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1、1,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,1,Chapter 14-15 Forward, Future and Option,Objective Understanding the definitions of forward, future and option Understanding the basic idea of synthetic 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chpt14-15,2,
2、Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,2,Contents,1 Distinction Between Forward & Futures Contracts 2 Futures Price 3 Financial future,4 Definition of an option 5 How an option works 6 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-
3、15,3,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,3,1 Distinction Between Forward & Futures Contracts,Forward: parties agree to exchange some item in the future at a delivery price specified now the forward price is defined as the delivery price which makes the current market v
4、alue of the contract zero no money is paid in the present by either party to the other the face value of the contract is the quantity of the item specified in the contract multiplied by the forward price the party who agrees to buy the specified takes the long position, and the party who agrees to s
5、ell the item takes 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chpt14-15,4,Who pays what to whom,If 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 l
6、ower 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chpt14-15,5,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,5,Future: terms,Listing: Open, High, Low, Settle, Change, Lifetime high, Lifetime low, Open interest
7、Mark-to-market at the end of each trading day based on that days settlement price. Margin requirement: the exchange requires that there be enough collateral posted in each account to cover any losses. Margin call: if the collateral in your account falls below a prespecified level, you will receive a
8、 margin call from 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chpt14-15,6,An illustration,Based 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 your
9、 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 who w
10、as 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chpt14-15,7,Daily realization of gains and losses,Such 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
11、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chpt14-15,8,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,8,Summarized characteristics for future,standard contracts immune from the credit worthiness of buyer and seller because exchange stands bet
12、ween traders contracts marked to market daily margin 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chpt14-15,9,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,9,2 Futures Price,Arbitrageurs place an upper bound on futures prices by locking in a sure profit on
13、 futures prices if the spread between the futures price and spot price becomes greater than the cost of carry: F - S C the cost of carry varies as a function 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chpt14-15,10,Copyright 2009 Pearson Education, Inc
14、. Publishing as Prentice Hall,10,3 Financial Futures,We now focus on financial futures standardized contracts for future delivery of stocks, bonds, indices, and foreign currency they have no intrinsic value, but represent claims on future cash flows they have very low storage costs settlement is usu
15、ally 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chpt14-15,11,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,11,Financial Futures,With no storage cost, the relationship between the forward and the spot is Any deviation from this will result in an arbitrage oppo
16、rtunity,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chpt14-15,12,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,12,Financial Futures: Example,Consider shares in Bablonics, Inc, trading at $50 each, ($5,000 for a round lot); assume 6-month T-bills yield 6% (compounded s
17、emiannually),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chpt14-15,13,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,13,Bablonics, Inc (Continued),1 Purchase one round lot of stock at spot This results in a negative cash flow today of $5,000 (out), and will generate a
18、cash flow of 100*Spot6m (in) in 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chpt14-15,14,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,14,Bablonics, Inc (Continued),2 Cover todays negative cash flow by selling short $5,000 worth of 6-month T-bills with a fa
19、ce value of 5000 (1+ 0.06/2)0.5 = $5,150 The 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chpt14-15,15,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,15,Bablonics, Inc (Continued),3 Cov
20、er 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 of this forward contract in six months will be $(Spot6m - 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chpt14-15,16,Copyright 2009 Pe
21、arson Education, Inc. Publishing as Prentice Hall,16,Bablonics, 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chpt14-15,17,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,17,Bablonics, In
22、c (Continued),Cash Flow in 6-Months + $Spot6m (settle long stock) - $5,150 (settle short bond) +($5,150 - $Spot6m) (settle forward) = $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chpt14-15,18,Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall,18,Bablonics, Inc (Conclusio
23、n),If your net risk-free investment was zero, and you receive nothing that is what you should expect and you expect to: received positive value with no risk, then the rule of one price has been violated lose value with no risk, then reverse the direction of all transactions, and again you profit wit
24、h 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chpt14-15,19,4 Definition of an Option,Recall 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
25、堡盐伺拳拆泼舶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chpt14-15,20,5 How Options Work,The Language of Options Contingent Claim: Any asset whose future pay-off depends upon the outcome of an uncertain event Call: an option to buy Put: an option to sell Strike or Exercise Price: the fixed price specified
26、in an option contract Expiration or Maturity Date: The date after which an option cant be exercised American 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chpt14-15,21,European Option: an option that can o
27、nly be exercised on the maturity date Tangible Value: The hypothetical value of an option if it were exercised immediately At-the-Money: an option with a strike price equal to the value of the underlying asset Out-of-the-Money: an option thats not at-the-money, but has no tangible value In-the-Money
28、: an option with a tangible value Time Value: the difference between an options market value and its tangible value Exchange-Traded Option: A standardized option that an exchange stands behind in the case of a default Over the Counter Option: An option on a security that is not an exchange-traded op
29、tion,胎检搁鸽酶慑湛哉呀蚁渤载孜芝扰攘靠嚎泥殃缸傲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chpt14-15,22,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chpt14-15,23,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chpt14-15,24,Investing with Options,The payoff diagram (terminal conditions, boundary conditions) for a
30、call and a put option, each with a 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chpt14-15,25,Option Payoff Diagrams,The value of an option at expiration follows immediately from its definition In the case of a call option with strike of $100
31、, if the stock price is $90 ($110), then 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chpt14-15,26,Call Option Payoff Dia
32、gram,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件chpt14-15金融学教学课件chpt14-15,27,Put 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chpt14-15,28,An example,Suppose you have $100,000 to invest. The riskless interest rate is 5% per year and the stock pays no dividends. Spot stock
33、 price is $100 and call premium is $10 Strategies: 1. invest all $100,000 in the stock 2. invest all $100,000 in calls 3.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chpt14-15,29,Payoff Diagrams for Alternative Bullish Stock Strat
34、egies,Strategy 2: leverage 10 times (slope 10 times the slope 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chpt14-15,30,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chpt14-15,31,6 Two-State (Binary) Option-Pricin
35、g,We are now going to derive a relatively simple model for evaluating options The 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 accuracy The advantage of the method is that it does not requir
36、e learning stochastic calculus, and yet it illustrates all the key steps 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chpt14-15,32,Binary Model Assumptions,Assume: the exercise price is equal to the forward price of the underlying stock optio
37、n prices then depend only on the volatility and time to maturity, and do not depend on interest rates the 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chpt14-15,33,Binary Model Assumptions,More specifically we assume: share price = strike price = $100 time
38、to maturity = 1 year dividend rate = interest rate = 0 stock prices either rise or 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chpt14-15,34,Binary Model: Call,Strategy: replicate the call using a portfolio of the underlying
39、 stock the riskless bond by the law of one price, the price of the actual call must equal 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chpt14-15,35,Binary Model: Call,Implementation: the synthetic call, C, is created by buying a fraction x of shares, of the
40、stock, S, and simultaneously selling short risk free bonds with a market value y the fraction 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chpt14-15,36,Binary Model: Call,Specification: We have an equation, and given the value of the terminal share price, we kno
41、w 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chpt14-15,37,Binary Model: Call,Solution: We now substitute the value of the parameters x=1/2, y = 40 into the equation to 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
42、彭瓶讣屑扯是金融学教学课件chpt14-15金融学教学课件chpt14-15,38,Binary Model: Put,Strategy: replicate the put using a portfolio of the underlying stock and riskless bond by the law of one price, the price of the actual put must equal the price of the synthetic put replicated above Minor changes to the call argument are m
43、ade 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chpt14-15,39,Binary Model: Put,Implementation: the synthetic put, P, is created by sell short a fraction x of shares, of the stock, S, and simultaneously buy risk free bonds with a market value y the fracti
44、on 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chpt14-15,40,Binary Model: Put,Specification: 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
45、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chpt14-15,41,Binary Model: Put,Solution: We now substitute the value of the parameters x=1/2, y = 60 into the equation to 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chpt14-15,42,Dynamic Replication and the Binomial Model,We now t
46、ake the next step towards greater realism by dividing the year into 2 sub-periods of half a year each. This gives 3 possible outcomes Our 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 option We first creat
47、e 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chpt14-15,43,Decision Tree for Dynamic Replication of Call Option,脊砌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chpt14-15,44,Reading the Decision Tree,The tree is constructed backwards because we know only the future
48、contingent call prices For Example, when constructing the weights for time 6-months, the option prices for 12-months are used For 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chpt14-15,