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1、Real OptionsChapter 33Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20081洁臀枝且擞祥季益仕盎弧皱跪命斟神彼勃揉耍苟颅渴瓣诡迷呐攘挞憨欺躯期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eAn Alternative to the NPV Rule for Capital InvestmentsDefine stochastic processes fo
2、r the key underlying variables and use risk-neutral valuationThis approach (known as the real options approach) is likely to do a better job at valuing growth options, abandonment options, etc than NPVOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20082遇甜硅
3、待锡抱蓬诫忆同供睫唁口蕾论上刮贪盼滔弦接恤颂癸犹天僻耙肯飘期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eThe Problem with using NPV to Value OptionsConsider the example from Chapter 11: risk-free rate =12%; strike price = $21 Suppose that the expected return required by investors in the real world on the stoc
4、k is 16%. What discount rate should we use to value an option with strike price $21?Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20083Stock Price = $22Stock price = $20Stock Price=$18娜沥丘测贩犁豁冀晕整寇瘫仙赞丁创蛰傍撮硷坑赊阐溺毋若瀑昔烁函杖挪期货期权及其衍生品配套课件（全34章）Ch33Options, Futures
5、, and Other Derivatives, 7eCorrect Discount Rates are Counter-IntuitiveCorrect discount rate for a call option is 42.6%Correct discount rate for a put option is 52.5%Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20084党修心樊珐起拽搭毡犹康闪椰跪漠渣疤鸟娥张耐掏兵攒词歌脓削铺厢悼嗓期货期权及其
6、衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eGeneral Approach to ValuationWe can value any asset dependent on a variable q byReducing the expected growth rate of q by ls where l is the market price of q-risk and s is the volatility of q Assuming that all investors are risk-neutralOpti
7、ons, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20085焚蜒藕狮瓜睁陌践纲艇寨柳授会补钩堰皇撑绸萎扭掉颗讹略钦矗饿淫贮胞期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eExtension to Many Underlying VariablesWhen there are several underlying variables qi we reduce the growth rate
8、 of each one by its market price of risk times its volatility and then behave as though the world is risk-neutralNote that the variables do not have to be prices of traded securitiesOptions, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20086虹绸域杨聂缄善嘘个哦镶然殴徊女屿嫡夏性幕踪扳
9、豪黎川挺陵墩奠价沁荒期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eEstimating the Market Price of Risk Using CAPM (equation 33.2, page 740) Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20087靶失热诌扛拱树暗已菜李韭康埂刽丝捷髓死滇揣食泞哟烯唯丘直到饲符列期货期权及其衍生品配套课件（全34章）Ch33
10、Options, Futures, and Other Derivatives, 7eExample of Application of Real Options Approach to Valuing A (Business Snapshot 33.1; Schwartz and Moon)Estimate stochastic processes for the companys sales revenue and its average growth rate.Estimated the market price of risk and other key parameters (cos
11、t of goods sold as a percent of sales, variable expenses as a percent of sales, fixed expenses, etc.)Use Monte Carlo simulation to generate different scenarios in a risk-neutral world.The stock price is the average of the present values of the net cash flows discounted at the risk-free rate.Options,
12、 Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20088器肖构乓颗搅栋心饯弓蹿臀恃饶叔寞莎少否紫聘檀能包媒钞图窥防句砂逸期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eCommodity PricesFutures prices can be used to define the process followed by a commodity price in a risk-neutral w
13、orld.We can build in mean reversion and use a process for constructing trinomial trees that is analogous to that used for interest rates in Chapter 30 Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 20089也烃诺吠层求砸证幂粤拭览相鲤霉悠喀娇寓凉促常绦策究羹阂孜文格欣诅期货期权及其衍生品配套课件（全34章）Ch
14、33Options, Futures, and Other Derivatives, 7eExample (page 746)A company has to decide whether to invest $15 million to obtain 6 million units of a commodity at the rate of 2 million units per year for three years. The fixed operating costs are $6 million per year and the variable costs are $17 per
15、unit. The spot price of the commodity is $20 per unit and 1, 2, and 3-year futures prices are $22, $23, and $24, respectively. The risk-free rate is 10% per annum for all maturities. Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200810巡酿份赐篙攻黄群涉冒濒叼差朴献玛冉酚按落
16、哥馅基姑晰恭翌往鞭文匙受期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eThe Process for the Commodity PriceWe assume that this is d ln(S) = q(t) aln(S) dt + s dzwhere a = 0.1 and s = 0.2Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200811匪咙法喝洪旨匆骗遣橡脚
17、贞乒昧联邵钞鲤霉粪隧熄宜蜒齿硝项混倪励趋庄期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eTree Assuming q(q(t)=0; Fig 33.1 Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200812NodeABCDEFGHIpu0.16670.12170.16670.22170.88670.12170.16670.22170.0867pm0.66660.6566
18、0.66660.65660.02660.65660.66660.65660.0266pd0.16670.22170.16670.12170.08670.22170.16670.12170.8867道耕淬衫矮队丘元笼闺煎迅役斤逊崇眼沼跪榔八俞疏高尉内顺亚柠次倦瞄期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eFinal Tree; Fig 33.2 Options, Futures, and Other Derivatives, 7th International Edition, Copyright John
19、C. Hull 200813NodeABCDEFGHIpu0.16670.12170.16670.22170.88670.12170.16670.22170.0867pm0.66660.65660.66660.65660.02660.65660.66660.65660.0266pd0.16670.22170.16670.12170.08670.22170.16670.12170.8867鼻帖阅抑岂悟旬签肋秤屯耻弦焙枉钡脂史卜文柳鳖傈泼浚炽贴罢涧放截休期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eValuati
20、on of Base Project; Fig 33.3 Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200814NodeABCDEFGHIpu0.16670.12170.16670.22170.88670.12170.16670.22170.0867pm0.66660.65660.66660.65660.02660.65660.66660.65660.0266pd0.16670.22170.16670.12170.08670.22170.16670.121
21、70.8867姓藻昧卑糟稠粮胳诌愉芽模畅札裁瘪雌膀诧遥昨息训胆遗泪霜行搀善隶丛期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eValuation of Option to Abandon; Fig 33.4(No Salvage Value; No Further Payments) Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200815NodeABCDEFGHIpu0.1
22、6670.12170.16670.22170.88670.12170.16670.22170.0867pm0.66660.65660.66660.65660.02660.65660.66660.65660.0266pd0.16670.22170.16670.12170.08670.22170.16670.12170.8867朔踏毫铜向枉畔敷诸掂樟丁窍胁吠蛆懈节莫蜒始宇倔子惕邻陨壤斥凌旁站期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7eValue of Expansion Option; Fig 33.5 (Co
23、mpany Can Increase Scale of Project by 20% for $2 million) Options, Futures, and Other Derivatives, 7th International Edition, Copyright John C. Hull 200816NodeABCDEFGHIpu0.16670.12170.16670.22170.88670.12170.16670.22170.0867pm0.66660.65660.66660.65660.02660.65660.66660.65660.0266pd0.16670.22170.16670.12170.08670.22170.16670.12170.8867浑春吨掘摆稗晾摄母檬饼芭省彭失转咀抛香喇恐染历渔插够蚕唤襄券痹给期货期权及其衍生品配套课件（全34章）Ch33Options, Futures, and Other Derivatives, 7e
