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Ch02_Futures Markets and the Use of Futures for Hedging(金融工程-华东师范大学 汤银才)

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ofstockprices(金融工程-华东师范大学汤银才).ppt

ofstockprices(金融工程-华东师范大学汤银才).ppt
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
10.3
Modeling Stock Prices
We can use any of the four types of stochastic processes to model stock prices
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
10.14
Generalized Wiener Processes
10.1
Model of the Behavior
of Stock Prices
Chapter 10
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
10.15
Generalized Wiener Processes
(continued)
Dx a Dt b Dt
Mean change in x in time T is aT Variance of change in x in time T is b2T Standard deviation of change in x in time

金融工程概论

金融工程概论

金融工具
（定价分析方法 （金融衍生工
数理量化方法） 具定价及应用）
金融技术 （套期保值、
套利）
参考书目与学习资源
选用教材：
郑振龙 《金融工程》，高等教育出版社，2016年9月第四版
参考教材：
[美]约翰.赫尔著《期权、期货和衍生证券》（王勇等译），机械 工业出版社，2010
[美]约翰.马歇尔，维普尔.班塞尔著：《金融工程》（宋逢明等 译）， 清华大学出版社， 1998
公司担心铜价会进一步下跌，如果６个月后的铜
价跌破60000元／吨时，那么公司将无法实现预 定的最低目标利润。
问题：
如何才能使公司避免市场铜价格的下跌 引起的利润急剧减少，而至少保证公司 完成最低目标利润？
金融工程师建议：
最简单的方法是在期货市场卖出６个月 后到期的与产量相同的铜期货合约 （10000吨），这种方法就是经典的套期 保值方法，也是最简单的套期保值方法， 它是一种比较有效的规避市场风险的方 法,当然还有其他比较复杂的方法，以后 课程将会讨论。
融问题, 综合性、实践性更强。 作为金融工程学科的涵义，在于综合地采用各种自然
科学和工程技术的方法（如机械工程用到金属材料与 热处理方面的技术，金融工程用到信息处理和人工智 能方面的技术），创造出各种有价值的产品和服务， 并创造出为设计、开发和实施这些产品和服务所需要 的技术方法。
2021/12/15
以解决金融问题为根本目的
企业管理者的需求：石油涨价了怎么办？汇率上升了怎么办？ 利率变化了怎么办？
个人的需求：怎样承担自己所愿意并且能够承担的风险，获 得自己所需要的收益？
金融机构的需求：怎么去迎合客户的需要？怎样创造出更多 的更具有创新意义的产品去吸引客户？面对多变的市场要如 何避免过大的风险？

金融保险-BlackScholesModel金融工程华东师范大学汤银才 精品

金融保险-BlackScholesModel金融工程华东师范大学汤银才 精品

11.8
The Expected Return Example
Take the following 5 annual returns: 10%, 12%, 8%, 9%, and 11%
The arithmetic average is
_
n
x
1 n
xi
1 5
(0.10
0.12
0.08
0.09
0.11)
E(ST ) S0 emT var(ST ) S02e2mT (e2T 1)
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
11.7
The Expected Return
➢ The expected value of the stock price is E(ST)=S0emT
➢ The expected continuously compounded return on the stock is E(h)=m – 2/2 (the geometric average)
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
11.4
Modeling Stock Prices in Finance
11.6
Continuously Compounded Rate of Return, h (Equation (11.7))

Ch04Hedging Strategies Using Futures(期权,期货和其他衍生物-第五版)

Ch04Hedging Strategies Using Futures(期权,期货和其他衍生物-第五版)

4.12
Reasons for Hed be out of the market for a short period of time. (Hedging may be cheaper than selling the portfolio and buying it back.) • Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outpeform the market.)
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
4.14
Changing Beta
• What position is necessary to reduce the beta of the portfolio to 0.75? • What position is necessary to increase the beta of the portfolio to 2.0?
b A
• where P is the value of the portfolio, b is its beta, and A is the value of the assets underlying one futures contract
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull
Fundamentals of Futures and Options Markets, 4th edition © 2001 by John C. Hull

大学金融英语chapter 13 Derivatives Markets 3：Futures and

大学金融英语chapter 13 Derivatives Markets 3：Futures and

Notes
8. to customize vt. 量身定做to make or build according to personal or individual specifications, e.g. customized terms 量身定做的条款或条件
9. to enforce vt. 强制执行to cause to take effect or to be fulfilled, e.g. to ~ all the terms of the contract 强制执行合同所有条款
Main Text
Meanings of Futures பைடு நூலகம்nd Forwards
Futures and forwards are actually contracts. A futures contract is an agreement to buy or sell a fixed
quantity of a particular commodity, currency, or security for delivery at a fixed date in the future at a fixed price. Futures provide an opportunity for those who must purchase goods regularly to hedge against changes in price. A forward contract is an agreement between a buyer and a seller requiring delivery of an asset at a specified future date at a price agreed at the time of making the forward contract with payment to be made upon delivery.

金融工程课件

金融工程课件
➢交易方案的制定者（市场参与者）——为满足客 户需要而构造出方案并将其出售给客户
➢新观念的创造者（创新者）——创造新的金融产 品与手段
➢钻法律空子者（在法律边缘活动的人）——精熟 会计和税法。
4、金融工程与金融理论关系
• 西方金融理论的含义（微观金融的三个 层次：Investment、Corporate Finance、 Asset Pricing）
Carnegie Mellon University Graduate School of Business Master of Science in Computational
Finance /mscf/
建立在工程学院的有 Princeton University Department of Operations Research & Financial
应用性
金融工程发展的动力源泉
金融工程的目的性
解决金融财务问题 盈利 风险管理 合理避税 逃避管制
金融工程的5个步骤
1、诊断：识别金融问题的实质和根源 2、分析：根据当前的体制、技术和金融
理论找出解决问题的最佳方案 3、生产：生产一种新工具 4、定价：确定生产成本和边际收益 5、修正：为满足每个客户的特殊需求，
➢公司治理问题，它讨论的是公司组织结构 和激励机制等问题。公司金融在国内往往 被译为公司财务，实际上其内容远远超出 了公司的财务问题。
金融工程的主要内容
• 固定收入证券 • 衍生证券 • 风险管理 • 金融产品的开发与创新
5、金融工程的工具
• 概念性工具：金融科学的思想和概念，包 括估值理论、投资组合理论、套期保值理 论、会计关系以及税收知识.
Engineering M.S.E. in Operations Research and Financial

Ch14_ValueatRis(金融工程学,华东师大)k

• It is easy to understand • It asks the simple question: “How bad can
things get?”
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
14.4
VaR and Regulatory Capital
Regulators require banks to keep capital for market risk equal to the average of VaR estimates for past 60 trading days using X=99 and N=10, times a multiplication factor. (Usually the multiplication factor equals 3)
day
year
252
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
14.7
Daily Volatility (continued)
200,000 10 $632,456
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University

ofStockPrices(金融工程-华东师范大学汤银才)


10.11
Properties of a Wiener Process
Mean of [z (T ) – z (0)] is 0 Variance of [z (T ) – z (0)] is T Standard deviation of [z (T ) – z (0)]
is T
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
2 years? ½ years? ¼ years? Dt years?
Taking limits we have defined a continuous variable, continuous time process
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
10.10
A Wiener Process (See pages 220-1)
The continuous time, continuous variable process proves to be the most useful for the purposes of valuing derivative securities

期权、期货及其他衍生产品课件2金融工程学


The basis arising from the difference between the two assets.
3.17
Choice of Contract


Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging.
3.11
Convergence of Futures to Spot
(Hedge initiated at time t1 and closed out at time t2)
Futures Price
Spot Price
Time t1 t2 3.12
Basis Risk



Basis is the difference between spot & futures Basis= Spot price of asset to be hedgedFutures price of contract used When the spot price increases by more than the futures prices, the basis increases,this is referred to as a strengthening of the basis. weakening of the basis Basis risk arises because of the uncertainty about the basis when the hedge is closed out
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– contract size is 100 oz. – futures price is US$400 per oz. – Initial margin(初始保证金) requirement is US$2,000/contract (US$4,000 in total) – maintenance margin(维持保证金) is US$1,500/contract (US$3,000 in total)
Day
2,660 + 1,340 = 4,000 . . . . . < 3,000
17-Jun 387.00 . . . . . .
24-Jun 392.30
(1,140) . . .
260
(2,600) . . .
(1,540)
2,740 + 1,260 = 4,000 . . . . . .
5,060 0
• Settled(结算) daily
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.3
Margins(保证金)
• A margin is cash or marketable securities deposited by an investor with his or her broker • The balance(余额) in the margin account（保证金帐户） is adjusted to reflect daily settlement • Margins minimize the possibility of a loss through a default(违约) on a contract
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.5
A Possible Outcome
Table 2.1, Page 25
Daily Gain (Loss) (US$) Cumulative Gain (Loss) (US$) Margin Account Margin Balance Call (US$) (US$) 4,000 (600) . . . (420) . . . (600) . . . (1,340) . . . 3,400 . . . 0 . . . 保证金催付 Futures Price (US$) 400.00 3-Jun 397.00 . . . . . . 11-Jun 393.30 . . . . . .
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 20 About Futures
• They are settled daily • Closing out(平仓) a futures position involves entering into an offsetting(反向) trade • Most contracts are closed out before maturity
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.8
Some Terminologies
• Open interest(未平仓合约数): the total number of contracts outstanding – equal to number of long positions or number of short positions • Settlement price(结算价格): the price just before the final bell each day – used for the daily settlement process • Volume of trading(交易量): the number of trades in 1 day
2.1
Futures Markets and the Use of Futures for Hedging
Chapter 2
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.10
Questions
• When a new trade is completed what are the possible effects on the open interest? • Can the volume of trading in a day be greater than the open interest?
2.2
Futures Contracts
• Available on a wide range of underlyings • Exchange traded • Specifications(规定) need to be defined:
– What can be delivered, – Where it can be delivered, & – When it can be delivered
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.14
Basis Risk
• Basis(基差) is the difference between spot price of asset to be hedged & futures price of contract used • Basis risk (基差风险) arises because of the uncertainty about the basis when the hedge is closed out
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.13
Long & Short Hedges
• A long futures hedge(多头期货套期保 值) is appropriate when you know you will purchase an asset in the future & want to lock in the price • A short futures hedge(空头期货套期保 值) is appropriate when you know you will sell an asset in the future & want to lock in the price
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.12
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
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.9
Convergence of Futures to Spot (Figure 2.1, page 32)
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2005
2.7
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. • A few contracts (for example, those on stock indices and Eurodollars) are settled in cash.
Futures Price
Spot Price