期权,期货及其衍生品第十弹
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。
赫尔《期权、期货及其他衍生产品》(第7版)课后习题详解(信用衍生品)
23.2 课后习题详解一、问答题1.解释一般信用违约互换与两点信用违约互换的区别。
Explain the difference between a regular credit default swap and a binary credit default swap.答：两者都是在某一特定的时期内对某一公司违约提供信用保险。
在一般信用违约互换中，收益是名义本金乘以1减去回收率的差；而在两点信用违约互换中，收益是名义本金。
2．某信用违约互换付费为每半年一次，付费溢价为60个基点，本金为3亿美元，交割方式为现金形式，假设违约发生在4年零2个月后，而信用违约互换价格的计算方所估计的最便宜可交割债券在刚刚违约时的价格等于面值的40％，列出此CDS出售方的现金流和支付时间。
A credit default swap requires a premiums of 60 basis points per year paid semiannually. The principal is $300 million and the credit default swap is settled in cash, A default occurs after four years and two months, and the calculation agent estimates that the price of the reference bond is 40% of its fuss value shortly after the default, List the cash flows and their timing for the buyer of the credit default swap.答：出售方在0.5年、l.0年、1.5年、2.0年、2.5年、3.0年、3.5年和4.0年收入900000美元（=300000000×0.0060×0.5）。
期权期货及其衍生品
THANKS
感谢观看
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。
约翰.赫尔_期权期货和其他衍生品第八版部分课后思考题
思考题1.1 远期合约长头寸与短期头寸之间的区别1)长头寸是买入，短头寸是卖出2)长头寸的收益是S-K 短头寸的收益是K-S1.2 期货合约与远期合约的区别1.3 卖出一个看涨期权与买入一个看跌期权的区别1)卖出看涨期权是一种义务，买入看跌期权是一种权利2)期初现金流不同3)收益公式不同卖出看涨期权买入看跌期权靠期权费赚利润1.4 期权与期货/远期合约的区别期货/远期合约，赋予它的持有者一个义务：以某个约定的价格买入或卖出标的资产。
期权合约，赋予它的持有者一个权利：以某个约定的价格买入或卖出标的资产。
1.5对冲、投机和套利之间的区别共同点：都是通过低买高卖或者高卖低买获利，都基于对未来市场预期的判断不同点：投机风险大，看涨看跌均没有保护性套期具有保护性对冲，如果货币市场流动性没问题，风险较低2.1 什么是逐日盯市逐日盯市制度，是指结算部门在每日闭市后计算、检查保证金账户余额，通过适时发出追加保证金通知，使保证金余额维持在一定水平之上，防止负债现象发生的结算制度。
2.2 保证金制度如何可以保证投资者免受违约风险？为了保证投资者保证金账户的资金余额在任何情况下都不为负值，设置了维持保证金，若保证金账户的余额低于维持保证金，投资者就会收到保证金催付，这部分资金称为变动保证金。
如果投资者未提供变动保证金，经纪人将出售该合约来平仓。
2.3一个交易的完成，会对未平仓合约数量产生什么样的影响?若交易是开仓，数量增加，若交易是平仓，则是减少2.4一天内发生的交易数量可以超过交易结束时未平仓合约的数量吗?交易数量包括开仓数量和平仓数量，若开仓=平仓，就会使未平仓数量为02.5设计一个新的期货合约时需要考虑哪几个重要方面？选择期货合约的标的资产、合约规模、交割月份3.1对冲的本质是什么？定义：为了减低另一项投资的风险而进行的投资。
目的：选择期货头寸，从而使得自身整体的投资风险尽量呈中性。
方法：用于对冲的期货交易，与需对冲的资产交易相比，头寸相等，在将来确定的时刻，操作方向相反。
【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。
期货及衍生品公式总结
1、当日盈亏a)商品期货当日盈亏=∑卖出价-当日结算价×卖出量+∑当日结算价-买入价×买入量+上日结算价-当日结算价×上日卖出持仓量-当日买入持仓量b)金融期货当日盈亏=∑卖出价-当日结算价×合约乘数×卖出量+∑当日结算价-买入价×合约乘数×买入量+上日结算价-当日结算价×上日卖出持仓量-当日买入持仓量×合约乘数2、结算准备金余额当日结算准备金余额=上日结算准备金余额+上日交易保证金余额-当日交易保证金余额+当日盈亏+入金-出金-交易手续费3、国债期货理论价格国债期货理论价格=现货价格+持有成本=现货价格+资金占用成本-利息收入4、股指期货理论价格Ft,T=St+StR-D×T-t/365= St1+ R-D×T-t/365Ft,T为t时买入的T时交割的股指期货理论价格St为t时股票指数R为资金市场年利率D为股指年股息率5、股指期货最优套期保值比率买卖套期合约数量=×现货总价值期货指数点×每点乘数6、逐日盯市结算公式（1）当日结存=上日结存+当日盈亏+入金-出金-手续费（2）客户权益=当日结存（3）商品期货的保证金占用=∑当日结算价×交易单位×持仓手数×公司的保证金比例（4）股指期货的保证金占用=∑当日结算价×合约乘数×交易单位×持仓手数×公司的保证金比例（5）风险度=保证金占用客户权益×100%7、现货多头、空头定义1现货多头2个：持有商品或资产、已按固定价格约定在未来购买某商品或资产2现货空头1个：已按固定价格约定在未来出售某商品或资产8、基差=现货价格-期货价格(1)正向市场：负基差,即期货>现货,远月>近月,反应持仓费(2)反向市场：正基差,即期货<现货,远月<近月,反应①近期对现货需求大②预计远期供给大,价格下降9、基差与套期保值效果10、期权的内涵价值P看涨期权内涵价值=标的资产价格-执行价格看跌期权内涵价值=执行价格-标的资产价格期权内涵价值总是大于等于0P>0实值期权P<0指的是计算结果虚值期权P=0平值期权11、期权的时间价值时间价值=权利金-内涵价值结论：①平值期权和虚值期权的时间价值总是大于等于0②实值美式期权的时间价值总是大于等于0③实值欧式期权的时间价值可能小于012、标的资产支付收益对期权价格的影响①标的资产支付收益对看涨期权价格的影响是负向的,即支付收益,价格低②标的资产支付收益对看跌期权价格的影响是正向的,即支付收益,价格高13、期权损益及运用a）买入看涨期权标的资产价格状态：①牛市②预期后市上涨③价格见底、市场波动扩大或隐含波动率低损益平衡点：执行价格+权利金损益：平仓损益=权利金卖出价-权利金买入价行权损益=标的资产卖价-执行价格-权利金运用：获取价差收益、降低卖出标的资产风险、规避标的资产价格上涨风险卖出套保的补充b）卖出看涨期权标的资产价格状态：①熊市②横盘、市场波动率低/收窄或隐含波动率高损益平衡点：执行价格+权利金损益：平仓损益=权利金买入价-权利金卖出价履约损益=执行价格-标的资产买价+权利金运用：获取权利金和价差收益、通过履约对冲标的资产多头头寸c）买入看跌期权标的资产价格状态：①熊市②预期后市下跌③价格见顶,波动率扩大损益平衡点：执行价格-权利金损益：平仓损益=权利金卖出价-权利金买入价行权损益=执行价格-标的资产买价-权利金运用：获取价差收益、规避标的资产价格下跌风险、作为买入套保的补充工具d）卖出看跌期权标的资产价格状态：①牛市②横盘,波动率收窄或隐含波动率扩大损益平衡点：执行价格-权利金损益：平仓损益=权利金买入价-权利金卖出价履约损益=标的资产买价-执行价格+权利金运用：获取权利金或价差收益、通过履约对冲标的资产空头头寸14、点值的计算变动一个点的价值、金额1非美元标价法下的点值等于汇率标价的最小变动单位乘以汇率2美元标价法下的点值等于汇率标价的最小变动单位除以汇率15、远期汇率计算远期汇率AA =即期汇率AAA+A A×A/AAAA+A A×A/AAAR表示利率,d表示交易期限16、升水、贴水升水,远期汇率>即期汇率贴水,远期汇率<即期汇率17、升贴水的计算升贴水=远期汇率−即期汇率即期汇率×AA月数18、掉期全价的计算1掉期点=|远端汇率-近端汇率|2近端买入,远端卖出近端掉期全价=即期汇率做市商卖价+近端掉期点做市商卖价+、-、-远端掉期全价=即期汇率做市商卖价+远端掉期点做市商买价+、-、+ 3近端卖出,远端买入近端掉期全价=即期汇率做市商买价+近端掉期点做市商卖价-、+、-远端掉期全价=即期汇率做市商买价+远端掉期点做市商买价-、+、+ 19、可交割国债的出让价格发票价格发票价格=国债期货交割结算价×转换因子+应计利息应计利息=可交割国债票面利率×100每年付息次数×配对缴款日−上一付息日当前付息周期实际天数20、隐含回购利率的计算隐含回购利率=(期货报价×转换因子+交割日应计利息)−国债购买价格国债购买价格×AAA交割日之前的天数21、国债基差的计算国债基差=国债现货价格-国债期货价格×转换因子21、修正久期法国债期货合约的计算对冲所需合约=债券组合市值×债券组合的修正久期期货合约市值×期货合约的修正久期= 债券组合市值×债券组合的修正久期AAA价格×期货合约面值÷AAA÷AAA转换因子×AAA修正久期22、基点价值法国债期货合约的计算对冲所需合约=债券组合基点价值期货合约面值÷AAA×AAA基点价值÷AAA转换因子。
期权、期货及其他衍生品(第8版)课后作业题解答(1-3章)
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 ST 为一年以后黄金的价格，则远期合约的收益为 ST -1000; 期权合约的受益为 ST -1100, 如果 ST >1000; -100, 如果 ST <1000 1.27 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% 1.31
期权期货与金融衍生品
期权、期货和其他衍生品Chapter 1 第一章What is a Derivative？什么是衍生品A derivative is an instrument whose value depends on, or is derived from, the value of another asset。
衍生品是一种金融工具，其价值取决于(衍生于)其他资产的价值。
Derivativesvs Primary Assets衍生品vs初级资产（标的资产)Primary Assets 初级资产Stocks 股票Fixed income 固定收益（利率)Foreign exchanges 外汇Loans 贷款Corporate bonds 公司债券Mortgages 住房抵押贷款Commodities 大宗商品Real Estate 房地产…。
.。
What is a Derivative? 什么是衍生品Commodity futures 商品期货(日本江户幕府时代，美国CBOT 1865）Index futures 指数期货（美国1982年KCBT，CME）Forwards远期合约（美国CBOT1848)Options期权(18世纪，美国CBOE1973）Swaps 互换（掉期美国1980s Swensen）Exotics 奇异期权（1980s）Credit derivatives 信用衍生品(1990s）（CMO，CLO, CDO，CDS，CDX，CMBS… ）Why Derivatives Are Important为什么衍生品很重要？Derivatives play a key role in transferring risks in the economy 转移经济活动中的风险Price discovery 价格发现The underlying assets include stocks，currencies，interest rates，commodities, debt instruments, electricity，insurance payouts，the weather, etc标的资产可以是股票，货币，利率，商品，债务，电力，保险支付金,天气等等。
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。
期权期货和其他衍生品第七版教学设计
期权期货和其他衍生品第七版教学设计前言期权期货和其他衍生品是现代金融市场的重要组成部分，其涉及的概念，技术和操作需要通过系统的教学才能被大众所掌握。
本文旨在介绍第七版《期权期货和其他衍生品》的教学设计，为开展相关教学工作提供帮助。
教学目标1.培养学生对于期权期货和其他衍生品的基础理论知识的掌握。
2.帮助学生在理论基础上了解金融市场中的各种衍生品工具，及其交易方式和风险控制方法。
3.培养学生主动的思考，能够运用所学知识解决实际问题。
教学内容1.期货市场基础知识–期货的定义、类型和特点–期货市场的组织形式和功能–期货交易的交割和结算方式2.期权市场基础知识–期权的定义、种类和特点–期权市场的组织形式和功能–期权交易的交割和结算方式3.期货和期权的风险管理方法–风险管理的重要性及其基本概念–风险管理的基本思路和方法–风险管理在期货和期权交易中的应用4.其他衍生品–涉及各类衍生品的基本概念、种类和特点–各类衍生品工具的交易方式和规则–对于各类衍生品的投资策略和风险管理方法教学方法1.讲授理论知识：通过课堂讲解，让学生了解期权期货及其他衍生品的相关概念、技术和操作，并通过适合的实例案例来让学生更好地理解。
2.小组讨论和分析：根据实际市场动态，要求学生结合市场新闻，在小组进行分析、探讨，并提出具体的操作建议，充分锻炼学生主动思考、研究和分析能力。
3.实践应用训练：提供模拟交易场景，让学生在虚拟环境中进行真实交易，感受风险管理、决策制定和操作执行等方面的实践操作。
4.案例研究模式：使用实际发生的案例进行分析和讨论，让学生从中学习到经验和教训。
教学评价1.学生的期末考试成绩。
2.学生的课堂表现和小组合作成果。
3.学生的模拟交易成绩和报告书的评估。
4.学生的第一篇期权期货报告书的撰写和评估。
教学资源1.教学参考书：《期权期货和其他衍生品》第七版，作者：赵晓华等。
2.教学案例库：包含大量实际情况下的交易案例，可供教学使用。
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.。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
7
Lower Bound for European Put Prices; No Dividends
(Equation 10.5, page 221)
p Ke -rT–S0
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
T:
s:
Life of option
Volatility of stock price
r
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
2
Effect of Variables on Option Pricing (Table 10.1, page 215)
16
Should Puts Be Exercised Early ?
Are there any advantages to exercising an American put when S0 = 60; T = 0.25; r=10% K = 100; D = 0
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
20
P: ST:
D:
American put option price Stock price at option maturity
PV of dividends paid during life of option Risk-free rate for maturity T with cont. comp.
19
Extensions of Put-Call Parity
American options; D = 0 S0 − K < C − P < S0 − Ke−rT
Equation 10.7 p. 224
European options; D > 0 c + D + Ke −rT = p + S0
Early Exercise
Usually there is some chance that an American option will be exercised early An exception is an American call on a nondividend paying stock This should never be exercised early
You want to hold the stock for the next 3 months? You do not feel that the stock is worth holding for the next 3 months?
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
15
Bounds for European or American Call Options (No Dividends)
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
17
Bounds for European and American Put Options (No Dividends)
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
18
The Impact of Dividends on Lower Bounds to Option Prices
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
13
An Extreme Situation
For an American call option: S0 = 100; T = 0.25; K = 60; D = 0 Should you exercise immediately? What should you do if
5
Lower Bound for European Call Option Prices; No Dividends (Equation 10.4, page 220)
c S0 –Ke -rT
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
9
Values of Portfolios
ST > K Portfolio A Call option Zero-coupon bond Total Portfolio C Put Option Share Total ST − K K ST 0 ST ST ST < K 0 K K K− ST ST K
T = 0.25 K =30
r = 10% D=0
What are the arbitrage possibilities when p = 2.25 ? p=1?
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012 12
6
Puts: An Arbitrage Opportunity?
Suppose that
p= 1 T = 0.5 K = 40 S0 = 37 r =5% D =0
Is there an arbitrage opportunity?
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
10
The Put-Call Parity Result (Equation
10.6, page 222)
Both are worth max(ST , K ) at the maturity of the options They must therefore be worth the same today. This means that
Equation 10.10 p. 230
American options; D > 0 S0 − D − K < C − P < S0 − Ke −rT
Equation 10.11 p. 230
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
Chapter 10 Properties of Stock Options
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
1
Notation
c: p: S0: K: European call option price European put option price Stock price today Strike price C: American call option price
8
Put-Call Parity: No Dividends
Consider the following 2 portfolios: Portfolio A: European call on a stock + zerocoupon bond that pays K at time T Portfolio C: European put on the stock + the stock
4
Calls: An Arbitrage Opportunity?
Suppose that
c=3 S0 = 20
T=1
K = 18
r = 10%
D=0
Is there an arbitrage opportunity?
Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull 2012
14
Reasons For Not Exercising a Call Early (No Dividends)
No income is sacrificed You delay paying the strike price Holding the call provides insurance against stock price falling below strike price