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1、Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall1Chapter 14-15 Forward, Future and OptionObjectiveUnderstanding the definitions of forward, future and optionUnderstanding the basic idea ofsynthetic security断娇窗釜控蔗舒误颅朱趁兴征捐愿镐纳蠕痪便焦碾绰丢闻意胡褥术坎纤翻金融学教学课件chpt14-15金融学教学课件chpt14-151Copyright 2
2、009 Pearson Education, Inc. Publishing as Prentice Hall2Contents1 Distinction Between Forward & Futures Contracts2 Futures Price3 Financial future4 Definition of an option5 How an option works6 Two-state option-pricing看抖担钳彻骂眩阶魏紫佬轮徐逼责贼才丽拂皱锈取藐州旗姥罗腕钨揽妆垢金融学教学课件chpt14-15金融学教学课件chpt14-152Copyright 2009 Pe
3、arson Education, Inc. Publishing as Prentice Hall31 Distinction Between Forward & Futures Contracts Forward:Forward: parties agree to exchange some item in the future at a parties agree to exchange some item in the future at a delivery price specified nowdelivery price specified now the forward pric
4、e is defined as the delivery price which the forward price is defined as the delivery price which makes the current market value of the contract zeromakes the current market value of the contract zero no money is paid in the present by either party to the no money is paid in the present by either pa
5、rty to the otherother the face value of the contract is the quantity of the item the face value of the contract is the quantity of the item specified in the contract multiplied by the forward pricespecified in the contract multiplied by the forward price the party who agrees to buy the specified tak
6、es the the party who agrees to buy the specified takes the long position, and the party who agrees to sell the item long position, and the party who agrees to sell the item takes the short positiontakes the short position街翁热鲤己蹄允常哑熏燎寥视蹲妮哇侣述毕悲乐覆眨志哪伦精续道楔侯睫金融学教学课件chpt14-15金融学教学课件chpt14-153Who pays what
7、to whomIf the spot price on the contract maturity date is higher than the forward price, the party who is long makes money. But if the spot price on the contract maturity date is lower than the forward price, the party who is short makes money.救际侈胰惹良宫莆钠欣正捏绰励瑚卑蹿仟痊讲朝腕云岗倪签为夏允戒棍垛金融学教学课件chpt14-15金融学教学课件c
8、hpt14-154Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall5Future: terms Listing: Listing: Open, High, Low, Settle, Change, Lifetime high, Open, High, Low, Settle, Change, Lifetime high, Lifetime low, Open interestLifetime low, Open interest Mark-to-market at the end of each trading
9、 day Mark-to-market at the end of each trading day based on that days settlement price.based on that days settlement price. Margin requirement: Margin requirement: the exchange requires that there be enough the exchange requires that there be enough collateral posted in each account to cover any los
10、ses.collateral posted in each account to cover any losses. Margin call: Margin call: if the collateral in your account falls below a if the collateral in your account falls below a prespecified level, you will receive a margin call from prespecified level, you will receive a margin call from the bro
11、ker asking you to add money.the broker asking you to add money.莫拐伪桌踞舔饭密起箔栋郝沛镶塌幼拐署锨爬楷膏岿腕冶娜纬寐洋埃拷噬金融学教学课件chpt14-15金融学教学课件chpt14-155An illustrationBased on table 13.1.You place an order to take a long position in a July wheat futures contract on June 22, 2006. the broker requires you to deposit money in
12、 your account, say $1,500, as margin.On June 23, the future price closes 2.25cents per bushel lower, thus you have lost 1.25*5,000=$112.50 that day. The broker takes that amount out of your account (mark to market). The money is transferred to the exchange, which transfers it to one of the parties w
13、ho was on the short side of the contract.竞粉磐优槽闺管咒鹅蕾贱竣训钒馅直驻能缸偿洗爱引岛论迫恼咳爷辖汇人金融学教学课件chpt14-15金融学教学课件chpt14-156Daily realization of gains and lossesSuch a process minimizes the possibility of contract default. And no matter how great their face value, the market value of future contracts is always 0 at t
14、he beginning of each day.师洗道弥搪蝎崭娥出吮庇适施桅详唯戎渺扶淡础贪秃蜜谤改吧拉懒皮鞘哮金融学教学课件chpt14-15金融学教学课件chpt14-157Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall8Summarized characteristics for futurestandard contractsstandard contractsimmune from the credit worthiness of buyer immune from the credit wort
15、hiness of buyer and seller becauseand seller becauseexchange stands between tradersexchange stands between traderscontracts marked to market dailycontracts marked to market dailymargin requirementsmargin requirements檄绍擒询诲违重仲蚌蜒镣绚步蚌垦乍玛庸吉欢铰矗辽糠郧拔庐捉假萍腮侮金融学教学课件chpt14-15金融学教学课件chpt14-158Copyright 2009 Pear
16、son Education, Inc. Publishing as Prentice Hall92 Futures PriceArbitrageurs place an upper bound on futures prices by locking in a sure profit on futures prices if the spread between the futures price and spot price becomes greater than the cost of carry: F - S Cthe cost of carry varies as a functio
17、n of time and warehousing organization相遣题货哨法诫禽躁坐锰瓤险肘琵绕橇硅训亩船荫嘱孜镑筐株痪彻堪拓据金融学教学课件chpt14-15金融学教学课件chpt14-159Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall103 Financial FuturesWe now focus on financial futures standardized contracts for future delivery of standardized contracts for fut
18、ure delivery of stocks, bonds, indices, and foreign currency stocks, bonds, indices, and foreign currency they have no intrinsic value, but represent they have no intrinsic value, but represent claims on future cash flowsclaims on future cash flows they have very low storage coststhey have very low
19、storage costs settlement is usually in cashsettlement is usually in cash半谩蓬镶虹夷孺爵撬僳辱另缠俗新靡蔚野傈殖滇谴怎汤有腔枣备距遮荡阴金融学教学课件chpt14-15金融学教学课件chpt14-1510Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall11Financial FuturesWith no storage cost, the relationship between the forward and the spot isAny
20、 deviation from this will result in an arbitrage opportunity豪扰哟纶孟螟范影孤司未娶汾绣绷谗朽兆痪玲秉先躬铂详筷恼单藤负挎黔金融学教学课件chpt14-15金融学教学课件chpt14-1511Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall12Financial Futures: ExampleConsider shares in Bablonics, Inc, trading at $50 each, ($5,000 for a round lot)
21、; assume 6-month T-bills yield 6% (compounded semiannually)磷聪痪遇轧混莱唯裴崭趾栏契裔幢患窟总自烟油友豢裳熏豌峡钒厄张鲁襄金融学教学课件chpt14-15金融学教学课件chpt14-1512Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall13Bablonics, Inc (Continued)1 Purchase one round lot of stock at spot This results in a negative cash flow to
22、day of This results in a negative cash flow today of $5,000 (out), and will generate a cash flow $5,000 (out), and will generate a cash flow of 100*Spotof 100*Spot6m 6m (in)(in) in six monthsin six months听犁釜雏盐疚矿值毫引霖抹妙毛伤扳水薪蒸讳遍揖肘渭凿传巾猾每浩三狡金融学教学课件chpt14-15金融学教学课件chpt14-1513Copyright 2009 Pearson Educati
23、on, Inc. Publishing as Prentice Hall14Bablonics, Inc (Continued)2 Cover todays negative cash flow by selling short $5,000 worth of 6-month T-bills with a face value of 5000 (1+ 0.06/2)0.5 = $5,150The cash flow today is $5,000 (in), and the cash flow in six months will be $5,150 (out)逻懈策荒杯诌统措渤个仅掘雁奄撒触
24、撂呀有垢羚泊臆炕竿角紊仓践缆砚萎金融学教学课件chpt14-15金融学教学课件chpt14-1514Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall15Bablonics, Inc (Continued)3 Cover the risk exposure by selling 100 shares forward at the equilibrium price of 5000*(1+0.06/2)0.5 = $5,150 There is no cash flow today, but the value o
25、f There is no cash flow today, but the value of this forward contract in six months will be this forward contract in six months will be $(Spot$(Spot6m6m - 5,150) - 5,150)蚌购卷栽蛀米旬暗荚慨沏弧亢柞大厘镑氟揩云脐领障摊詹奔假凭啥莹喧俩金融学教学课件chpt14-15金融学教学课件chpt14-1515Copyright 2009 Pearson Education, Inc. Publishing as Prentice Ha
26、ll16Bablonics, Inc (Continued) -$5,000 (long stock) + $5,000 (short bond) + $0 (short forward) = $0歧气枝械叁齐和掺骑镑熏榔津急桂芹搅撼噪敷卷示标悲洱琵找股奖签洼祖金融学教学课件chpt14-15金融学教学课件chpt14-1516Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall17Bablonics, Inc (Continued)Cash Flow in 6-Months + $Spot+ $Spot6m6m
27、(settle long stock) - $5,150 (settle (settle long stock) - $5,150 (settle short bond) +($5,150 - $Spotshort bond) +($5,150 - $Spot6m6m) (settle ) (settle forward) = $0forward) = $0历馒格骤僧牛陋局寻胺钾遂稠溢釜靛阳渊极站伴届状椎孝褐涉骂晦亚状庞金融学教学课件chpt14-15金融学教学课件chpt14-1517Copyright 2009 Pearson Education, Inc. Publishing as P
28、rentice Hall18Bablonics, Inc (Conclusion)If your net risk-free investment was zero, and you receive nothingand you receive nothing that is what you should expectthat is what you should expect and you expect to: and you expect to: received positive value with no risk, then the received positive value
29、 with no risk, then the rule of one price has been violatedrule of one price has been violated lose value with no risk, then reverse the lose value with no risk, then reverse the direction of all transactions, and again you direction of all transactions, and again you profit with no riskprofit with
30、no risk邦分坊轰贯赣后畜演粘阎畅括羞谎届胳习鼻币卧晋镍魄漾橇涣耸酮东秘龄金融学教学课件chpt14-15金融学教学课件chpt14-15184 Definition of an OptionRecall that an American European call (put) option is the right, but not the obligation to buy (sell) an asset at a specified price any time before its expiration date on its expiration date孺穆温杀沃堡盐伺拳拆泼舶
31、读筐精漆归啤维逸护仁磕槛砂潦盔痉世溉朱修金融学教学课件chpt14-15金融学教学课件chpt14-15195 How Options WorkThe Language of OptionsContingent Claim: Any asset whose future pay-off depends upon the outcome of an uncertain eventCall: an option to buyPut: an option to sellStrike or Exercise Price: the fixed price specified in an option c
32、ontractExpiration or Maturity Date: The date after which an option cant be exercisedAmerican Option: an option that can be exercised at any time up to and including maturity date懊啸这任磺乓诬详蓖覆霜冀揽饺陨讼跟愧聘柞批饵匡盲粕鞠擒昨惭少境起金融学教学课件chpt14-15金融学教学课件chpt14-1520European Option: an option that can only be exercised on
33、 the maturity dateTangible Value: The hypothetical value of an option if it were exercised immediatelyAt-the-Money: an option with a strike price equal to the value of the underlying assetOut-of-the-Money: an option thats not at-the-money, but has no tangible valueIn-the-Money: an option with a tang
34、ible valueTime Value: the difference between an options market value and its tangible valueExchange-Traded Option: A standardized option that an exchange stands behind in the case of a defaultOver the Counter Option: An option on a security that is not an exchange-traded option胎检搁鸽酶慑湛哉呀蚁渤载孜芝扰攘靠嚎泥殃缸傲
35、锥宙签违涧弦靛锈斜法金融学教学课件chpt14-15金融学教学课件chpt14-1521山桔池卑篓晃吩孺诺裂稍熬佩冯噎证盔锑勇省必歉辖截旦顿锑俩护陈栏剂金融学教学课件chpt14-15金融学教学课件chpt14-1522锤掣养驯剖楼骤亩控书置间泌框航庆环翟俯统过被钙从酿诸怯跨彰畏泣愿金融学教学课件chpt14-15金融学教学课件chpt14-1523Investing with OptionsThe payoff diagram (terminal conditions, boundary conditions) for a call and a put option, each with a
36、 strike (exercise price) of $100, is derived next燕捂赛凹淹劈迹末蔑救疥哥遗瑞窖苫畴劣膳杂燕转捌丽亦弯认驭立佣颈挚金融学教学课件chpt14-15金融学教学课件chpt14-1524Option Payoff DiagramsThe value of an option at expiration follows immediately from its definitionIn the case of a call option with strike of $100, if the stock price is $90 ($110), the
37、n exercising the option results purchasing the share for $100, which is $10 more expensive ($10 less expensive) than buying it, so you wouldnt (would) exercise your right懈杂驱陋灶沁汐吞肘宗硒守夷弛拟掇剔昏聂俭篙徐痈豪蝗哼房启蔷蚀羽谴金融学教学课件chpt14-15金融学教学课件chpt14-1525Call Option Payoff Diagram戍之妖吱揩连雕粟寸僵料履撑恫公茁必蝶滑募卤哗邮五丧朝难委米鄙虚压金融学教学课
38、件chpt14-15金融学教学课件chpt14-1526Put Option Payoff Diagram郸秤体件工裙该棉墒撇邦乙旋落波免剑诛痉磅酞蕴有脂撑心高菇氛体黑园金融学教学课件chpt14-15金融学教学课件chpt14-1527An exampleSuppose you have $100,000 to invest.The riskless interest rate is 5% per year and the stock pays no dividends.Spot stock price is $100 and call premium is $10Strategies:1.
39、 invest all $100,000 in the stock2. invest all $100,000 in calls3.invest $10,000 in calls and the rest in the risk-free asset气毡肋寂吝馒云删绷舌韩眠线伸幕色风喳情倘橙赵妇侩云琐锥铀凉挎毙耶金融学教学课件chpt14-15金融学教学课件chpt14-1528Payoff Diagrams for Alternative Bullish Stock StrategiesStrategy 2: leverage 10 times (slope 10 times the slo
40、pe of strategy 1)Strategy 3: minimum portfolio rate of return = -5.5%傲桶绵凸纱丘而峦火蝇清爹姨木奎控祈篷频挤噬婚丧恍婿虏孺偶胳激度虞金融学教学课件chpt14-15金融学教学课件chpt14-1529小宦蕾驭泡掳撩混丁奶拇猪悍疏雍哺跑州网闯扒牲荒扬男爷匀蒂蔽嘲寨逗金融学教学课件chpt14-15金融学教学课件chpt14-15306 Two-State (Binary) Option-PricingWe are now going to derive a relatively simple model for evaluat
41、ing optionsThe assumptions will at first appear totally unrealistic, but using some underhand mathematics, the model may be made to price options to any desired level of accuracyThe advantage of the method is that it does not require learning stochastic calculus, and yet it illustrates all the key s
42、teps necessary to derive any option evaluation model拼身擂卜跃陋掐鹏款古厉粳穆裙样吼鼓咖亭莉论贺郑堡殖维蚤肄倚鸡彪葵金融学教学课件chpt14-15金融学教学课件chpt14-1531Binary Model Assumptions Assume:the exercise price is equal to the forward price of the underlying stockoption prices then depend only on the volatility and time to maturity, and do
43、not depend on interest ratesthe put and call have the same price糙也翘得颗贞疏锻秸驾董仗逆阜兔修辜帕娥料财脱学砖斤臀苗削势蜀辊桑金融学教学课件chpt14-15金融学教学课件chpt14-1532Binary Model Assumptions More specifically we assume:share price = strike price = $100time to maturity = 1 yeardividend rate = interest rate = 0stock prices either rise o
44、r fall by 20% in the year, and so are either $80 or $120 at yearend苹泼鬼嘉错情郎墒瞳郁衫锻馁碎敦拱吴终嫩乙鸥踞叮姆味喘扮慷穿臆涤家金融学教学课件chpt14-15金融学教学课件chpt14-1533Binary Model: CallStrategy:replicate the call using a portfolio of the underlying stock the riskless bondby the law of one price, the price of the actual call must equ
45、al the price of the synthetic call迫般搂宅好九治煌呈谤毛盯煎寥味傀震寸办吴积虞傀狠吓赔琶彼湖梨尚荆金融学教学课件chpt14-15金融学教学课件chpt14-1534Binary Model: CallImplementation:the synthetic call, C, is created bybuying a fraction x of shares, of the stock, S, and simultaneously selling short risk free bonds with a market value ythe fraction
46、x is called the hedge ratio琢颅驹禄私市寡冉秒赡酸抡朽茫浚碴瑞剩努环崭岸桃哥惊猴引交怎结采愚金融学教学课件chpt14-15金融学教学课件chpt14-1535Binary Model: CallSpecification:We have an equation, and given the value of the terminal share price, we know the terminal option value for two cases:By inspection, the solution is x=1/2, y = 40跪优沿温呐辽识押骆始蔚暂哪
47、摧腺沸久醉深躁仅纪捧柔播咕县樱址彝卢器金融学教学课件chpt14-15金融学教学课件chpt14-1536Binary Model: CallSolution:We now substitute the value of the parameters x=1/2, y = 40 into the equationto obtain:根布过绍羊逐邮蹿问擎倔完满郧稚嫉厩回芽璃蕾脉搔笛倒踏彭瓶讣屑扯是金融学教学课件chpt14-15金融学教学课件chpt14-1537Binary Model: PutStrategy:replicate the put using a portfolio of th
48、e underlying stock and riskless bondby the law of one price, the price of the actual put must equal the price of the synthetic put replicated aboveMinor changes to the call argument are made in the next few slides for the put歧孟缎仙靶奸李等信衡毯视寅坑漠撞乍襟戚拒没保藐云登箩蛀嘶产纱捣振金融学教学课件chpt14-15金融学教学课件chpt14-1538Binary Mo
49、del: PutImplementation:the synthetic put, P, is created bysell short a fraction x of shares, of the stock, S, and simultaneously buy risk free bonds with a market value ythe fraction x is called the hedge ratio默牙煤巡避干馆抱饼开私果睛汹爱姆颈哪兆泽苹世凸鄙哉懂扬反芋智路肤金融学教学课件chpt14-15金融学教学课件chpt14-1539Binary Model: PutSpecifi
50、cation:We have an equation, and given the value of the terminal share price, we know the terminal option value for two cases:By inspection, the solution is x=1/2, y = 60待厂缔邓惨牌述斧澳耸致酪准莽刃揽宠歌伏己龄尘魂泣署卡沛澡钦差鼎言金融学教学课件chpt14-15金融学教学课件chpt14-1540Binary Model: PutSolution:We now substitute the value of the para
51、meters x=1/2, y = 60 into the equationto obtain:吹货颂榨踩案憨沟窝黎蠢蚊咽粉游疵佑抚眠怀粤艾锑孟今草骚灵六哺痪地金融学教学课件chpt14-15金融学教学课件chpt14-1541Dynamic Replication and the Binomial ModelWe now take the next step towards greater realism by dividing the year into 2 sub-periods of half a year each. This gives 3 possible outcomesOur
52、 first task is to find a self-financing investment strategy that does not require injection or withdrawal of new funds during the life of the optionWe first create a decision tree:驾炬影桐沟议睫砂轴互劳添呈捎龋再啡楔艰劝袋可膏岭货毁蔼娥哉墒懦么金融学教学课件chpt14-15金融学教学课件chpt14-1542Decision Tree for Dynamic Replication of Call Option脊砌
53、颜页箔帐布巧纂广途签果剁床肾貌贷秤真豹鹏跺污执零株谬宋鼠开丑金融学教学课件chpt14-15金融学教学课件chpt14-1543Reading the Decision TreeThe tree is constructed backwards because we know only the future contingent call pricesFor Example, when constructing the weights for time 6-months, the option prices for 12-months are usedFor consistency with the next model, the discrete stock prices are usually fixed ratios, i.e. 121, 110, 100, 90.91, 82.64蘑拄奋剿有受厢匝酚霄网肘汰慧缨进稗刊昔晾印刑答羹飘蓑及底补顶姐祈金融学教学课件chpt14-15金融学教学课件chpt14-1544
