期权期货及其衍生品第6弹
约翰.赫尔,期权期货和其他衍生品(third edition)习题答案
12.1 一个证券组合当前价值为＄1000万，β值为1.0，S&P100目前位于250，解释一个执行价格为240。
标的物为S&P100的看跌期权如何为该组合进行保险？当S&P100跌到480，这个组合的期望价值是10 ×（480/500）=＄9.6million.买看跌期权10，000，000/500=20，000可以防止这个组合下跌到＄9.6million下的损失。
因此总共需要200份合约12.2 “一旦我们知道了支付连续红利股票的期权的定价方法，我们便知道了股票指数期权、货币期权和期货期权的定价”。
请解释这句话。
一个股票指数类似一个连续支付红利的股票12.3 请说明日圆看涨期权与日圆期货看涨期权的不同之处一个日元的看涨期权给了持有者在未来某个时刻以确定的价格购买日圆的权利，一个日圆远期看涨期权给予持有者在未来时刻远期价格超过特定范围按原先价格购买日圆的权利。
如果远期齐权行使，持有者将获得一个日圆远期和约的多头。
12.4请说明货币期权是如何进行套期保值的？12.5 计算3个月期，处于平价状态的欧式看涨股票指数期权的价值。
指数为250。
无风险年利率为10%，指数年波动率为18%，指数的年红利收益率为3%。
一个日元的看涨期权给了持有者在未来某个时刻以确定的价格购买日圆的权利，一个日圆远期看涨期权给予持有者在未来时刻远期价格超过特定范围按原先价格购买日圆的权利。
如果远期齐权行使，持有者将获得一个日圆远期和约的多头。
12.6 有一美式看涨期货期权，期货合约和期权合约同时到期。
在任何情况下期货期权比相应的标的物资产的美式期权更值钱？当远期价格大于即期价格时，美式远期期权在远期和约到期前的价值大于相对应的美式期权/12.7 计算5个月有效期的欧式看跌期货期权的价值。
期货价格为＄19，执行价格为＄20，无风险年利率为12%。
期货价格的年波动率为20%。
本题中12.8 假设交易所构造了一个股票指数。
20170711-东方证券-衍生品系列研究之(六)：商品期货中的alpha策略
商品期货中的alpha策略
目录
一、研究方法 .................................................................................................................. 3
1.1 背景................................................................................................................................................. 3 1.2 品种选择 ........................................................................................................................................ 3 1.3 回测时间段选择 ............................................................................................................................ 5 1.4 合约选择 ........................................................................................................................................ 5 1.5 多空组合构建 ................................................................................................................................ 5 1.6 多头组合构建 ................................................................................................................................ 6
期权期货及其衍生品
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期权期货及其衍生品
期权期货及其衍生品是金融市场的重要组成部分，它们为投资者提 供了丰富的投资策略和风险管理工具。
期权期货及其衍生品的重要性
风险管理
期权期货及其衍生品可以帮助投资者管理风险，通过买入 或卖出相应的衍生品，投资者可以控制风险敞口，减少潜 在的损失。
投资策略
期权期货及其衍生品为投资者提供了丰富的投资策略，如 套期保值、套利交易、价差交易等，这些策略有助于投资 者实现投资目标。
详细描述
期货是一种标准化的金融合约，买卖双方约定在未来某一特定日期或该日之前按照约定的价格交割标的资产。期 货市场是一个高度组织化和规范化的市场，具有价格发现、套期保值和投机等功能。通过期货交易，参与者可以 规避价格波动风险、锁定未来采购或销售成本、进行套利交易等。
衍生品市场概述
总结词
衍生品市场是金融市场的一个重要组成部分，主要交易各种衍生品合约，如期权、期货、掉期等。衍 生品市场具有高风险、高收益的特点，对经济和金融市场的影响深远。
权。
详细描述
期权是一种金融合约，其价值来源于标的资产的价格变动。持有期权的人有权在未来的 特定时间或之前，以特定价格买入或卖出标的资产。根据权利的不同，期权可以分为看 涨期权和看跌期权。看涨期权赋予持有者买入标的资产的权利，而看跌期权赋予持有者
卖出标的资产的权利。
期货定义与功能
总结词
期货是一种标准化的金融合约，买卖双方约定在未来某一特定日期或该日之前按照约定的价格交割标的资产。期 货市场具有价格发现、套期保值和投机等功能。
06
结论
期权期货及其衍生品的影响
市场波动性
期权期货及其衍生品可以增加市场的 波动性，因为它们为投资者提供了更 多的交易策略和机会，从而增加了市 场的交易量。
期货期权及其衍生品配套课件Ch06
Edition, Copyright © John C. Hull 2019
15
Forward Rates and Eurodollar
Futures continued
A convexity adjustment often made is
Forward Rate=Futures Rate−0.5s2T1T2 T1 is the time to maturity of the forward contract T2 is the time to maturity of the rate underlying the forward contract (90 days later that T1) s is the standard deviation of the short rate (typically about 1.2%)
Edition, Copyright © John C. Hull 2019
7
Eurodollar Futures (Page 136-141)
A Eurodollar is a dollar deposited in a bank outside the United States Eurodollar futures are futures on the 3-month Eurodollar deposit rate (same as 3-month LIBOR rate) One contract is on the rate earned on $1 million A change of one basis point or 0.01 in a Eurodollar futures quote corresponds to a contract price change of $25
期权期货和其他衍生品第六版课程设计
期权、期货和其他衍生品第六版课程设计一、课程概述本课程主要介绍期权、期货和其他衍生品的基本概念、市场情况以及交易策略和风险控制方法。
通过对各种衍生品的案例分析和实操操作，帮助学生掌握交易技巧和风险管理方法，并提高其应对金融市场挑战的能力。
二、课程目标1.了解期权、期货及其他衍生品的基础知识和市场情况；2.掌握多种衍生品的分析方法、交易策略和风险控制方法；3.能够运用所学知识进行实操操作，提高操作技巧；4.加强风险意识，提高风险防范和应对能力。
三、课程大纲第一章衍生产品概述1.衍生品的基础知识2.衍生品的分类和市场情况3.衍生品的价值和定价第二章期货市场1.期货合约的基础知识2.期货市场基础和市场情况3.期货市场的交易策略和技巧4.期货市场的风险控制方法第三章期权市场1.期权合约的基础知识2.期权市场基础和市场情况3.期权市场的交易策略和技巧4.期权市场的风险控制方法第四章期权和期货的应用1.期权和期货的基本操作策略2.期权和期货的投资组合3.期权和期货的交易技巧和风险控制方法第五章其他衍生品1.外汇衍生品2.计算机衍生品3.大宗商品衍生品4.生物科技衍生品第六章衍生品风险控制1.衍生品市场的风险和机会2.风险策略和风险管理方法3.风险管理案例分析第七章衍生品交易技巧1.高效交易的基本技巧和原则2.资金管理和交易心态控制3.交易技巧的实操案例分析四、课程论文为了进一步加深学生对于各类衍生品的理解和应用，本课程要求每位学生完成一篇论文，内容包括衍生品的分析和交易策略，以及风险控制方案等。
论文长度不少于2000字。
五、评估方式1.课堂出勤情况（10%）2.课堂参与和作业（20%）3.论文质量（40%）4.期中和期末考试（30%）六、参考书目1.《金融衍生品，期权期货与其他金融产品》，约翰·C.霍尔，第7版；2.《期货与期权市场的交易和分析基础》，Robert W. Kolb，第5版；3.《金融工程与衍生品》，John C. Hull，第8版；4.《资产与衍生品的定价与交易》，Kerry E. Back，第2版。
期权、期货及其他衍生品定价理论教学大纲
期权、期货及其他衍生品定价理论教学大纲制作人吴可任课教师吴可一、课程名称：期权、期货及其他衍生品定价理论Option, Futures, and other Derivatives Pricing theory二、课程编码：三学时与学分学时：32 /2四、先修课程证券投资分析，金融工程学五、课程教学目标本课程为金融工程概论的后续课程。
专门讲授金融衍生产品的定价与套利技术。
要求学生学习和掌握各种金融衍生产品定价与市场套利技术。
包括期权、期货、远期、互换等产品的定价与套利技术；期权定价模型的扩展、数值求解、奇异期权定价，以及在险价值求解。
目的是要求学生通过定价理论与方法的学习，深入理解和掌握金融产品的定价与套利的关系。
为熟练与科学运用金融衍生产品工具有效进行套期保值和套利奠定坚实的理论基础和技术基础。
六、适用学科专业经济、金融专业及管理学专业七、基本教学内容与学时安排第一章金融工程的基本分析方法（4学时）第一节MM理论及其涵义第二节无套利定价法第三节风险中性定价法第四节状态价格定价技术第五节积木组合分析法第二章远期和期货的定价（4学时）第一节金融远期和期货市场概述第二节远期价格和期货价格的关系第三节远期定价及其应用第三章互换定价方法（4学时）第一节互换市场概述第二节金融互换的种类第三节互换的定价及其应用第四章B-S期权定价模型（4学时）第一节期权市场概述第二节证券价格的变化过程第三节B-S模型推导第四节B-S期权定价公式的实证研究和应用第五节股票指数期权、货币期权、期货期权定价第五章B-S期权定价公式的扩展（4学时）第一节B-S定价公式的缺陷第二节交易成本第三节波动率微笑和波动率期限结构第四节随机波动率第五节不确定的参数第六节跳跃扩展过程第七节崩盘模型第六章期权定价的数值解法（4学时）第一节二叉树期权定价模型第二节蒙特卡洛模拟第三节有限差分法第五章奇异期权定价（4学时）第一节奇异期权概述第二节奇异期权定价第七章套期保值与套利（4学时）第一节套期保值与套利的概念第二节基于衍生工具的套期保值技术第三节基于衍生工具的套利技术第八章在险价值（4学时）第一节在险价值的定义第二节资产组合的在险价值计算第三节衍生工具在险价值计算第四节蒙特卡罗模拟与历史模拟八、教材及参考书：教材：1．郑振龙，金融工程学，厦门大学出版社出版2.John Hull， Option, Futures, and other Derivatives 清华大学出版社参考书：1．郑振龙，金融工程学，厦门大学出版社出版2．孙金龙史永东，现代金融工程中国金融出版社3．陈信华，金融衍生工具，上海财经大学出版社4．洛伦兹·格利茨，金融工程学（修订版），经济科学出版社5. 叶永刚、郑康彬，金融工程概论，武汉大学出版社6．陆家骝，现代金融经济学，东北财经大学出版社九、考核方式书面考试＋小论文，参考平时作业。
期权 期货及其他衍生品 第 版 课后作业题解答 章
1第一次作业参考答案第1章1.26远期合约多头规定了一年后以每盎司1000美元买入黄金，到期远期合约必须执行，交易双方权利义务对等；期权合约多头规定了一年后以每盎司1000美元买入黄金的权利，到期合约可以不执行，也可以执行，交易双方权利义务不对等。
假设S T为一年以后黄金的价格，则远期合约的收益为S T-1000;期权合约的受益为S T-1100,如果S T>1000;-100,如果S T<10001.27投资人承诺在7月份以40美元的执行价格买入股票。
如果未来股票价格跌至37美元以下，则该投资人赚取的3美元期权费不足以弥补期权上的损失，从而亏损。
当未来股票价格为37-40美元时，交易对手会执行期权，此时，投资人此时同样有正收益。
如果未来股票价格高于40美元，该期权不会被对手执行，此时投资者仅赚取期权费。
1.28远期：购入三个月期限的300万欧元的欧元远期合约，并在三个月后，用到期的远期合约进行支付300万欧元。
期权：购入三个月期限的300万欧元的欧元看涨期权，如果三个月后汇率高于期权约定执行汇率，则执行该期权，反之则不执行该期权。
1.29当股票到期价格低于30美元时，两个期权合约都与不会被执行，该投资者无头寸;当股票价格高于32.5美元时,两个期权都会执行，该投资者无头寸，若股票价格在30-32.5美元之间时，该投资者买入期权会被执行，卖出的期权不会被执行，因此该投资者持有长头寸。
1.30（低买高卖）借入1000美元资金，买入黄金，同时在卖出一年期的黄金远期合约，锁定到期的价格1200美元，到期偿还本金和利息。
到期时的受益为1200-1000（1+10%）=100；收益率为100/1000=10%1.312由于期权存在杠杆效应，看张期权的风险更大，同时收益率也更高。
假设股票在S时，购入看涨期权和购入股票无差异，则100*（S-94)=2000（S-95）-9400即S=100。
如果未来股票价格高于100美元，则购入看涨期权合约则盈利更高，反之，如果未来股票价格低于100美元，则购入股票比购入期权合约盈利更多。
期权期货及其它衍生品计算题
1.5 一个投资者进入了一个远期合约的空头：在该合约中，投资者能够以 1.5000 的汇率（美元/ 英镑）卖出100000 英镑。
当远期合约到期时的汇率为（a ）1.4900 ，（b ）1.5200 时，投资者的损益分别为多少？1.13 假如1 份在3 月份到期的看涨期权价格为2.50 美元，期权执行价格为50 美元。
假设期权一直被持有到到期日，在什么情形下期权持有人会盈利？在什么情形下持有人会行使期权？画出期权多头的盈利与在期权到期时股票价格之间关系的图形。
1.14 假如一个在6 月份到期、执行价格为60 美元的看跌期权价格为4 美元。
假设期权被一直持有到到期日。
在什么情形下期权的卖出方会盈利？在什么情形下期权会被行使？画出一个期权空头在到期时的收益与股票价格之间的关系图1.26 某交易员按3 美元的价格买进执行价格为30 美元的看涨期权，交易员是否会在选择行使期权的情况下而亏损？为什么？1.27 某交易员按5 美元的价格卖出1 份执行价格为40 美元的看跌期权。
交易员的最大盈利与最大亏损是多少？为什么？1.6 某交易员进入期货价格每磅50 美分的棉花远期合约空头方。
合约的规模是50000 磅棉花。
当合约结束时棉花的价格分别为（ a ）每磅48.20 美分，（b ）每磅51.30 美分，对应以上价格交易员的盈亏为多少？1.9 你认为某股票价格将要上升，股票的当前价格为29 美元，而3 个月期限，执行价格为30 美元的看涨期权价格为2.90 美元，你总共有5800 美元的资金。
说明两种投资方式：一种是利用股票，另一种是利用期权。
股票投资策略，当3 个月后股票市场价格为15 时的盈亏，当3 个月后股票市场价格为50 时的盈亏期权投资策略，当3 个月后股票市场价格为15 时的盈亏，当3 个月后股票市场价格为50 时的盈亏1.10 假如你拥有5000 只股票，每股价格为25 美元。
你如何采用看跌期权而使你投资的价值在将来4 个月内得到保护？A. 买入执行价格为25 美元的看涨期权B. 买入执行价格为25 美元的看跌期权C. 卖出执行价格为25 美元的看涨期权D. 卖出执行价格为25 美元的看跌期权1.18 一家美国公司得知在6 个月后要支付100 万加元。
约翰.赫尔,期权期货和其他衍生品(third edition)习题答案
CH99.1 股票现价为$40。
已知在一个月后股价为$42或$38。
无风险年利率为8％（连续复利）。
执行价格为$39的1个月期欧式看涨期权的价值为多少？ 解：考虑一资产组合：卖空1份看涨期权；买入Δ份股票。
若股价为$42，组合价值则为42Δ－3；若股价为$38，组合价值则为38Δ 当42Δ－3＝38Δ，即Δ＝0.75时，组合价值在任何情况下均为$28.5，其现值为：，0.08*0.0833328.528.31e −=即：－f ＋40Δ＝28.31 其中f 为看涨期权价格。
所以，f ＝40×0.75－28.31＝$1.69另解：（计算风险中性概率p ） 42p －38（1－p ）＝，p ＝0.56690.08*0.0833340e期权价值是其期望收益以无风险利率贴现的现值，即： f ＝（3×0.5669＋0×0.4331）＝$1.690.08*0.08333e−9.2 用单步二叉树图说明无套利和风险中性估值方法如何为欧式期权估值。
解：在无套利方法中，我们通过期权及股票建立无风险资产组合，使组合收益率等价于无风险利率，从而对期权估值。
在风险中性估值方法中，我们选取二叉树概率，以使股票的期望收益率等价于无风险利率，而后通过计算期权的期望收益并以无风险利率贴现得到期权价值。
9.3什么是股票期权的Delta ？解：股票期权的Delta 是度量期权价格对股价的小幅度变化的敏感度。
即是股票期权价格变化与其标的股票价格变化的比率。
9.4某个股票现价为$50。
已知6个月后将为$45或$55。
无风险年利率为10％（连续复利）。
执行价格为$50，6个月后到期的欧式看跌期权的价值为多少？ 解：考虑如下资产组合，卖1份看跌期权，买Δ份股票。
若股价上升为$55，则组合价值为55Δ；若股价下降为$45，则组合价值为：45Δ－5 当55Δ＝45Δ－5，即Δ＝－0.50时，6个月后组合价值在两种情况下将相等，均为$－27.5，其现值为：，即：0.10*0.5027.5$26.16e −−=− －P ＋50Δ＝－26.16所以，P ＝－50×0.5＋26.16＝$1.16 另解：求风险中性概率p0.10*0.505545(1)50p p e+−= 所以，p ＝0.7564看跌期权的价值P ＝0.10*0.50(0*0.75645*0.2436)$1.16e −+=9.5 某个股票现价为$100。
衍生品市场入门期货与期权基础
衍生品市场入门期货与期权基础衍生品是金融市场中的重要交易工具，广泛应用于各个领域。
期货和期权是衍生品市场中最常见的两种交易形式，它们具有不同的特点和功能。
本文将介绍衍生品市场的基本概念和期货、期权的基础知识，帮助读者了解和进入衍生品市场。
什么是衍生品？衍生品是金融市场中对冲风险、增加投资收益和实现投资策略的重要工具。
它们的价值来源于其基础资产，如股票、商品、外汇等。
衍生品的价格变动与基础资产价格的变动密切相关。
衍生品市场包括期货市场和期权市场。
在这些市场中，交易者可以通过买入或卖出期货合约或期权合约来获取利润或对冲风险。
期货基础知识什么是期货？期货是一种标准化合约，约定在未来某个时间以预定价格交割特定数量的某种标的资产。
标的资产可以是商品（如原油、黄金）、金融产品（如股指、债券）等。
期货交易在交易所进行，并受到监管机构的监管。
期货的特点标准化：期货合约具有明确的交割日期、交割地点、交割品种等规定，便于交易者进行买卖。
杠杆效应：由于只需要支付一小部分保证金，就能控制价值较大的合约，所以期货交易具有较大的杠杆效应。
高流动性：期货合约在交易所上进行交易，具有良好的流动性，买卖双方容易找到对手方。
零和游戏：期货市场上买家和卖家通过合约交易，利润是互相转移的，没有新增利润。
为什么投资者选择期货？对冲风险：投资者可以利用期货合约对冲自己持有的资产或产品的价格风险，降低投资组合的风险。
赚取利润：投资者可以通过预测市场走势并及时买入或卖出期货合约来赚取差价利润。
市场参与：期货市场具有高流动性和透明度，能为投资者提供更多的投资机会和灵活性。
期权基础知识什么是期权？期权是一种购买或销售标的资产在未来特定时间内按约定价格买入或卖出的权利。
与期货不同，期权给予了持有者选择行使权利与否的自由。
期权的特点双向选择：买方享有选择是否行使权利的自由，而卖方必须根据买方意愿履行合约。
权利金：购买期权需要支付一定数量的权利金作为费用，而卖方则获得权利金作为收入。
期权期货及衍生品 约翰赫尔 第九版 课后答案HullOFOD9eSolutionsCh10
CHAPTER 10Mechanics of Options MarketsPractice QuestionsProblem 10.1.An investor buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.The investor makes a profit if the price of the stock on the expiration date is less than $37. In these circumstances the gain from exercising the option is greater than $3. The option will be exercised if the stock price is less than $40 at the maturity of the option. The variation of the investor’s profit with the s tock price in Figure S10.1.Figure S10.1: Investor’s profit in Problem 10.1Problem 10.2.An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.The investor makes a profit if the price of the stock is below $54 on the expiration date. If the stock price is below $50, the option will not be exercised, and the investor makes a profit of $4. If the stock price is between $50 and $54, the option is exercised and the investor makes a profit between $0 and $4. The variation of the investor’s profit with the stoc k price is asshown in Figure S10.2.Figure S10.2: Investor’s profit in Problem 10.2Problem 10.3.An investor sells a European call option with strike price of K and maturity T and buys a put with the sam e strike price and maturity. Describe the investor’s position.The payoff to the investor ismax (0)max (0)T T S K K S --,+-,This is T K S - in all circumstances. The investor’s position is the same as a short position in a forward contract with delivery price K .Problem 10.4.Explain why margin accounts are required when clients write options but not when they buy options.When an investor buys an option, cash must be paid up front. There is no possibility of future liabilities and therefore no need for a margin account. When an investor sells an option, there are potential future liabilities. To protect against the risk of a default, margins are required.Problem 10.5.A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b) May 30?On April 1 options trade with expiration months of April, May, August, and November. On May 30 options trade with expiration months of June, July, August, and November.Problem 10.6.A company declares a 2-for-1 stock split. Explain how the terms change for a call option witha strike price of $60.The strike price is reduced to $30, and the option gives the holder the right to purchase twice as many shares.Problem 10.7.“Employee stock options issued by a company are different from regular exchange-traded call options on the company’s stock because they can affect the capital structure of the company.” Explain this statement.The exercise of employee stock options usually leads to new shares being issued by the company and sold to the employee. This changes the amount of equity in the capital structure. When a regular exchange-traded option is exercised no new shares are issued and the company’s capital structure is not affected.Problem 10.8.A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) the NASDAQ OMX and (b) the over-the-counter market for trading?The NASDAQ OMX offers options with standard strike prices and times to maturity. Options in the over-the-counter market have the advantage that they can be tailored to meet the precise needs of the treasurer. Their disadvantage is that they expose the treasurer to some credit risk. Exchanges organize their trading so that there is virtually no credit risk.Problem 10.9.Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.Ignoring the time value of money, the holder of the option will make a profit if the stock price at maturity of the option is greater than $105. This is because the payoff to the holder of the option is, in these circumstances, greater than the $5 paid for the option. The option will be exercised if the stock price at maturity is greater than $100. Note that if the stock price is between $100 and $105 the option is exercised, but the holder of the option takes a loss overall. The profit from a long position is as shown in Figure S10.3.Figure S10.3:Profit from long position in Problem 10.9Problem 10.10.Suppose that a European put option to sell a share for $60 costs $8 and is held until maturity. Under what circumstances will the seller of the option (the party with the short position) make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.Ignoring the time value of money, the seller of the option will make a profit if the stock price at maturity is greater than $52.00. This is because the cost to the seller of the option is in these circumstances less than the price received for the option. The option will be exercised if the stock price at maturity is less than $60.00. Note that if the stock price is between $52.00 and $60.00 the seller of the option makes a profit even though the option is exercised. The profit from the short position is as shown in Figure S10.4.Figure S10.4:Profit from short position in Problem 10.10Problem 10.11.Describe the terminal value of the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. Show that the European put option has the same value as a European call option with the same strike price and maturity.The terminal value of the long forward contract is:0T S F -where T S is the price of the asset at maturity and 0F is the forward price of the asset at thetime the portfolio is set up. (The delivery price in the forward contract is also 0F .)The terminal value of the put option is:0max (0)T F S -,The terminal value of the portfolio is therefore00max (0)T T S F F S -+-,0max (0]T S F =,-This is the same as the terminal value of a European call option with the same maturity as the forward contract and an exercise price equal to 0F . This result is illustrated in the Figure S10.5.Figure S10.5: Profit from portfolio in Problem 10.11We have shown that the forward contract plus the put is worth the same as a call with the same strike price and time to maturity as the put. The forward contract is worth zero at the time the portfolio is set up. It follows that the put is worth the same as the call at the time the portfolio is set up.Problem 10.12.A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the same maturity. The call costs $3 and the put costs $4. Draw a diagram showing the va riation of the trader’s profit with the asset price.Figure S10.6 shows the variation of the trader’s position with the asset price. We can divide the alternative asset prices into three ranges:a) When the asset price less than $40, the put option provides a payoff of 40T S - and thecall option provides no payoff. The options cost $7 and so the total profit is 33T S -.b) When the asset price is between $40 and $45, neither option provides a payoff. There is a net loss of $7.c) When the asset price greater than $45, the call option provides a payoff of 45T S - and the put option provides no payoff. Taking into account the $7 cost of the options, the total profit is 52T S -.The trader makes a profit (ignoring the time value of money) if the stock price is less than $33 or greater than $52. This type of trading strategy is known as a strangle and is discussed in Chapter 12.Figure S10.6: Profit from trading strategy in Problem 10.12Problem 10.13.Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.The holder of an American option has all the same rights as the holder of a European option and more. It must therefore be worth at least as much. If it were not, an arbitrageur could short the European option and take a long position in the American option.Problem 10.14.Explain why an American option is always worth at least as much as its intrinsic value.The holder of an American option has the right to exercise it immediately. The Americanoption must therefore be worth at least as much as its intrinsic value. If it were not anarbitrageur could lock in a sure profit by buying the option and exercising it immediately.Problem 10.15.Explain carefully the difference between writing a put option and buying a call option.Writing a put gives a payoff of min(0)T S K -,. Buying a call gives a payoff ofmax(0)T S K -,. In both cases the potential payoff is T S K -. The difference is that for a written put the counterparty chooses whether you get the payoff (and will allow you to get it only when it is negative to you). For a long call you decide whether you get the payoff (and you choose to get it when it is positive to you.)Problem 10.16.The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation’s foreign exchange risk. Discuss the a dvantages and disadvantages of each.Forward contracts lock in the exchange rate that will apply to a particular transaction in the future. Options provide insurance that the exchange rate will not be worse than some level. The advantage of a forward contract is that uncertainty is eliminated as far as possible. The disadvantage is that the outcome with hedging can be significantly worse than the outcome with no hedging. This disadvantage is not as marked with options. However, unlike forward contracts, options involve an up-front cost.Problem 10.17.Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity in four months. Explain how the terms of the option contract change when there isa) A 10% stock dividendb) A 10% cash dividendc) A 4-for-1 stock splita) The option contract becomes one to buy 50011550⨯.= shares with an exercise price401.13636=..b) There is no effect. The terms of an options contract are not normally adjusted for cash dividends.c) The option contract becomes one to buy 50042000⨯=, shares with an exercise price of404$10=.Problem 10.18.“If most of the call options on a stock are in the money, it is likely that the stock price has risen rapidly in the last few months.” Discuss this statement.The exchange has certain rules governing when trading in a new option is initiated. These mean that the option is close-to-the-money when it is first traded. If all call options are in the money it is therefore likely that the stock price has increased since trading in the option began.Problem 10.19.What is the effect of an unexpected cash dividend on (a) a call option price and (b) a put option price?An unexpected cash dividend would reduce the stock price on the ex-dividend date. This stock price reduction would not be anticipated by option holders. As a result there would be a reduction in the value of a call option and an increase the value of a put option. (Note that the terms of an option are adjusted for cash dividends only in exceptional circumstances.)Problem 10.20.Options on General Motors stock are on a March, June, September, and December cycle. What options trade on (a) March 1, (b) June 30, and (c) August 5?a)March, April, June and Septemberb)July, August, September, Decemberc)August, September, December, March.Longer dated options may also trade.Problem 10.21.Explain why the market maker’s bid-offer spread represents a real cost to options investors.A “fair” price for the option can reasonably be assumed to be half way between the bid and the offer price quoted by a market maker. An investor typically buys at the market maker’s offer and sells at the market maker’s bid. Each time he or she does this there i s a hidden cost equal to half the bid-offer spread.Problem 10.22.A United States investor writes five naked call option contracts. The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?The two calculations are necessary to determine the initial margin. The first gives⨯.+.⨯-=,500(3502573)5950The second gives⨯.+.⨯=,500(350157)4600The initial margin is the greater of these, or $5,950. Part of this can be provided by the initial amount of 50035$1750⨯.=,received for the options.Further QuestionsProblem 10.23.Calculate the intrinsic value and time value from the mid-market (average of bid andoffer) prices the September 2013 call options in Table 1.2. Do the same for the September 2013 put options in Table 1.3. Assume in each case that the current mid-market stock price is $871.30.For strike prices of 820, 840, 860, 880, 900, and 920 the intrinsic values of call options are 51.30, 31.30, 11.30, 0, 0, and 0. The mid-market values of the options are 76.90, 63.40, 51.75, 41.30, 32.45 and 25.20. The time values of the options are given by what is left from themid-market value after the intrinsic value has been subtracted. They are 25.60, 32.10, 40.45, 41.30, 32.45, and 25.20, respectively.For strike prices of 820, 840, 860, 880, 900, and 920, the intrinsic values of put options are 0, 0, 0, 8.70, 28.70, and 48.70. The mid-market values of the options are 24.55, 31.40, 39.65, 49.30, 60.05, and 72.55. The time values of the options are given by what is left from the mid-market value after the intrinsic value has been subtracted. They are 24.55, 31.40, 39.65, 40.60, 31.35 and 23.85, respectively.Note that for both puts and calls the time value is greatest when the option is close to the money.Problem 10.24.A trader has a put option contract to sell 100 shares of a stock for a strike price of $60. What is the effect on the terms of the contract of:(a) A $2 dividend being declared(b) A $2 dividend being paid(c) A 5-for-2 stock split(d) A 5% stock dividend being paid.(a)No effect(b)No effect(c)The put option contract gives the right to sell250 shares for $24 each(d)The put option contract gives the right to sell 105 shares for 60/1.05 = $57.14 Problem 10.25.A trader writes five naked put option contracts, with each contract being on 100 shares. The option price is $10, the time to maturity is six months, and the strike price is $64.(a) What is the margin requirement if the stock price is $58?(b) How would the answer to (a) change if the rules for index options applied?(c) How would the answer to (a) change if the stock price were $70?(d) How would the answer to (a) change if the trader is buying instead of selling the options?(a)The margin requirement is the greater of 500×(10 + 0.2×58) = 10,800 and500×(10+0.1×64) = 8,200. It is $10,800.(b)The margin requirement is the greater of 500×(10+0.15×58) = 9,350 and500×(10+0.1×64) = 8,200. It is $9,350.(c)The margin requirement is the greater of 500×(10+0.2×70-6) = 9,000 and500×(10+0.1×64) = 8,200. It is $9,000.(d)No margin is required if the trader is buyingProblem 10.26.The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50 is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram illustrating how the investor’s profit or loss varies wi th the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?Figure S10.7 shows the way in which the investor’s profit varies with the stock price in the first case. For stock prices less than $30 there is a loss of $1,200. As the stock price increases from $30 to $50 the profit increases from –$1,200 to $800. Above $50 the profit is $800. Students may express surprise that a call which is $10 out of the money is less expensive than a put which is $10 out of the money. This could be because of dividends or the crashophobia phenomenon discussed in Chapter 20.Figure S10.8 shows the way in which the profit varies with stock price in the second case. In this case the profit pattern has a zigzag shape. The problem illustrates how many different patterns can be obtained by including calls, puts, and the underlying asset in a portfolio.Figure S10.7:Profit in first case considered Problem 10.26Figure S10.8:Profit for the second case considered Problem 10.26Problem 10.27.“If a company does not do better than its competitors but the stock market goes up, executives do very well from their stock options. This makes no sense” Discuss th is viewpoint. Can you think of alternatives to the usual executive stock option plan that take the viewpoint into account.Executive stock option plans account for a high percentage of the total remuneration received by executives. When the market is rising fast, many corporate executives do very well out of their stock option plans — even when their company does worse than its competitors. Large institutional investors have argued that executive stock options should be structured so that the payoff depends how the company has performed relative to an appropriate industry index. In a regular executive stock option the strike price is the stock price at the time the option is issued. In the type of relative-performance stock option favored by institutional investors, the strike price at time t is 00t S I I where 0S is the company’s stock price at the time theoption is issued, 0I is the value of an equity index for the industry in which the companyoperates at the time the option is issued, and t I is the value of the index at time t . If the company’s performance equals the performance of the industry, the options are alway sat-the-money. If the company outperforms the industry, the options become in the money. If the company underperforms the industry, the options become out of the money. Note that a relative performance stock option can provide a payoff when both the market and the company’s stock price decline.Relative performance stock options clearly provide a better way of rewarding seniormanagement for superior performance. Some companies have argued that, if they introduce relative performance options when their competitors do not, they will lose some of their top management talent.Problem 10.28.Use DerivaGem to calculate the value of an American put option on a nondividend paying stock when the stock price is $30, the strike price is $32, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is 1.5 years. (Choose B inomial American for the “option type” and 50 time steps.)a. What is the option’s intrinsic value?b. What is the option’s time value?c. What would a time value of zero indicate? What is the value of an option with zero time value?d. Using a trial and error approach calculate how low the stock price would have to be for the time value of the option to be zero.DerivaGem shows that the value of the option is 4.57. The option’s intrinsic value is 3230200-=.. The option’s time value is therefore 457200257.-.=.. A time value of zero would indicate that it is optimal to exercise the option immediately. In this case the value of the option would equal its intrinsic value. When the stock price is 20, DerivaGem gives the value of the option as 12, which is its intrinsic value. When the stock price is 25, DerivaGem gives the value of the options as 7.54, indicating that the time value is still positive (054=.). Keeping the number of time steps equal to 50, trial and error indicates the time value disappears when the stock price is reduced to 21.6 or lower. (With 500 time steps this estimate of how low the stock price must become is reduced to 21.3.)Problem 10.29.On July 20, 2004 Microsoft surprised the market by announcing a $3 dividend. Theex-dividend date was November 17, 2004 and the payment date was December 2, 2004. Its stock price at the time was about $28. It also changed the terms of its employee stock options so that each exercise price was adjusted downward to Pre-dividend Exercise Price ClosingPrice 300ClosingPrice$-.⨯The number of shares covered by each stock option outstanding was adjusted upward to⨯Number of Shares Pre-dividend ClosingPrice-.ClosingPrice300$"Closing Price" means the official NASDAQ closing price of a share of Microsoft common stock on the last trading day before the ex-dividend date.Evaluate this adjustment. Compare it with the system used by exchanges to adjust for extraordinary dividends (see Business Snapshot 10.1).Suppose that the closing stock price is $28 and an employee has 1000 options with a strike price of $24. Microsoft’s adjustment involves changing the strike price to ⨯=.and changing the number of options to 100028251120 242528214286⨯=,. The system used by exchanges would involve keeping the number of options the same and reducing the strike price by $3 to $21.The Microsoft adjustment is more complicated than that used by the exchange because it requires a knowledge of the Microsoft’s stock price immediately before the stock goesex-dividend. However, arguably it is a better adjustment than the one used by the exchange. Before the adjustment the employee has the right to pay $24,000 for Microsoft stock that is worth $28,000. After the adjustment the employee also has the option to pay $24,000 for Microsoft stock worth $28,000. Under the adjustment rule used by exchanges the employee would have the right to buy stock worth $25,000 for $21,000. If the volatility of Microsoft remains the same this is a less valuable option.One complication here is that Microsoft’s volatility does not remain the same. It can be expected to go up because some cash (a zero risk asset) has been transferred to shareholders. The employees therefore have the same basic option as before but the volatility of Microsoft can be expected to increase. The employees are slightly better off because the value of an option increases with volatility.。
期权与期货课件第6章 期权市场机制
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©中央财经大学期权与期货
第六章 期权市场机制
第三节 期权合约条款和保证金
©中央财经大学期权与期货
第三节 期权合约条款和保证金 一、合约条款
合约条款 标的资产 合约类型 合约单位 合约到期月份 行权价格
行权价格间距
行权方式
交割方式
条款介绍
标的资产是期权合约对应的资产，期权买卖双方约定买入或卖出的对象
到期日
到期月份的第四个星期三（遇法定节假日顺延）
行权日
同合约到期日，行权指令提交时间为9:15-9:25，9:30-11:30，13:00-15:30
交收日 交易时间
委托类型 买卖类型
行权日次一交易日
上午9:15-9:25，9:30-11:30（9:15-9:25为开盘集合竞价时间）下午13:00-15:00（14:57-15:00为收盘集合 竞价时间） 普通限价委托、市价剩余转限价委托、市价剩余撤销委托、全额即时限价委托、全额即时市价委托以 及业务规则规定的其他委托类型
9个（1个平值合约、4个虚值合约、4个实值合约） 3元或以下为0.05元，3元至5元（含）为0.1元，5元至10元（含）为0.25元，10元至20元（含）为0.5元 ，20元至50元（含）为1元，50元至100元（含）为2.5元，100元以上为5元 到期日行权（欧式）
交割方式
实物交割（业务规则另有规定的除外）
➢ 时间价值(intrinsic value)，是指随着时间的推移，期权获利的可能性，而期权的买方愿意为 这种获利的可能性买单的那部分价值。
✓ 一般从期权价格中扣除内涵价值得到时间价值的数值
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©中央财经大学期权与期货
第二节 期权的价值构成与价值状态 一、期权的内涵价值与时间价值
【经典】约翰赫尔 期权期货其他衍生品 课后习题解答 完整 中文版-1-20习题解答【完整版】
第一章1.1请解释远期多头与远期空头的区别。
答：远期多头指交易者协定将来以某一确定价格购入某种资产；远期空头指交易者协定将来以某一确定价格售出某种资产。
1.2请详细解释套期保值、投机与套利的区别。
答：套期保值指交易者采取一定的措施补偿资产的风险暴露；投机不对风险暴露进行补偿，是一种“赌博行为”；套利是采取两种或更多方式锁定利润。
1.3请解释签订购买远期价格为$50的远期合同与持有执行价格为$50的看涨期权的区别。
答：第一种情况下交易者有义务以50$购买某项资产（交易者没有选择），第二种情况下有权利以50$购买某项资产（交易者可以不执行该权利）。
1.4一位投资者出售了一个棉花期货合约，期货价格为每磅50美分，每个合约交易量为50，000磅。
请问期货合约结束时，当合约到期时棉花价格分别为（a）每磅48.20美分；（b）每磅51.30美分时，这位投资者的收益或损失为多少？ 答：(a)合约到期时棉花价格为每磅$0.4820时，交易者收入：（$0.5000-$0.4820）×50，000＝$900;(b)合约到期时棉花价格为每磅$0.5130时，交易者损失:($0.5130-$0.5000) ×50，000=$6501.5假设你出售了一个看跌期权，以$120执行价格出售100股IBM的股票，有效期为3个月。
IBM股票的当前价格为$121。
你是怎么考虑的？你的收益或损失如何？答：当股票价格低于$120时，该期权将不被执行。
当股票价格高于$120美元时，该期权买主执行该期权，我将损失100(st-x)。
1.6你认为某种股票的价格将要上升。
现在该股票价格为$29,3个月期的执行价格为$30的看跌期权的价格为$2.90.你有$5,800资金可以投资。
现有两种策略：直接购买股票或投资于期权，请问各自潜在的收益或损失为多少？答：股票价格低于$29时，购买股票和期权都将损失，前者损失为$5,800$29×(29-p),后者损失为$5，800;当股票价格为（29，30），购买股票收益为$5,800$29×(p-29),购买期权损失为$5,800;当股票价格高于$30时，购买股票收益为$5,800 $29×(p-29)，购买期权收益为$$5,800$29×(p-30)-5,800。
期权期货和其他衍生品 第五、六章答案(双数题)
期权期货及其他衍生产品作业第五章5.2答：远期价格是远期合约中的交割价格，它是双方约定的价格，约定好了就不会变动，到期直接按此价格交割。
而远期合约价值是远期合约内在的价值，是由于标的资产价格的变化导致此合约或盈或亏，这个价值就是用来计算这个合约是赢是亏的。
5.4解：由题意，股指的当前价格S0=350，无风险收益率r=8%，股息收益率q=4%，T=4/12。
则期货价格F0=S0e(r-q)T=350e(0.08-0.04)4/12=354.7美元。
所以，4个月期的期货价格为354.7美元。
5.6答：便利收益用于衡量持有实际资产比仅持有期货合约而带来的额外好处，包括从本地的商品暂时性短缺中获利，以及为了保持生产线正常运作的能力。
持有成本等于标的资产存储成本加上融资成本再减去资本收益。
假设期货价格为F0，即期价格为S0，便利收益率为y，持有成本为c，则有:F0=S0e(c-y)T5.8答：股指的期货价格低于其将来预期价格。
假设k为投资者对于股指期货投资要求的投资收益率，r为无风险利率，S T为到期日的资产价格。
由于股指价格与股票市场有正相关性投资者对股指所期望的收益率要大于无风险利率，及k>r,F0=E(S T)e（r-k）T，得F0<E(ST)，所以股指的期货价格低于其将来预期价格。
5.10解：由题意，股指的当前价格S0=150，无风险收益率r=7%，股息收益率q=3.2%，T=6/12。
则期货价格F0=S0e(r-q)T=150e(0.07-0.032)6/12=152.88所以，6个月期期货价格为152.885.12解：期货理论价格F0=S0e(r-q)T=400e(0.1-0.04)4/12=408美元>实际价格405美元，认为期货价格被低估了，应该买入。
因此，应当以即期价格卖空股票，并进入一个期货合约长头寸。
5.14解：期货理论价格为F0=S0e(r-rf)T=0.8e(0.05-0.02)*2/12=0.804美元<实际价格0.81美元，期货价格过高，因此应该进入瑞郎期货合约短头寸（假设进入的是1000美元的），同时借入美元买入瑞郎。
期权期货和其他衍生品约翰赫尔第九版答案 (2)
期权期货和其他衍生品约翰赫尔第九版答案简介《期权期货和其他衍生品》是由约翰·赫尔（John C. Hull）编写的一本经典教材，是金融衍生品领域的权威参考书籍之一。
该书第九版是在第八版的基础上进行了更新和修订，以适应当前金融市场的动态变化。
本文档旨在提供《期权期货和其他衍生品第九版》的答案，帮助读者更好地理解和应用书中的知识点。
以下将按照书籍的章节顺序，逐一给出答案。
第一章期权市场的基本特征1.什么是期权？答：期权是一种金融衍生品，它赋予买方在特定时间以特定价格买入或卖出标的资产的权力，而不是义务。
可以将期权分为看涨期权和看跌期权。
2.期权的四个基本特征是什么？答：期权的四个基本特征是价格、到期日、标的资产和行权方式。
价格即期权的成交价，到期日是期权到期的日期，标的资产是期权合约要买入或卖出的资产，而行权方式则决定了期权何时可以行使。
3.什么是期权合约？答：期权合约是买卖双方约定的具体规定和条件，包括标的资产、行权价格、到期日等。
它规定了买方在合约到期前是否可以行使期权。
第二章期权定价：基础观念1.定价模型的基本原理是什么？答：期权定价模型的基本原理是假设市场是有效的，即不存在无风险套利机会。
通过建立基于风险中性概率的模型，可以计算期权的理论价值。
2.什么是风险中性概率？答：风险中性概率是指在假设市场是有效的情况下，使得在无套利条件下资产价格在期望值与当前价格之间折现的概率。
风险中性概率的使用可以将市场中的现金流折算为无风险利率下的现值。
3.什么是期权的内在价值和时间价值？答：期权的内在价值是指期权当前即时的价值，即行权价格与标的资产价格之间的差额。
时间价值是期权除去内在价值后剩余的价值，它受到时间、波动率和利率等因素的影响。
第三章期权定价模型：基础知识1.什么是布莱克斯科尔斯期权定价模型？答：布莱克斯科尔斯期权定价模型是一种用于计算欧式期权价格的数学模型。
它基于连续性投资组合原理，使用了假设市场是完全有效的和无交易成本的条件，可以通过著名的布拉克斯科尔斯公式来计算期权的价格。
赫尔《期权、期货及其他衍生产品》(第7版)课后习题详解(利率衍生品标准市场模型)
28.2 课后习题详解一、问答题1. 一家企业签署了一项上限合约，合约将3个月期LIBOR利率上限定为每年10％，本金为2000万美元。
在重置日3个月的LIBOR利率为每年12％。
根据利率上限协议，收益将如何支付，付款日为何时?A company caps three-month LIBOR at 10% per annum. The principal amount is $20 million. On a reset date, three-month LIBOR is 12% per annum. What payment would this lead to under the cap? When would the payment be made?答：应支付的数量为：20000000×0.02×0.25=100000（美元），该支付应在3个月后进行。
2. 解释为什么一个互换期权可以看作是一个债券期权。
Explain why a swap option can be regarded as a type of bond option.答：互换期权是是基于利率互换的期权，它给予持有者在未来某个确定时间进入一个约定的利率互换的权利。
利率互换可以被看作是固定利率债券和浮动利率债券的交换。
因而，互换期权可以看成是固定利率债券和浮动利率债券的交换的选择权。
在互换开始时，浮动利率债券的价值等于其本金额。
这样互换期权就可以被看作是以债权的面值为执行价格、以固定利率债券为标的资产的期权。
即互换期权可以看作是一个债券期权。
3. 采用布莱克模型来对一个期限为1年，标的资产为10年期债券的欧式看跌期权定价。
假定债券当前价格为125美元，执行价格为110美元，1年期利率为每年10％，债券远期价格的波动率为每年8％，期权期限内所支付票息的贴现值为10美元。
Use Black’s model to value a one-year European put option on a 10-year bond. Assume that the current value of the bond is $125, the strike price is $110, the one-year interest rate is 10% per annum, the bond's price volatility is 8% per annum, and the present value of the coupons to be paid during the life of the option is $10.答：根据布莱克模型，F0=(125-10)e0.1×1=127.09，K=110，P（0，T）=e-0.1×1，σB=0.08和T=1.0。
中华人民共和国期货和衍生品法
中华人民共和国期货和衍生品法文章属性•【制定机关】全国人大常委会•【公布日期】2022.04.20•【文号】中华人民共和国主席令第一一一号•【施行日期】2022.08.01•【效力等级】法律•【时效性】现行有效•【主题分类】期货正文中华人民共和国主席令第一一一号《中华人民共和国期货和衍生品法》已由中华人民共和国第十三届全国人民代表大会常务委员会第三十四次会议于2022年4月20日通过，现予公布，自2022年8月1日起施行。
中华人民共和国主席习近平2022年4月20日中华人民共和国期货和衍生品法（2022年4月20日第十三届全国人民代表大会常务委员会第三十四次会议通过）目录第一章总则第二章期货交易和衍生品交易第一节一般规定第二节期货交易第三节衍生品交易第三章期货结算与交割第四章期货交易者第五章期货经营机构第六章期货交易场所第七章期货结算机构第八章期货服务机构第九章期货业协会第十章监督管理第十一章跨境交易与监管协作第十二章法律责任第十三章附则第一章总则第一条为了规范期货交易和衍生品交易行为，保障各方合法权益，维护市场秩序和社会公共利益，促进期货市场和衍生品市场服务国民经济，防范化解金融风险，维护国家经济安全，制定本法。
第二条在中华人民共和国境内，期货交易和衍生品交易及相关活动，适用本法。
在中华人民共和国境外的期货交易和衍生品交易及相关活动，扰乱中华人民共和国境内市场秩序，损害境内交易者合法权益的，依照本法有关规定处理并追究法律责任。
第三条本法所称期货交易，是指以期货合约或者标准化期权合约为交易标的的交易活动。
本法所称衍生品交易，是指期货交易以外的，以互换合约、远期合约和非标准化期权合约及其组合为交易标的的交易活动。
本法所称期货合约，是指期货交易场所统一制定的、约定在将来某一特定的时间和地点交割一定数量标的物的标准化合约。
本法所称期权合约，是指约定买方有权在将来某一时间以特定价格买入或者卖出约定标的物（包括期货合约）的标准化或非标准化合约。
期货、期权及其他衍生品习题集
第2章期货市场的运作机制【2.1】说明未平仓合约数量与交易量的区别。
【2.2】说明自营经纪人与佣金经纪人的区别。
【2.3】假定你进入纽约商品交易所的一个7月份白银期货合约的短头寸，在合约中你能够以每盎司10.20美元的价格卖出白银。
期货合约规模为5000盎司白银。
最初保证金为4000美元，维持保证金为3000美元，期货价格如何变动会导致保证金的催付通知？你如果不满足催付通知会有什么后果？【2.4】假定在2009年9月一家公司进入了2010年5月的原油期货合约的长头寸。
在2010年3月公司将合约平仓。
在进入合约时期货价格（每桶）68.30美元，在平仓时价格为70.50美元，在2009年12月底为69.10美元。
每个合约是关于1000桶原油的交割。
公司的盈利是多少？什么时间实现该盈利？对以下投资者应如何征税？（a）对冲者；（b）投机者。
假定公司年度末为12月31日。
【2.5】止损指令为在2美元卖出的含义是什么？什么时候可采用这一指令。
一个限价指令为在2美元卖出的含义是什么？什么时候可采用这一指令。
【2.6】结算中心管理的保证金账户的运作与经纪人管理的保证金账户的运作有什么区别？【2.7】外汇期货市场、外汇即期市场、以及外汇远期市场的汇率报价的区别是什么？【2.8】期货合约的短头寸方有势有权选择交割的资产种类、交割地点以及交割时间等。
这些选择权会使期货价格上升还是下降？解释原因。
【2.9】设计一个新的期货合约时需要考虑那些最重要的方面。
【2.10】解释保证金如何保证投资者免受违约风险。
【2.11】某投资者净土两个7月橙汁期货合约的长寸头。
每个期货合约的规模均为15000磅橙汁。
当前期货价格为每磅160美分。
最初保证金每个合约6000美元，维持保证金为每个合约4500美元。
怎样的价格变化会导致保证金的催付？在哪种情况下可以从保证金账户中提取2000美元。
【2.12】如果在交割期间内期货价格大于即期价格，证明存在套利机会。
期权期货及衍生品 约翰赫尔 第九版 课后答案HullOFOD9eSolutionsCh10
CHAPTER 10Mechanics of Options MarketsPractice QuestionsProblem 10.1.An investor buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.The investor makes a profit if the price of the stock on the expiration date is less than $37. In these circumstances the gain from exercising the option is greater than $3. The option will be exercised if the stock price is less than $40 at the maturity of the option. The variation of the investor’s profit with the s tock price in Figure S10.1.Figure S10.1: Investor’s profit in Problem 10.1Problem 10.2.An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? Draw a diagram showing the variation of the investor’s profit with the stock price at the maturity of the option.The investor makes a profit if the price of the stock is below $54 on the expiration date. If the stock price is below $50, the option will not be exercised, and the investor makes a profit of $4. If the stock price is between $50 and $54, the option is exercised and the investor makes a profit between $0 and $4. The variation of the investor’s profit with the stoc k price is asshown in Figure S10.2.Figure S10.2: Investor’s profit in Problem 10.2Problem 10.3.An investor sells a European call option with strike price of K and maturity T and buys a put with the sam e strike price and maturity. Describe the investor’s position.The payoff to the investor ismax (0)max (0)T T S K K S --,+-,This is T K S - in all circumstances. The investor’s position is the same as a short position in a forward contract with delivery price K .Problem 10.4.Explain why margin accounts are required when clients write options but not when they buy options.When an investor buys an option, cash must be paid up front. There is no possibility of future liabilities and therefore no need for a margin account. When an investor sells an option, there are potential future liabilities. To protect against the risk of a default, margins are required.Problem 10.5.A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b) May 30?On April 1 options trade with expiration months of April, May, August, and November. On May 30 options trade with expiration months of June, July, August, and November.Problem 10.6.A company declares a 2-for-1 stock split. Explain how the terms change for a call option witha strike price of $60.The strike price is reduced to $30, and the option gives the holder the right to purchase twice as many shares.Problem 10.7.“Employee stock options issued by a company are different from regular exchange-traded call options on the company’s stock because they can affect the capital structure of the company.” Explain this statement.The exercise of employee stock options usually leads to new shares being issued by the company and sold to the employee. This changes the amount of equity in the capital structure. When a regular exchange-traded option is exercised no new shares are issued and the company’s capital structure is not affected.Problem 10.8.A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) the NASDAQ OMX and (b) the over-the-counter market for trading?The NASDAQ OMX offers options with standard strike prices and times to maturity. Options in the over-the-counter market have the advantage that they can be tailored to meet the precise needs of the treasurer. Their disadvantage is that they expose the treasurer to some credit risk. Exchanges organize their trading so that there is virtually no credit risk.Problem 10.9.Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the option depends on the stock price at maturity of the option.Ignoring the time value of money, the holder of the option will make a profit if the stock price at maturity of the option is greater than $105. This is because the payoff to the holder of the option is, in these circumstances, greater than the $5 paid for the option. The option will be exercised if the stock price at maturity is greater than $100. Note that if the stock price is between $100 and $105 the option is exercised, but the holder of the option takes a loss overall. The profit from a long position is as shown in Figure S10.3.Figure S10.3:Profit from long position in Problem 10.9Problem 10.10.Suppose that a European put option to sell a share for $60 costs $8 and is held until maturity. Under what circumstances will the seller of the option (the party with the short position) make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option.Ignoring the time value of money, the seller of the option will make a profit if the stock price at maturity is greater than $52.00. This is because the cost to the seller of the option is in these circumstances less than the price received for the option. The option will be exercised if the stock price at maturity is less than $60.00. Note that if the stock price is between $52.00 and $60.00 the seller of the option makes a profit even though the option is exercised. The profit from the short position is as shown in Figure S10.4.Figure S10.4:Profit from short position in Problem 10.10Problem 10.11.Describe the terminal value of the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to the forward price of the asset at the time the portfolio is set up. Show that the European put option has the same value as a European call option with the same strike price and maturity.The terminal value of the long forward contract is:0T S F -where T S is the price of the asset at maturity and 0F is the forward price of the asset at thetime the portfolio is set up. (The delivery price in the forward contract is also 0F .)The terminal value of the put option is:0max (0)T F S -,The terminal value of the portfolio is therefore00max (0)T T S F F S -+-,0max (0]T S F =,-This is the same as the terminal value of a European call option with the same maturity as the forward contract and an exercise price equal to 0F . This result is illustrated in the Figure S10.5.Figure S10.5: Profit from portfolio in Problem 10.11We have shown that the forward contract plus the put is worth the same as a call with the same strike price and time to maturity as the put. The forward contract is worth zero at the time the portfolio is set up. It follows that the put is worth the same as the call at the time the portfolio is set up.Problem 10.12.A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the same maturity. The call costs $3 and the put costs $4. Draw a diagram showing the va riation of the trader’s profit with the asset price.Figure S10.6 shows the variation of the trader’s position with the asset price. We can divide the alternative asset prices into three ranges:a) When the asset price less than $40, the put option provides a payoff of 40T S - and thecall option provides no payoff. The options cost $7 and so the total profit is 33T S -.b) When the asset price is between $40 and $45, neither option provides a payoff. There is a net loss of $7.c) When the asset price greater than $45, the call option provides a payoff of 45T S - and the put option provides no payoff. Taking into account the $7 cost of the options, the total profit is 52T S -.The trader makes a profit (ignoring the time value of money) if the stock price is less than $33 or greater than $52. This type of trading strategy is known as a strangle and is discussed in Chapter 12.Figure S10.6: Profit from trading strategy in Problem 10.12Problem 10.13.Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.The holder of an American option has all the same rights as the holder of a European option and more. It must therefore be worth at least as much. If it were not, an arbitrageur could short the European option and take a long position in the American option.Problem 10.14.Explain why an American option is always worth at least as much as its intrinsic value.The holder of an American option has the right to exercise it immediately. The Americanoption must therefore be worth at least as much as its intrinsic value. If it were not anarbitrageur could lock in a sure profit by buying the option and exercising it immediately.Problem 10.15.Explain carefully the difference between writing a put option and buying a call option.Writing a put gives a payoff of min(0)T S K -,. Buying a call gives a payoff ofmax(0)T S K -,. In both cases the potential payoff is T S K -. The difference is that for a written put the counterparty chooses whether you get the payoff (and will allow you to get it only when it is negative to you). For a long call you decide whether you get the payoff (and you choose to get it when it is positive to you.)Problem 10.16.The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation’s foreign exchange risk. Discuss the a dvantages and disadvantages of each.Forward contracts lock in the exchange rate that will apply to a particular transaction in the future. Options provide insurance that the exchange rate will not be worse than some level. The advantage of a forward contract is that uncertainty is eliminated as far as possible. The disadvantage is that the outcome with hedging can be significantly worse than the outcome with no hedging. This disadvantage is not as marked with options. However, unlike forward contracts, options involve an up-front cost.Problem 10.17.Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity in four months. Explain how the terms of the option contract change when there isa) A 10% stock dividendb) A 10% cash dividendc) A 4-for-1 stock splita) The option contract becomes one to buy 50011550⨯.= shares with an exercise price401.13636=..b) There is no effect. The terms of an options contract are not normally adjusted for cash dividends.c) The option contract becomes one to buy 50042000⨯=, shares with an exercise price of404$10=.Problem 10.18.“If most of the call options on a stock are in the money, it is likely that the stock price has risen rapidly in the last few months.” Discuss this statement.The exchange has certain rules governing when trading in a new option is initiated. These mean that the option is close-to-the-money when it is first traded. If all call options are in the money it is therefore likely that the stock price has increased since trading in the option began.Problem 10.19.What is the effect of an unexpected cash dividend on (a) a call option price and (b) a put option price?An unexpected cash dividend would reduce the stock price on the ex-dividend date. This stock price reduction would not be anticipated by option holders. As a result there would be a reduction in the value of a call option and an increase the value of a put option. (Note that the terms of an option are adjusted for cash dividends only in exceptional circumstances.)Problem 10.20.Options on General Motors stock are on a March, June, September, and December cycle. What options trade on (a) March 1, (b) June 30, and (c) August 5?a)March, April, June and Septemberb)July, August, September, Decemberc)August, September, December, March.Longer dated options may also trade.Problem 10.21.Explain why the market maker’s bid-offer spread represents a real cost to options investors.A “fair” price for the option can reasonably be assumed to be half way between the bid and the offer price quoted by a market maker. An investor typically buys at the market maker’s offer and sells at the market maker’s bid. Each time he or she does this there i s a hidden cost equal to half the bid-offer spread.Problem 10.22.A United States investor writes five naked call option contracts. The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?The two calculations are necessary to determine the initial margin. The first gives⨯.+.⨯-=,500(3502573)5950The second gives⨯.+.⨯=,500(350157)4600The initial margin is the greater of these, or $5,950. Part of this can be provided by the initial amount of 50035$1750⨯.=,received for the options.Further QuestionsProblem 10.23.Calculate the intrinsic value and time value from the mid-market (average of bid andoffer) prices the September 2013 call options in Table 1.2. Do the same for the September 2013 put options in Table 1.3. Assume in each case that the current mid-market stock price is $871.30.For strike prices of 820, 840, 860, 880, 900, and 920 the intrinsic values of call options are 51.30, 31.30, 11.30, 0, 0, and 0. The mid-market values of the options are 76.90, 63.40, 51.75, 41.30, 32.45 and 25.20. The time values of the options are given by what is left from themid-market value after the intrinsic value has been subtracted. They are 25.60, 32.10, 40.45, 41.30, 32.45, and 25.20, respectively.For strike prices of 820, 840, 860, 880, 900, and 920, the intrinsic values of put options are 0, 0, 0, 8.70, 28.70, and 48.70. The mid-market values of the options are 24.55, 31.40, 39.65, 49.30, 60.05, and 72.55. The time values of the options are given by what is left from the mid-market value after the intrinsic value has been subtracted. They are 24.55, 31.40, 39.65, 40.60, 31.35 and 23.85, respectively.Note that for both puts and calls the time value is greatest when the option is close to the money.Problem 10.24.A trader has a put option contract to sell 100 shares of a stock for a strike price of $60. What is the effect on the terms of the contract of:(a) A $2 dividend being declared(b) A $2 dividend being paid(c) A 5-for-2 stock split(d) A 5% stock dividend being paid.(a)No effect(b)No effect(c)The put option contract gives the right to sell250 shares for $24 each(d)The put option contract gives the right to sell 105 shares for 60/1.05 = $57.14 Problem 10.25.A trader writes five naked put option contracts, with each contract being on 100 shares. The option price is $10, the time to maturity is six months, and the strike price is $64.(a) What is the margin requirement if the stock price is $58?(b) How would the answer to (a) change if the rules for index options applied?(c) How would the answer to (a) change if the stock price were $70?(d) How would the answer to (a) change if the trader is buying instead of selling the options?(a)The margin requirement is the greater of 500×(10 + 0.2×58) = 10,800 and500×(10+0.1×64) = 8,200. It is $10,800.(b)The margin requirement is the greater of 500×(10+0.15×58) = 9,350 and500×(10+0.1×64) = 8,200. It is $9,350.(c)The margin requirement is the greater of 500×(10+0.2×70-6) = 9,000 and500×(10+0.1×64) = 8,200. It is $9,000.(d)No margin is required if the trader is buyingProblem 10.26.The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50 is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram illustrating how the investor’s profit or loss varies wi th the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?Figure S10.7 shows the way in which the investor’s profit varies with the stock price in the first case. For stock prices less than $30 there is a loss of $1,200. As the stock price increases from $30 to $50 the profit increases from –$1,200 to $800. Above $50 the profit is $800. Students may express surprise that a call which is $10 out of the money is less expensive than a put which is $10 out of the money. This could be because of dividends or the crashophobia phenomenon discussed in Chapter 20.Figure S10.8 shows the way in which the profit varies with stock price in the second case. In this case the profit pattern has a zigzag shape. The problem illustrates how many different patterns can be obtained by including calls, puts, and the underlying asset in a portfolio.Figure S10.7:Profit in first case considered Problem 10.26Figure S10.8:Profit for the second case considered Problem 10.26Problem 10.27.“If a company does not do better than its competitors but the stock market goes up, executives do very well from their stock options. This makes no sense” Discuss th is viewpoint. Can you think of alternatives to the usual executive stock option plan that take the viewpoint into account.Executive stock option plans account for a high percentage of the total remuneration received by executives. When the market is rising fast, many corporate executives do very well out of their stock option plans — even when their company does worse than its competitors. Large institutional investors have argued that executive stock options should be structured so that the payoff depends how the company has performed relative to an appropriate industry index. In a regular executive stock option the strike price is the stock price at the time the option is issued. In the type of relative-performance stock option favored by institutional investors, the strike price at time t is 00t S I I where 0S is the company’s stock price at the time theoption is issued, 0I is the value of an equity index for the industry in which the companyoperates at the time the option is issued, and t I is the value of the index at time t . If the company’s performance equals the performance of the industry, the options are alway sat-the-money. If the company outperforms the industry, the options become in the money. If the company underperforms the industry, the options become out of the money. Note that a relative performance stock option can provide a payoff when both the market and the company’s stock price decline.Relative performance stock options clearly provide a better way of rewarding seniormanagement for superior performance. Some companies have argued that, if they introduce relative performance options when their competitors do not, they will lose some of their top management talent.Problem 10.28.Use DerivaGem to calculate the value of an American put option on a nondividend paying stock when the stock price is $30, the strike price is $32, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is 1.5 years. (Choose B inomial American for the “option type” and 50 time steps.)a. What is the option’s intrinsic value?b. What is the option’s time value?c. What would a time value of zero indicate? What is the value of an option with zero time value?d. Using a trial and error approach calculate how low the stock price would have to be for the time value of the option to be zero.DerivaGem shows that the value of the option is 4.57. The option’s intrinsic value is 3230200-=.. The option’s time value is therefore 457200257.-.=.. A time value of zero would indicate that it is optimal to exercise the option immediately. In this case the value of the option would equal its intrinsic value. When the stock price is 20, DerivaGem gives the value of the option as 12, which is its intrinsic value. When the stock price is 25, DerivaGem gives the value of the options as 7.54, indicating that the time value is still positive (054=.). Keeping the number of time steps equal to 50, trial and error indicates the time value disappears when the stock price is reduced to 21.6 or lower. (With 500 time steps this estimate of how low the stock price must become is reduced to 21.3.)Problem 10.29.On July 20, 2004 Microsoft surprised the market by announcing a $3 dividend. Theex-dividend date was November 17, 2004 and the payment date was December 2, 2004. Its stock price at the time was about $28. It also changed the terms of its employee stock options so that each exercise price was adjusted downward to Pre-dividend Exercise Price ClosingPrice 300ClosingPrice$-.⨯The number of shares covered by each stock option outstanding was adjusted upward to⨯Number of Shares Pre-dividend ClosingPrice-.ClosingPrice300$"Closing Price" means the official NASDAQ closing price of a share of Microsoft common stock on the last trading day before the ex-dividend date.Evaluate this adjustment. Compare it with the system used by exchanges to adjust for extraordinary dividends (see Business Snapshot 10.1).Suppose that the closing stock price is $28 and an employee has 1000 options with a strike price of $24. Microsoft’s adjustment involves changing the strike price to ⨯=.and changing the number of options to 100028251120 242528214286⨯=,. The system used by exchanges would involve keeping the number of options the same and reducing the strike price by $3 to $21.The Microsoft adjustment is more complicated than that used by the exchange because it requires a knowledge of the Microsoft’s stock price immediately before the stock goesex-dividend. However, arguably it is a better adjustment than the one used by the exchange. Before the adjustment the employee has the right to pay $24,000 for Microsoft stock that is worth $28,000. After the adjustment the employee also has the option to pay $24,000 for Microsoft stock worth $28,000. Under the adjustment rule used by exchanges the employee would have the right to buy stock worth $25,000 for $21,000. If the volatility of Microsoft remains the same this is a less valuable option.One complication here is that Microsoft’s volatility does not remain the same. It can be expected to go up because some cash (a zero risk asset) has been transferred to shareholders. The employees therefore have the same basic option as before but the volatility of Microsoft can be expected to increase. The employees are slightly better off because the value of an option increases with volatility.。
约翰.赫尔《期权、期货和其他衍生品》复习总结
定。 我国目前交易的所有期货合约均需在交易所指定仓库进行交割。
价格和头寸限制 期货报价
商品期货合约的报价一般是按照单位商品价格进行报价。 金融期货Байду номын сангаас约则是按照点数来进行报价。 涨跌幅限制 为了期货合约价格出现投机性的暴涨暴跌, 交易所一般对期货合约价格
每日最大波动幅度进行限制。 超过该涨跌幅度的报价将被视为无效，不能成交。 合约持仓限制（头寸的限额） 期货交易所一般对单个投资者在单一期货合约上的持仓（头寸）有最大
平仓：获取一个与初始交易头寸相反的头寸。 平仓是指在交割期之前，进入一个与已持有的合约有相同交割月份、相同数量、 同种商品、相反头寸的新期货合约。
期货的运作机制 期货合约条款的规定 标的资产：指期货合约双方约定在到期时买卖的商品。
对交割品的品质进行详细的规定, 从而保证交割物的价值。 对品质与标准不符的替代交割品价格升水或者贴水进行规定。 商品期货合约侧重对商品物理性质的规定。 金融期货合约侧重对交割物的期限和利率的规定。 指数类期货合约以现金进行结算, 因此不需要交割物条款。
合约规模：合约的面额指的是交割物的数量, 而不是交割物的实际价值。无论采 用实物交割还是现金交割，期货合约必须规定合约的大小，即未来交割的标的资 产的数量。高合约面额有利于节省交易成本。低合约面额则有利于吸引中小投资 者参与市场, 提高市场流动性。
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Treasury Bill Prices in the US
Bond: 8% 30/360
Assumes 30 days per month and 360 days per year. When coupons are paid on March 1 and Sept 1, how much interest is earned between March 1 and April 1?
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Example
Most recent settlement price = 90.00 Conversion factor of bond delivered = 1.3800 Accrued interest on bond =3.00 Price received for bond is 1.3800×90.00+3.00 = $127.20 per $100 of principal
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Example
Suppose you buy (take a long position in) a contract on November 1 The contract expires on December 21 The prices are as shown How much do you gain or lose a) on the first day, b) on the second day, c) over the whole time until expiration?
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Examples continued
T-Bill: 8% Actual/360:
8% is earned in 360 days. Accrual calculated by dividing the actual number of days in the period by 360. How much interest is earned between March 1 and April 1?
Corporate Bonds: 30ts:
Actual/360
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Examples
P 360(100Y) n
Y iscashpriceper $100 P is quotedprice
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Treasury Bond Price Quotes in the U.S
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Example continued
If on Nov. 1 you know that you will have $1 million to invest on for three months on Dec 21, the contract locks in a rate of
Cash price = Quoted price + Accrued Interest
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Treasury Bond Futures
Pages 132-136
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Eurodollar Futures (Page 136-141)
A Eurodollar is a dollar deposited in a bank outside the United States Eurodollar futures are futures on the 3-month Eurodollar deposit rate (same as 3-month LIBOR rate) One contract is on the rate earned on $1 million A change of one basis point or 0.01 in a Eurodollar futures quote corresponds to a contract price change of $25
This corresponds to the $25 per basis point rule
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Forward Rates and Eurodollar Futures (Page 139-141)
Eurodollar futures contracts last as long as 10 years For Eurodollar futures lasting beyond two years we cannot assume that the forward rate equals the futures rate
100 - 97.12 = 2.88%
In the example you earn 100 – 97.42 = 2.58% on $1 million for three months (=$6,450) and make a gain day by day on the futures contract of 30×$25 =$750
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Example
Date Nov 1 Nov 2 Nov 3 ……. Dec 21
Quote 97.12 97.23 96.98 …… 97.42
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CBOT T-Bonds & T-Notes
Factors that affect the futures price:
Delivery can be made any time during the delivery month Any of a range of eligible bonds can be delivered The wild card play
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Eurodollar Futures continued
A Eurodollar futures contract is settled in cash When it expires (on the third Wednesday of the delivery month) the final settlement price is 100 minus the actual three month Eurodollar deposit rate
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Formula for Contract Value (page
137)
If Q is the quoted price of a Eurodollar futures contract, the value of one contract is 10,000[100-0.25(100-Q)]
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Conversion Factor
The conversion factor for a bond is approximately equal to the value of the bond on the assumption that the yield curve is flat at 6% with semiannual compounding