期权期货与衍生证券(第五版)-CH02HullOFOD5Ebw
期货期权及其衍生品配套(全34章)Ch01PPT课件
期货交易是一种衍生品交易，其基础资产可以是商品、外汇或股票等。交易双方 通过签订期货合约的方式，约定在未来某一特定时间和价格上交割指定数量的基 础资产。期货交易的主要目的是为了规避风险或进行套期保值。
期货交易规则与流程
总结词
期货交易具有严格的交易规则和流程， 包括保证金制度、逐日盯市、交割制度 等。
卖出看跌期权策略
当预期标的资产价格下跌时，卖出看 跌期权获得赚取收益的权利，但获得 权利金。
组合策略
跨式期权组合策略
同时买入相同行权价格的看涨和看跌 期权，以获得赚取收益的权利，但需 支付权利金。
宽跨式期权组合策略
同时买入不同行权价格的看涨和看跌 期权，以获得赚取收益的权利，但需 支付权利金。
06
04
Theta
衡量期权价格对Rho
衡量期权价格对无风险利率的敏感度。
风险度量与控制
风险度量
通过计算期权价格的敏感性指标，如Delta、 Gamma、Theta、Vega和Rho等，来评估 期权的风险敞口。
风险控制
通过设置止损点、动态调整持仓结构、使用 对冲策略等方式，降低或消除期权交易的风 险敞口。
期权风险管理
希腊字母及其应用
希腊字母
包括Delta、Gamma、Theta、Vega和Rho等， 用于描述期权价格变动与标的资产价格、波动
率、剩余到期时间等变量的敏感性。
01
Gamma
衡量Delta对标的资产价格的敏感度。
03
Vega
衡量期权价格对波动率的敏感度。
05
02
Delta
衡量标的资产价格变动对期权价格的影响程 度。
期货期权及其衍生品配套(全34章 )ch01ppt课件
Ch05Interest Rate Markets(期权,期货和其他衍生物-第五版)
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
5.3
Zero Rates
A zero rate (or spot rate), for maturity T is the rate of interest earned on an investment that provides a payoff only at time T
Calculation of Forward Rates
Table 5.4, page 104
Zero Rate for Year (n ) 1 2 3 (% per annum) 10.0 10.5 10.8 11.0 11.4 Forward Rate (% per annum)
5.14
an n -year Investment for n th Year
Ch06Swaps(期权,期货和其他衍生物-第五版)
Swaps
Chapter 6
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
6.2
Nature of Swaps
A swap is an agreement to exchange cash flows at specified future times according to certain specified rules
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. of Principal
• In an interest rate swap the principal is not exchanged • In a currency swap the principal is exchanged at the beginning and the end of the swap
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
An Example of a “Plain Vanilla” Interest Rate Swap
• An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million • Next slide illustrates cash flows
(本科)Ch5衍生证券ppt课件
（本科）Ch5衍生证券ppt课件
根据参与期货交易的方向不同，可以把股指期货 套期保值交易划分为买入套期保值和卖出套期保值两 类。 1、买入股指期货套期保值（多头保值）
如果投资者计划在一段时期之后买入股票，但又预测股市 会在近期上涨，即可以通过买入股指期货合约锁定股票未 来的买入成本。
我国于2010年4月16日起推出沪深300股指期货，2015年4月 16日又推出了中证500股指期货和上证50股指期货。
（本科）Ch5衍生证券ppt课件
（二）国债期货
国债期货（Treasury future）是指通过有组织的交易场所 预先确定买卖价格并于未来特定时间内进行钱券交割的国 债派生交易方式。国债期货属于金融期货的一种，是一种 高级的金融衍生工具。
（本科）Ch5衍生证券ppt课件
五、我国的金融期货交易历程
（本科）Ch5衍生证券ppt课件
第二节 期权衍生证券
（本科）Ch5衍生证券ppt课件
一、金融期权的含义与种类
（一）金融期权的含义
金融期权（financial option），是在期货基础上产生的一 种金融衍生产品，是指以金融商品或金融期货合约为标的 物的期权交易的合约。
期货合约以当日结算价作为计算当日盈亏的依据。具体计 算公式如下：
当日盈亏 = ∑[（卖出成交价-当日结算价）×卖出量]+ ∑[（ 当日结算价-买入成交价）×买入量]+（上一交易日结算价 -当日结算价）×（上一交易日卖出持仓量-上一交易日买 入持仓量）
当日盈亏在当日结算时进行划转，盈利划入结算准备金， 亏损从结算准备金中划出。
Ch13Futures Options(期权,期货和其他衍生物-第五版)
13.11
Valuing the Option
• The portfolio that is long 0.8 futures short 1 option is worth –1.592 • The value of the futures is zero • The value of the option must therefore be 1.592
Growth Rates For Futures Prices
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
Black’s Model
(Equations 13.7 and 13.8, page 280)
where
1 d p ud
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
Valuing European Futures Options
• We can use the formula for an option on a stock paying a continuous dividend yield Set S0 = current futures price (F0) Set q = domestic risk-free rate (r ) • Setting q = r ensures that the expected growth of F in a risk-neutral world is zero
赫尔《期权、期货及其他衍生产品》教材精讲(期货市场的运作机制)【圣才出品】
第2章期货市场的运作机制第一部分本章要点1．期货市场的具体运作机制。
将讨论合约条款的约定、保证金账户的运作、交易所的组织结构、市场监管规则、期货报价方式及期货的财会和税务处理等内容。
我们还将讨论，并解释造成这两类合约所实现的收益不同的原因。
2．期货与远期合约的不同之处。
第二部分重难点导学2.1 背景知识假定现在是3月5日，一位纽约的投资者指示他的经纪人买入5000蒲式耳玉米，资产交割时间在7月份，经纪人会马上将这一指令通知芝加哥交易所。
同时，假定另一位在堪萨斯州的投资者指示她的经纪人卖出5000蒲式耳玉米，资产交割时间也是7月份，她的经纪人也会马上将客户的指令通知芝加哥交易所。
这时双方会同意某个交易价格，从而交易成交。
几个概念：期货的长头寸（long futures position）；期货的短头寸（short futures position）。
期货价格（futures price）；期货合约的平仓。
2.2 期货合约的规定·资产品种·合约的规模·交割地点·交割时间有时交割资产的备选方案也会被说明。
2.2.1 资产商品期货标的资产的质量可能有很大差别。
金融期货合约中的标的资产定义通常明确。
2.2.2 合约的规模合约的规模（contract size）：每一合约中交割资产的数量。
2.2.3 交割的安排交割地点必须由交易所指定，这对那些运输费用昂贵的商品尤其重要。
当选用交割地点时，期货的短头寸方所收入的价格会随着交割地点的不同而得以调整。
期货交割地点离商品生产地越远，交割价格越高。
2.2.4 交割月份期货合约通常以其交割月份来命名。
交易所必须指定交割月份内的准确交割时间。
对于许多期货而言，交割时间区间为整个月。
2.2.5 报价交易所定义报价的方式各不相同，例如，在美国，原油期货报价以美元和美分计量，而中长期国债期货报价是以1美元以及1/32美元来报价的。
2.2.6 价格和头寸的限额跌停（limit down）：价格下跌的金额等于每日价格限额。
期货期权及其衍生品配套(全34章)Ch29PPT课件
期货期权的分类
按行权时间
欧式期权和美式期权。欧式期权 只能在到期日行权，而美式期权 可以在到期日及之前任何时间行 权。
按交易场所
场内期权和场外期权。场内期权 在交易所交易，有标准化合约， 而场外期权则在交易双方之间直 接进行，合约条款可定制。
期货期权及其衍生品配套(全34章 )ch29ppt课件
目录
• 期货期权概述 • 期货期权的发展历程 • 期货期权的交易策略 • 期货期权的定价与风险控制 • 期货期权的监管与法规 • 期货期权市场的未来展望
01 期货期权概述
期货期权的定义
期货期权是一种金融衍生品，其标的资产为期货合约。期货期权赋予持有者在未 来某一特定日期或该日之前的任何时间，以固定价格购买或出售期货合约的权利 ，但不强制执行。
有限差分模型
利用偏微分方程描述期货期权价格的动态变化， 通过求解方程得到期货期权的理论价格。
期货期权的风险管理
风险识别
01
识别期货期权交易中可能面临的市场风险、信用风险、流动性
风险等，为风险管理提供基础。
风险度量
02
利用各种风险度量工具和技术，如VaR、敏感性分析、压力测试
等，对期货期权的风险进行量化评估。
对期货交易所的设立、组织架构、职责、 监督管理等方面进行了规定。
《期货公司监督管理办法》
对期货公司的设立、业务范围、风险管理 、监督管理等方面进行了规定。
《期货投资者保障基金管理办法 》
对期货投资者保障基金的筹集、使用和管 理进行了规定。
期货期权交易的风险警示
市场风险
由于市场行情的变化，期权价 格可能会出现大幅波动，投资 者需要继续发挥其风险管理功能，帮助投资者对冲风险、降低投资 组合波动。
期权期货和其他衍生品第五版教学设计
期权期货和其他衍生品第五版教学设计简介这是一份关于期权期货和其他衍生品第五版教学设计的文档。
本教学设计旨在帮助学生掌握期权、期货等衍生品的基本概念、市场机制以及交易策略，从而提升他们在实践中的能力和竞争力。
学习目标本教学设计的学习目标包括： - 理解期权、期货等衍生品的基本概念、市场机制和风险管理； - 掌握衍生品市场的交易策略和技巧； - 理解衍生品市场的实际应用，包括对冲、套利和投机等； - 运用衍生品交易知识和技巧，开展模拟交易和实盘操作。
教学内容本教学设计的教学内容主要包括以下几个方面： 1. 期权基础知识 - 期权的定义和基本特征； - 期权的分类； - 期权的定价模型和影响因素； - 期权交易策略。
2. 期货基础知识 - 期货的定义和基本特征； - 期货市场的组织结构和交易规则； - 期货的定价模型和影响因素； - 期货交易策略。
3. 其他衍生品基础知识 - 期权期货之外的其他衍生品； - 其他衍生品的分类和特点； - 其他衍生品交易策略。
4. 衍生品市场实际应用 - 对冲、套利和投机策略； - 实战操作案例分析； - 模拟交易和实盘操作。
教学方法本教学设计采用多种教学方法，包括讲授、案例分析、模拟交易和实盘操作等。
讲授通过讲授方式，将基础知识系统地传授给学生，包括期权、期货等衍生品的定义、分类、定价模型等。
讲授过程中，可以采用多媒体教学方式，增加学生的参与度。
案例分析通过案例分析，将理论知识与实际操作相结合，让学生更好的理解和掌握交易策略。
案例分析应该从市场行情、交易策略、风险管理等多个方面进行，帮助学生形成对衍生品市场的全面认识。
模拟交易通过模拟交易，让学生亲身体验交易过程，提升实践操作能力。
模拟交易可以通过搭建虚拟衍生品交易平台进行，学生可以在平台上进行模拟交易，体验交易操作的实际过程。
通过模拟交易，学生可以更好的理解和掌握交易策略，并更好的应对市场变化。
实盘操作通过实盘操作，让学生真正感受到衍生品交易的风险和挑战。
10习题解答期权期货及其他衍生品5版中文答案
第10章 股票价格的行为模式10.1说一个地区的气温服从马尔可夫过程，有什么含义？你认为温度确实可以服从马尔可夫过程吗？假设你必须从以下已知条件下预报未来气温a)当前气温，b)气温历史记录和c)季节平均气温和季节气温变化趋势方面的知识。
如果气温服从一个马尔可夫过程，气温的历史记录将是不相关的。
为了回答这个问题的第二部分，你可以考虑在五月份的第一个星期的下列景象：1） 星期一到星期三天气温暖；星期五非常寒冷。
2） 星期一到星期五都非常寒冷。
你预测这个周末的气温会是怎样的呢？如果你在第二中情形下更悲观，那么气温就不服从一个马尔可夫过程。
10.2基于股票价格过去历史的交易准则是否总是可以获得高于平均收益率的收益？请讨论这个问题。
首先要说明的是任何交易准则只能因为好运才能获得高于平均收益率的收益。
关键问题是风险调整时，一个交易准则能否不断地适应市场。
对于一个交易准则可能做到这点，然而，当足够多的投资者知道这个准则并按这个准则进行投资时，利润将消失。
为了说明这点，考虑一个小公司影响的现象，当对风险做合适的调整，在小公司股票上的资产组合比对大公司股票的资产组合更有效。
在1980年代早期相关论文发表后，公众基金被设立用来利用这种现象。
有证据表明正是由于这导致了这种现象的消失。
10.3 一家公司的现金头寸，用百万美元衡量，服从一般化的维纳过程，每月的漂移率为0.1，方差率为0.16，初始现金头寸为2.0。
（a ） 分别说明1个月后、6个月后和1年后，现金头寸的可能的分布是什么？ （b ） 6个月后和1年后负责现金头寸的可能性为多少？ （c ） 未来的什么时间负现金头寸的可能性最大？10.4一家公司的现金头寸，用百万美元衡量，服从一般化的维纳过程，每季度的漂移率为1.5，方差率为4.0。
如果要求公司在1年后负值现金流的概率小于5%，公司的初始现金流要多高？假设公司初始现金头寸是x.，在一年后其现金头寸的可能分布是(4( 2.0,4)x x φφ+×=+ 在一年后一个负现金流的可能性是 2.0()4x N +−这里N （x ）是一个小于x 的标准正态变量（0期望，标准差为1.0）的累计分布，从正态分布表可以得出：2.0()04x N .05+−= 当2.01.64494x +−=−例如：当x=4.5796，初始现金头寸必须是4560000美元。
[考研专业课课件] 赫尔《期货、期权及其他衍生产品》 课件 第1章 导 言
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《期权、期货及其他衍生产品》
第1章 导 言
第一部分 本章要点
●衍生市场的发展 ●远期、期货和期权市场的发展
●市场参与者如何使用衍生产品
第二部分 重难点导学
1．1 1．2 衍生市场的发展 远期、期货和期权市场的发展
1．2．1 远期合约
远期合约：在将来某一指定时刻以约定 价格买入或卖出某一产品的合约。远期合约 是在场外交易市场中金融机构之间或金融机 构与其客户之间的交易。
1.441的价格卖出3000万英镑。
实际效果：卖出英镑而收入美元,数量为 43230000美元。 注意，一个公司选择不对冲可能会比选择对 冲的盈利效果更好，也有可能更差。为什么？
例5：采用期权对冲。考虑某投资者在某年5 月份拥有1000股微软股票的情形。股票价格为每 股28美元。投资者十分担心今后2个月股票下跌， 所以想买入期权保护。
图1-2
交易产生的净盈利（假定为欧式期权）
1．3 交易员的种类
交易员可以分为三大类： 对冲者：采用衍生产品合约来减少自身面临 的由于市场变化而产生的风险。 投机者：利用这些产品对今后市场变量的走 向下赌注。 套利者：采用两个或更多相互抵消的交易来 锁定盈利。
1．3．1
对冲者
例3：利用远期对冲。假定今天是2010年5月 24日，一家美国的进口公司ImpoaCo得知在2010年
期权合约：赋予持有者去做某事的权利的合 约。 看涨期权的持有者有权在将来某一特定时间 以某一确定价格买入某种资产；看跌期权的持有 者有权在将来某一特定时间以某一确定价格卖出 某种资产。 美式期权是指在到期前的任何时刻，期权持
有人均可以行使期权；欧式期权是指期权持有人
只能在到期这一特定时刻行使期权。
Ch05-远期合约和期货定价-期权期货及衍生品(Hull)
the value of a short forward contract is (K – F0 )e–rT
Options, Futures, and Other Derivatives, 8th Edition,
Options, Futures, and Other Derivatives, 8th Edition,
17
Index Arbitrage
When F0 > S0e(r-q)T an arbitrageur buys the stocks underlying the index and sells futures When F0 < S0e(r-q)T an arbitrageur buys futures and shorts or sells the stocks underlying the index
Is there an arbitrage opportunity?
Options, Futures, and Other Derivatives, 8th Edition
7
Another Arbitrage Opportunity?
Suppose that:
The spot price of nondividend-paying stock is $40 The 3-month forward price is US$39 The 1-year US$ interest rate is 5% per annum
Options, Futures, and Other Derivatives, 8th Edition
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。
期权期货与衍生证券
衍生工具专题之期权张晟2011301000145 数学与应用数学专业课程：期权、期货与衍生证券一、期权市场的起源和发展期权（option）,又称选择权，其交易的雏形早在公元前400年就存在。
17世纪前期的阿姆斯特丹出现了最早的市场。
18世纪，股票期权市场已经有了一定发展，但后来由于英国出现了“南海泡沫事件”，股票期权被看成投机和欺诈的象征，由此股票期权交易被禁止长达一百年。
1973年4月26日，芝加哥期权交易所成立，同时开始买权交易，这标志着期权交易步入了合约标准化、交易规范化的道路。
1977年，芝加哥期权交易所开始有卖权交易。
1982年，芝加哥货币交易所开始进行S&P500期权交易，它标志着股票指数期权诞生。
同年，芝加哥期权交易所首次引入美国国库券期权交易，这成为利率期权交易的开端。
1982年，加拿大蒙特利尔交易所首次引入外汇期权。
同年12月，费城股票交易所也开始了外汇期权交易。
1984年，外汇期货期权在芝加哥商品交易所的国际货币市场登台表演。
随后，期货期权迅速扩展到欧洲美元存款、90天短期及长期国债、国内存单等债务凭证期货以及黄金期货和股指期货上面，几乎所有的期货都有相应的期权交易。
二、期权的定义期权是两个交易对手之间签订的协议，它允许期权买方在将来的指定日期之前享有按照固定价格买进或卖出一定数量标的物的权利，同时不承担任何义务。
一旦买方决定执行期权合约，期权卖方就有责任卖出或买进期权合约规定的标的物。
有关期权的重要概念：（1）期权费：期权的买方（多头方）为获得期权合约所规定的权利而在购买期权时向卖方（空头方）支付的费用，也成为“期权的价格”。
影响期权费的因素有：标的资产到期的市场价格、市场上的无风险利率水平、期权期限长短、期权的执行价格。
（2）执行价格：期权合约中所规定的买卖标的资产的价格，无论现货市场价格如何变化，期权买方都有权利以此价格来买卖标的资产。
（3）执行期：通过期权合约购买或出售标的资产的时间，如果期权合约在到期时或到期之前没有被执行，那么期权合约自动消失。
期货期权及其衍生品配套(全34章)Ch06PPT课件
组合期权策略
跨式期权组合
同时买入相同行权价格的看涨和看跌期权，以获得赚取收益 的权利和承担义务的组合。
宽跨式期权组合
同时买入行权价格不同但数量相同的看涨和看跌期权，以获 得赚取收益的权利和承担义务组合。
04 期权风险管理
波动率管理
总结词
波动率是衡量期权价格变动的重要指标 ，对期权交易策略的成功与否具有关键 作用。
权所能获得的收益，时间价值则反映了期权有效期长短及标的资产价格
波动性对期权价格的影响。
二叉树模型
定义
二叉树模型是一种用于描述标的资产价格变 动的模型，其基本思想是将标的资产价格的 变动过程分解为一系列连续的二叉树形状的 变动。
适用范围
参数
二叉树模型需要输入标的资产的初始 价格、波动率、无风险利率、到期时 间和步数等参数。
02 期权定价理论
期权定价的基本原理
01
定义
期权是一种金融衍生品，其持有人在特定时间内以特定价格购买或出售
标的资产的权利，但不承担必须执行该权利的义务。
02
分类
根据执行时间不同，期权可分为欧式期权和美式期权；根据标的资产不
同，可分为股票期权、期货期权等。
03
期权价格
期权价格由内在价值和时间价值两部分组成，内在价值是指立即执行期
05 期权市场的发展与监管
国际期权市场的发展
北美期权市场
北美期权市场起步较早，发展成 熟，是全球最大的期权交易市场
之一。
欧洲期权市场
欧洲期权市场发展相对较晚，但近 年来发展迅速，交易量逐年攀升。
亚洲期权市场
亚洲期权市场主要集中在中国、日 本、印度等国家，发展潜力巨大。
中国期权市场的现状与未来发展
Ch02Mechanics of Futures and Forward Markets(期权,期货和其他衍生物-第五版)
2.4
Example of a Futures Trade
• An investor takes a long position in 2 December gold futures contracts on June 5
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
A Possible Outcome
Table 2.1, Page 21
Daily Gain (Loss) (US$) Cumulative Gain (Loss) (US$) Margin Account Margin Balance Call (US$) (US$) 4,000 (600) . . . (420) . . . (600) . . . (1,340) . . . 3,400 . . . 0 . . . Futures Price (US$) 400.00 5-Jun 397.00 . . . . . . 13-Jun 393.30 . . . . . .
5,060 0
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
2.6
Other Key Points About Futures
• They are settled daily • Closing out a futures position involves entering into an offsetting trade • Most contracts are closed out before maturity
JohnHull期货期权和衍生证券章习题解答(终审稿)
J o h n H u l l期货期权和衍生证券章习题解答公司内部档案编码：[OPPTR-OPPT28-OPPTL98-OPPNN08]CHAPTER 13Wiener P rocesses and It’s LemmaPractice QuestionsProblem .What would it mean to assert that the temperature at a certain place follows a Markov process Do you think that temperatures do, in fact, follow a Markov processImagine that you have to forecast the future temperature from a) the current temperature, b) the history of the temperature in thelast week, and c) a knowledge of seasonal averages and seasonal trends. If temperature followed a Markov process, the history of the temperature in the last week would be irrelevant.To answer the second part of the question you might like to consider the following scenario for the first week in May:(i) Monday to Thursday are warm days; today, Friday, is a very cold day.(ii) Monday to Friday are all very cold days.What is your forecast for the weekend If you are more pessimistic in the case of the second scenario, temperatures do not follow a Markov process.Problem .Can a trading rule based on the past history of a stock’sprice ever produce returns that are consistently above average Discuss.The first point to make is that any trading strategy can, just because of good luck, produce above average returns. The key question is whether a trading strategy consistently outperforms the market when adjustments are made for risk. It is certainly possible that a trading strategy could do this. However, when enough investors know about the strategy and trade on the basis of the strategy, the profit will disappear.As an illustration of this, consider a phenomenon known as the small firm effect. Portfolios of stocks in small firms appear to have outperformed portfolios of stocks in large firms when appropriateadjustments are made for risk. Research was published about this in the early 1980s and mutual funds were set up to take advantage of the phenomenon. There is some evidence that this has resulted in the phenomenon disappearing. Problem .A company’s cash position, measured in millions of dollars, follows a generalized Wiener process with a drift rate of per quarter and a variance rate of per quarter. How high does thecompany’s initial cash position have to be for the company to have a less than 5% chance of a negative cash position by the end of one yearSuppose that the company’s initial cash position is x . The probability distribution of the cash position at the end of one year is (40544)(2016)x x ϕϕ+⨯.,⨯=+.,where ()m v ϕ, is a normal probability distribution with mean m and variance v . The probability of a negative cash position at the end of one year is204x N +.⎛⎫- ⎪⎝⎭where ()N x is the cumulative probability that a standardized normalvariable (with mean zero and standard deviation is less than x . From normal distribution tables200054x N +.⎛⎫-=. ⎪⎝⎭when:20164494x +.-=-.., when 45796x =.. The initial cash position must therefore be$ million. Problem .Variables 1X and 2X follow generalized Wiener processes withdrift rates 1μ and 2μ and variances 21σ and 22σ. What process does 12X X + follow if:(a)The changes in 1X and 2X in any short interval of time are uncorrelated(b)There is a correlation ρ between the changes in 1X and 2X inany short interval of time(a)Suppose that X 1 and X 2 equal a 1 and a 2 initially. After a time period of length T , X 1 has the probability distribution2111()a T T ϕμσ+,and 2X has a probability distribution2222()a T T ϕμσ+,From the property of sums of independent normally distributedvariables, 12X X + has the probability distribution()22112212a T a T T T ϕμμσσ+++,+.,22121212()()a a T T ϕμμσσ⎡⎤+++,+⎣⎦This shows that 12X X + follows a generalized Wiener process withdrift rate 12μμ+ and variance rate 2212σσ+.(b) In this case the change in the value of 12X X + in a short interval of time t ∆ has the probability distribution:22121212()(2)t t ϕμμσσρσσ⎡⎤+∆,++∆⎣⎦If 1μ, 2μ, 1σ, 2σ and ρ are all constant, arguments similar to those in Section show that the change in a longer period of time T is22121212()(2)T T ϕμμσσρσσ⎡⎤+,++⎣⎦The variable,12X X +, therefore follows a generalized Wiener processwith drift rate 12μμ+ and variance rate 2212122σσρσσ++. Problem .Consider a variable,S , that follows the processdS dt dz μσ=+For the first three years, 2μ= and 3σ=; for the next three years, 3μ= and 4σ=. If the initial value of the variable is 5, what is the probability distribution of the value of the variable at the end of year sixThe change in S during the first three years has the probability distribution(2393)(627)ϕϕ⨯,⨯=,The change during the next three years has the probability distribution(33163)(948)ϕϕ⨯,⨯=,The change during the six years is the sum of a variable with probability distribution (627)ϕ, and a variable with probability distribution (948)ϕ,. The probability distribution of the change is therefore (692748)ϕ+,+(1575)ϕ=,Since the initial value of the variable is 5, the probabilitydistribution of the value of the variable at the end of year six is (2075)ϕ,Problem .Suppose that G is a function of a stock price, S and time. Suppose that S σ and G σ are the volatilities of S and G . Show that when the expected return of S increases by S λσ, the growth rate of G increases by G λσ, where λ is a constant.From It’s lemmaG S GG S Sσσ∂=∂ Also the drift of G is222212G G G S S S t S μσ∂∂∂++∂∂∂where μ is the expected return on the stock. When μ increases byS λσ, the drift of G increases byS GS Sλσ∂∂ orG G λσThe growth rate of G , therefore, increases by G λσ. Problem .Stock A and stock B both follow geometric Brownian motion. Changes in any short interval of time are uncorrelated with eachother. Does the value of a portfolio consisting of one of stock A and one of stock B follow geometric Brownian motion Explain your answer.Define A S , A μ and A σ as the stock price, expected return and volatility for stock A. Define B S , B μ and B σ as the stock price, expected return and volatility for stock B. Define A S ∆ and B S ∆ as the change in A S and B S in time t ∆. Since each of the two stocks follows geometric Brownian motion,A A A A A S S t S μσε∆=∆+B B B B B S S t S μσε∆=∆+where A ε and B ε are independent random samples from a normal distribution.()(A B A A B B A A A B B B S S S S t S S μμσεσε∆+∆=+∆++ This cannot be written as()()A B A B A B S S S S t S S μσ∆+∆=+∆++for any constants μ and σ. (Neither the drift term nor thestochastic term correspond.) Hence the value of the portfolio does not follow geometric Brownian motion. Problem .The process for the stock price in equation isS S t S μσε∆=∆+where μ and σ are constant. Explain carefully the difference between this model and each of the following:S t S S t S t S μσεμσεμσε∆=∆+∆=∆+∆=∆+Why is the model in equation a more appropriate model of stock price behaviorthan any of these three alternativesIn:S S t S μσε∆=∆+the expected increase in the stock price and the variability of the stock price are constant when both are expressed as a proportion (or as a percentage) of the stock price In:S t μ∆=∆+the expected increase in the stock price and the variability of the stock price are constant in absolute terms. For example, if theexpected growth rate is $5 per annum when the stock price is $25, it is also $5 per annum when it is $100. If the standard deviation of weekly stock price movements is $1 when the price is $25, it is also $1 when the price is $100. In:S S t μ∆=∆+the expected increase in the stock price is a constant proportion of the stock price while the variability is constant in absolute terms. In:S t S μσ∆=∆+the expected increase in the stock price is constant in absoluteterms while the variability of the proportional stock price change is constant. The model:S S t S μσ∆=∆+is the most appropriate one since it is most realistic to assume that the expected percentage return and the variability of the percentage return in a short interval are constant. Problem .It has been suggested that the short-term interest rate,r , follows the stochastic process()dr a b r dt rc dz =-+where a , b , and c are positive constants and dz is a Wiener process. Describe the nature of this process.The drift rate is ()a b r -. Thus, when the interest rate is above b the drift rate is negative and, when the interest rate is below b , the drift rate is positive. The interest rate is thereforecontinually pulled towards the level b . The rate at which it is pulled toward this level is a . A volatility equal to c is superimposed upon the “pull” or the drift.Suppose 04a =., 01b =. and 015c =. and the current interest rate is 20% per annum. The interest rate is pulled towards the level of 10% per annum. This can be regarded as a long run average. Thecurrent drift is 4-% per annum so that the expected rate at the end of one year is about 16% per annum. (In fact it is slightly greater than this, because as the interest rate decreases, the “pull” decreases.) Superimposed upon the drift is a volatility of 15% per annum.Problem .Suppose that a stock price, S , follows geometric Brownian motion with expected return μ and volatility σ:dS S dt S dz μσ=+What is the process followed by the variable n S Show that n S also follows geometric Brownian motion.If ()n G S t S ,= then 0G t ∂/∂=, 1n G S nS -∂/∂=, and 222(1)n G S n n S -∂/∂=-. Using It’s lemma:21[(1)]2dG nG n n G dt nG dz μσσ=+-+This shows that n G S = follows geometric Brownian motion where the expected return is21(1)2n n n μσ+-and the volatility is n σ. The stock price S has an expected return of μ and the expected value of T S is 0T S e μ. The expected value of n T S is212[(1)]0n n n T n S eμσ+-Problem .Suppose that x is the yield to maturity with continuouscompounding on a zero-coupon bond that pays off $1 at time T . Assume that x follows the process0()dx a x x dt sx dz=-+where a , 0x , and s are positive constants and dz is a Wiener process. What is the process followed by the bond priceThe process followed by B , the bond price, is fro m It’ s lemma:222021()2B B B B dB a x x s x dt sxdz x t x x ⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦∂∂∂∂=-+++∂∂∂∂Since:()x T t B e --=the required partial derivatives are()()22()22()()()()x T t x T t x T t Bxe xB t BT t e T t B x BT t e T t B x------∂==∂∂=--=--∂∂=-=-∂ Hence:22201()()()()2dB a x x T t x s x T t Bdt sx T t Bdz⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦=---++---Problem (Excel Spreadsheet)A stock whose price is $30 has an expected return of 9% and avolatility of 20%. In Excel simulate the stock price path over 5 years using monthly time steps and random samples from a normal distribution. Chart the simulated stock price path. By hitting F9 observe how the path changes as the random sample change.The process ist S t S S ∆⨯ε⨯⨯+∆⨯⨯=∆20.009.0Where t is the length of the time step (=1/12) and is a random sample from a standard normal distribution.Further QuestionsProblem .Suppose that a stock price has an expected return of 16% per annum and a volatility of 30% per annum. When the stock price at the end of a certain day is $50, calculate the following: (a) The expected stock price at the end of the next day. (b) The standard deviation of the stock price at the end of the next day. (c) The 95% confidence limits for the stock price at the end of the next day.(d)(e)With the notation in the text2()S t t Sϕμσ∆∆,∆In this case 50S =, 016μ=., 030σ=. and 1365000274t ∆=/=.. Hence(016000274009000274)50(0000440000247)S ϕϕ∆.⨯.,.⨯.=.,.and2(50000044500000247)Sϕ∆⨯.,⨯.that is,(002206164)Sϕ∆.,.(a)The expected stock price at the end of the next day is therefore (b)The standard deviation of the stock price at the end of the next0785=.(c)95% confidence limits for the stock price at the end of the next day are 500221960785and 500221960785.-.⨯..+.⨯..,4848and 5156..Note that some students may consider one trading day rather than one calendar day. Then 1252000397t ∆=/=.. The answer to (a) is then . The answer to (b) is . The answers to part (c) are and . Problem .A company’s cash position, measured in millions of dollars,follows a generalized Wiener process with a drift rate of per month and a variance rate of per month. The initial cash position is .(a)What are the probability distributions of the cash positionafter one month, six months, and one year(b)What are the probabilities of a negative cash position at theend of six months and one year(c) At what time in the future is the probability of anegative cash position greatest(a)The probability distributions are:(2001016)(21016)ϕϕ.+.,.=.,.(20060166)(26096)ϕϕ.+.,.⨯=.,.(201201612)(32196)ϕϕ.+.,.⨯=.,.(b)The chance of a random sample from (26096)ϕ.,. being negative is(265)N N ⎛=-. ⎝where ()N x is the cumulative probability that a standardizednormal variable [., a variable with probability distribution(01)ϕ,] is less than x . From normal distribution tables(265)00040N -.=.. Hence the probability of a negative cashposition at the end of six months is %.Similarly the probability of a negative cash position at theend of one year is(230)00107N N ⎛=-.=. ⎝or %.(c) In general the probability distribution of the cashposition at the end of x months is(2001016)x x ϕ.+.,.The probability of the cash position being negative is maximized when:is minimized. Define11223122325025250125(250125)y x xdy x xdxx x----==+.=-.+.=-.+.This is zero when 20x= and it is easy to verify that220d y dx/> for this value of x. It therefore gives a minimum value for y. Hence the probability of a negative cash positionis greatest after 20 months.Problem .Suppose that x is the yield on a perpetual government bond that pays interest at the rate of $1 per annum. Assume that x is expressed with continuous compounding, that interest is paid continuously on the bond, and that x follows the process()dx a x x dt sx dz=-+where a,x, and s are positive constants and dz is a Wiener process. What is the process followed by the bond price What is the expected instantaneous return (including interest and capital gains) to the holder of the bondThe process followed by B, the bond price, is from It’s lemma:222021()2B B B BdB a x x s x dt sxdzx t x x⎡⎤⎢⎥⎢⎥⎢⎥⎣⎦∂∂∂∂=-+++∂∂∂∂In this case1Bx=so that:222312B B Bt x x x x∂∂∂=;=-;=∂∂∂Hence 2202322021121()21()dB a x x s x dt sxdz x x x s s a x x dt dz x x x ⎡⎤=--+-⎢⎥⎣⎦⎡⎤=--+-⎢⎥⎣⎦The expected instantaneous rate at which capital gains are earned from the bond is therefore: 2021()s a x x x x--+ The expected interest per unit time is 1. The total expectedinstantaneous return is therefore:20211()s a x x x x --+ When expressed as a proportion of the bond price this is: 202111()s a x x x x x ⎛⎫⎛⎫--+ ⎪ ⎪⎝⎭⎝⎭20()a x x x s x =--+Problem .If S follows the geometric Brownian motion process in equation , what is the process followed by (a) y = 2S, (b) y=S 2 , (c) y=e S , and (d) y=e r(T-t)/S. In each case express the coefficients of dt and dz in terms of y rather than S.(a) In this case 2y S ∂/∂=, 220y S ∂/∂=, and 0y t ∂/∂= so thatIt’(b) s lemma gives(c)22dy S dt S dz μσ=+ordy y dt y dz μσ=+(d) In this case 2y S S ∂/∂=, 222y S ∂/∂=, and 0y t ∂/∂= so thatIt’(e) s lemma gives(f)2222(2)2dy S S dt S dz μσσ=++or2(2)2dy y dt y dz μσσ=++(g) In this case S y S e ∂/∂=, 22S y S e ∂/∂=, and 0y t ∂/∂= so thatIt’(h) s lemma gives(i)22(2)S S S dy Se S e dt Se dz μσσ=+/+or22[ln (ln )2]ln dy y y y y dt y y dz μσσ=+/+(d)In this case ()2r T t y S e S y S -∂/∂=-/=-/,22()3222r T t y S e S y S -∂/∂=/=/, and ()r T t y t re S ry -∂/∂=-/=- so thatIt’(e) s lemma gives (f)2()dy ry y y dt y dz μσσ=--+-or2()dy r y dt y dz μσσ=-+--Problem .A stock price is currently 50. Its expected return and volatility are 12% and 30%, respectively. What is the probability that the stock price will be greater than 80 in two years (Hint 80T S > whenln ln 80T S >.)The variable ln T S is normally distributed with mean 20ln (2)S T μσ+-/and standard deviation σ050S =, 012μ=., 2T =, and 030σ=. so that the mean and standard deviation of ln T S are2ln 50(012032)24062+.-./=. and 00424.=., respectively. Also,ln804382=.. The probability that 80T S > is the same as theprobability that ln 4382T S >.. This is 4382406211(0754)0424N N .-.⎛⎫-=-. ⎪.⎝⎭where ()N x is the probability that a normally distributed variable with mean zero and standard deviation 1 is less than x . From the tables at the back of the book (0754)0775N .=. so that the required probability is .Problem (See Excel Worksheet)Stock A, whose price is $30, has an expected return of 11% and a volatility of 25%. Stock B, whose price is $40, has an expected return of 15% and a volatility of 30%. The processes driving the returns are correlated with correlation parameter . In Excel,simulate the two stock price paths over three months using daily time steps and random samples from normal distributions. Chart the results and by hitting F9 observe how the paths change as the random samples change. Consider values of equal to , , and .The processes aret S t S S A A A A ∆⨯ε⨯⨯+∆⨯⨯=∆25.011.0t S t S S B B B B ∆⨯ε⨯⨯+∆⨯⨯=∆30.015.0Where t is the length of the time step (=1/252) and the ’s are correlated samples from standard normal distributions.。
期权期货和其他衍生品第五版课程设计 (2)
期权期货和其他衍生品第五版课程设计课程简介本课程是关于期权期货和其他衍生品的理论与实践的综合性课程。
本课程旨在通过理论教学、案例分析、模拟交易等方式，让学生了解期权、期货、互换、衍生品等金融工具的基本概念、交易原理、应用场景以及未来趋势等内容。
通过本课程的学习，学生将掌握期权期货等衍生品的风险管理、投资组合优化、价值评估等方面的理论与实践技能。
课程目标1.熟悉期权、期货等金融衍生品的基本概念、交易原理等；2.掌握期权、期货等金融衍生品的应用场景和未来趋势；3.掌握期权、期货等金融衍生品的投资策略、风险管理等方面的理论与实践技能；4.能够使用模拟交易等工具进行实践操作，把理论知识应用于实践中。
课程内容第一章期权基础1.期权概述2.期权市场结构3.期权交易原理4.期权价格理论第二章期货基础1.期货市场概述2.期货交易原理3.期货价格理论第三章互换基础1.互换概述2.互换交易原理3.互换价格理论第四章衍生品基础1.衍生品概述2.衍生品种类与交易原理3.衍生品定价与风险管理第五章期权期货交易策略1.期权期货交易心理学2.期权期货交易策略设计3.期权期货交易模拟实践第六章期权期货风险管理1.期权期货风险管理概述2.市场风险、信用风险、操作风险等风险控制技巧3.风险控制案例分析课程设置理论教学本课程理论教学采用讲授、案例分析、互动讨论等方式进行，全程共计40个课时，课时长度为45分钟。
模拟交易本课程的模拟交易环节通过使用虚拟交易平台进行，学生可在模拟交易平台中实践操作期权、期货等金融衍生品，提升实践技能。
实际案例分析本课程通过实际案例的分析，让学生对期权、期货等金融衍生品的应用场景、交易策略、风险管理等方面有更深刻的了解。
教学模式本课程采用小班授课，每个班级控制在30人以内，以便更好地进行讨论和互动。
评估方式1.平时成绩：包括课堂参与、模拟交易表现等，占总成绩的50%；2.期末考试：根据课程内容设置，占总成绩的50%。
期货期权及其衍生品配套(全34章)Ch09PPT课件
风险对冲策略
买入保护性看跌期权
为避免标的资产价格下跌的风险，同 时赚取权利金收益。
动态对冲策略
根据市场走势不断调整对冲头寸，以 实现风险的有效管理。
05 期权市场的监管与法规
期权市场的监管机构
中国证券监督管理委员会
负责制定和执行期权市场的相关法规，监管 市场运行，保护投资者权益。
Vega
衡量期权价格对波 动率的敏感性。
Delta
衡量标的资产价格 变动对期权价格的 影响。
Theta
衡量期权价格对时 间变化的敏感性。
Rho
衡量期权价格对无 风险利率的敏感性。
波动率微笑与波动率期限结构
波动率微笑
指不同到期日的期权，其隐含波动率不同，形成波动率与行权价格之间的关系曲 线。
波动率期限结构
投资者保护
期权市场监管机构通过制定和执 行相关法律法规，保护投资者的 合法权益，防止市场操纵和欺诈
行为。
投资者教育
期权市场监管机构和相关机构积极 开展投资者教育活动，提高投资者 的风险意识和投资技能，引导投资 者理性投资。
纠纷解决机制
期权市场建立了纠纷解决机制，为 投资者提供维权途径，保障投资者 的合法权益。
期权买方
拥有权利的一方，有权在期权有效期内行使权利。
期权卖方
承担义务的一方，在期权被行使时必须履行相应的义务。
期货期权的分类
按标的物分类
商品期货期权、金融期货期权。
按交易方式分类
买入期权、卖出期权。
按行权时间分类
欧式期权、美式期权。
期货期权与股票期权的比较
01
标的物
期货期权的标的物是期货合约，股票期权的标的物是股票。
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Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
400.00 5-...Jun 397....00 13-...Jun 393....30 19-...Jun 387....00 26-Jun 392.30
Mechanics of Futures Markets
Chapter 2
1
Futures Contracts
Available on a wide range of underlying assets
Exchange traded Specifications need to be defined:
The balance in the margin account is adjusted to reflect daily settlement
Margins minimize the possibility of a loss through a default on a contract
What can be delivered, Where it can be delivered, When it can be delivered
Settled daily
2
Margins
A margin is cash or marketable securities deposited by an investor with his or her broker
Settled at maturity Delivery or final cash settlement usually occurs
FUTURES Exchange traded Standard contract Range of delivery dates
Settled daily Contract usually closed out
prior to maturity
13
Foreign Exchange Quotes
Futures exchange rates are quoted as the number of USD per unit of the foreign currency
Forward exchange rates are quoted in the same way as spot exchange rates. This means that GBP, EUR, AUD, and NZD are USD per unit of foreign currency. Other currencies (e.g., CAD and JPY) are quoted as units of the foreign currency per USD.
12
Forward Contracts vs Futures Contracts
TABLE 2.3 (p. 36)
FORWARDS Private contract between 2 parties
Non-standard contract Usually 1 specified delivery date
(6... 00) (4... 20) (1,1... 40) 260
(...600) (1,...340) (2,...600) (1,540)
4,000
3,4...00
0...
2,6...60
+ 1,3.40 .
= <
4,000 3,000
2,7...40 + 1,2...60 = 4,000
5,060
6
Delivery
If a contract is not closed out before maturity, it usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses.
Settlement price: the price just before the final bell each day used for the daily settlement process
Volume of trading: the number of trades in 1 day
8
Convergence of Futures to Spot
(Figure 2.1, page 23)
Futures Price
Spot Price
Time
(a)
Spot Priቤተ መጻሕፍቲ ባይዱe Futures
Price
Time
(b)
9
Questions
When a new trade is completed what are the possible effects on the open interest?
Regulators try to prevent questionable trading practices by either individuals on the floor of the exchange or outside groups
11
Accounting & Tax If a contract is used for Hedging: it is logical to recognize profits (losses) at the same time as on the item being hedged Speculation: it is logical to recognize profits (losses) on a mark to market basis Roughly speaking, this is what the treatment of futures in the U.S.and many other countries attempts to achieve
Can the volume of trading in a day be greater than the open interest?
10
Regulation of Futures
Regulation is designed to protect the public interest
(US$4,000 in total) maintenance margin is US$1,500/contract
(US$3,000 in total)
4
A Possible Outcome
Table 2.1, Page 25
Daily Cumulative Margin
Futures Gain
0
5
Other Key Points About Futures
They are settled daily Closing out a futures position
involves entering into an offsetting trade Most contracts are closed out before maturity
A few contracts (for example, those on stock indices and Eurodollars) are settled in cash
7
Some Terminology
Open interest: the total number of contracts outstanding equal to number of long positions or number of short positions
3
Example of a Futures Trade
An investor takes a long position in 2 December gold futures contracts on June 5
contract size is 100 oz. futures price is US$400 margin requirement is US$2,000/contract
14