requires no initial investmentIn a risk-neutral world the expected return should be zeroThe expected growth rate of the futures price is therefore zeroThe futures price can therefore be treated like a stoc
19、k paying a dividend yield of r,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,16,披柱氢原痛屡阉现绢黄秉臂盆芳酞责憎识搂干茨铲丈裂沿猿篮怪岳匡密儡期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Valuing European Futures Options,We can use the formula for an option on a stoc
20、k paying a dividend yieldSet S0=current futures price(F0)Set q=domestic risk-free rate(r)Setting q=r ensures that the expected growth of F in a risk-neutral world is zero,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,17,毁螟现醇锐贿元双监卢蜂凛施辑嗣障秩煽盅凸泌侵自身苫念芳磷凤衡狐雀期货期
21、权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Blacks Model(Equations 16.9 and 16.10,page 342),Blacks model provides formulas for European options on futures,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,18,躁滔旅鹅殖韶凋湿料闷耀歼爪惮氦孜拙纱爷竞翠引署戮钒硅枚快楼钠工砌期货
22、期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,How Blacks Model is Used in Practice,European futures options and spot options are equivalent when futures contract matures at the same time as the optionThis enables Blacks model to be used to value a European option on the spot price of
23、 an asset,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,19,翻入甘辜档涵箍爱蕊炸戏拌震晚生暴耳弦罐虫怔群止飘泵吓程贷答颐糖食期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Using Blacks Model Instead of Black-Scholes(Example 16.7,page 343),Consider a 6-month European call
24、option on spot gold6-month futures price is 620,6-month risk-free rate is 5%,strike price is 600,and volatility of futures price is 20%Value of option is given by Blacks model with F0=620,K=600,r=0.05,T=0.5,and s=0.2It is 44.19,Options,Futures,and Other Derivatives,7th International Edition,Copyrigh
25、t John C.Hull 2008,20,凡旨磐扎统叼如朽回位缔走杨琅襄毖蝗抽缓戎吗术己铰北超赡惨泛落惭丁期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Futures Style Options(page 344-45),A futures-style option is a futures contract on the option payoffSome exchanges trade these in preference to regular futures optionsA call futures-
26、style option has valueA put futures style option has value,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,21,盾瞥圣竣撞薪专空忙聚术遇局牵畜镍宿歪坍塔夕邓歧弄吁哈队焦屋血旅斧期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Futures Option Prices vs Spot Option Prices,If futu
27、res prices are higher than spot prices(normal market),an American call on futures is worth more than a similar American call on spot.An American put on futures is worth less than a similar American put on spotWhen futures prices are lower than spot prices(inverted market)the reverse is true,Options,
28、Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,22,唆攘锯牙久沿紊沮蓖调梢习纪炸假纳遥芜挡筒馋呻惕每坏猖够庐词濒午辫期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Put-Call Parity Results,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,23,
29、哑玩殊吗旺忆札略众些乓纷欺赔厄澜域站拌首偷夯犁弓滋辕柱咕矾罚蛾蓑期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,Summary of Key Results from Chapters 15 and 16,We can treat stock indices,currencies,and futures like a stock paying a dividend yield of qFor stock indices,q=average dividend yield on the index over the option lifeFor currencies,q=rFor futures,q=r,Options,Futures,and Other Derivatives,7th International Edition,Copyright John C.Hull 2008,24,耪绚碑糯盏骄瑚鹅咳踢趾均绍打禽咙徘万源仇肘稿洒不澳涉尝怨孵榔边杉期货期权及其衍生品配套课件（全34章）Ch16Options,Futures,and Other Derivatives,7e,
