Ch13_The Greek Letters(金融工程学,华东师大).
合集下载
金融工程(上海交大 吴文锋)
• 代表性成果
– Black-Scholes期权定价公式 – 期权二项式定价方法等
《金融工程》讲义，Copyrights © 2003，吴文锋、吴冲锋
24
Black-Schole 原假设
改变的情况 无风险利率满足随机的情形
贡献者 Merton（1973）
(1) 无 风 险 利 率为定常数
(2)连续模型
25
《金融工程》讲义，Copyrights © 2003，吴文锋、吴冲锋
(4) 欧 式 看 涨 期 权
美式看跌期权
Parkinson（1977）
美式期权最优提早执行的条件
Cox和Rubinstein（1985）， Geseke和Shastri（1985） Turnbull and Wakeman(1991) ， Levy(1992) ， Vorst(1992, 1996) ， Milesky and Posner(1998) Cox和Ross（1976）
8
第二部分
为什么要学习《金融工程》 金融工程的核心问题
金融工程的基本概念 金融工程的发展背景
《金融工程》讲义，Copyrights © 2003，吴文锋、吴冲锋
9
1、金融工程的核心问题
定价
• 普通产品：
– 价值规律的支配 – 供求关系
• 金融产品：
– 受什么支配？ – 供求关系？
《金融工程》讲义，Copyrights © 2003，吴文锋、吴冲锋
10
2、普通商品与金融产品的区别
（1）金融产品供给的特殊性 （2）金融产品需求的特殊性 （3）金融产品定价的特殊性 （4）金融产品获得长期收益的困难性 （5）金融产品价格波动的巨大性
《金融工程》讲义，Copyrights © 2003，吴文锋、吴冲锋
《货币金融学(第十三版)》英文版教学课件mishkin_econ13e_ppt_10
The Spread of Government Deposit Insurance Throughout the World: Is This a Good Thing?
• Has government deposit insurance helped improve the performance of the financial system and prevent banking crises? The answer seems to be “no.” Research at the World Bank seems to answer “no,” since on average, the adoption of explicit government deposit insurance is associated with less banking sector stability and a higher incidence of banking crises. Furthermore, on average, deposit insurance seems to retard financial development.
Copyright © 2022, 2019, 2016 Pearson Education, Inc. All Rights Reserved
Types of Financial Regulation: Restrictions on Asset Holdings
• Attempts to restrict financial institutions from too much risk taking: – Bank regulations ▪ Promote diversification ▪ Prohibit holdings of common stock – Capital requirements ▪ Minimum leverage ratio (for banks) ▪ Basel Accord: risk-based capital requirements ▪ Regulatory arbitrage
《货币金融学(第十三版)》英文版教学课件mishkin_econ13e_ppt_09
$90M
$80M $10M
Bank Capital
Blank
$10M
Blank
– Suppose a bank’s required reserves are 10%.
– If a bank has ample excess reserves, a deposit outflow does not necessitate changes in other parts of its balance sities
Required reserves
Loans
+$10 +$90
Checkable deposits
Blank
+$100
Blank
• Asset transformation: selling liabilities with one set of characteristics and using the proceeds to buy assets with a different set of characteristics
• The bank borrows short and lends long
Copyright © 2022, 2019, 2016 Pearson Education, Inc. All Rights Reserved
General Principles of Bank Management
• Liquidity Management • Asset Management • Liability Management • Capital Adequacy Management • Credit Risk • Interest-rate Risk
数学专业英语吴炯圻
New Words & Expressions:algebra 代数学 geometrical 几何的algebraic 代数的 identity 恒等式arithmetic 算术, 算术的 measure 测量，测度axiom 公理 numerical 数值的, 数字的conception 概念，观点 operation 运算constant 常数 postulate 公设logical deduction 逻辑推理 proposition 命题division 除，除法 subtraction 减，减法 formula 公式 term 项，术语trigonometry 三角学 variable 变化的，变量2.1 数学、方程与比例Mathematics, Equation and Ratio4Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches.1－A What is mathematics数学来源于人类的社会实践，比如工农业生产，商业活动，军事行动和科学技术研究。
And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics.反过来，数学服务于实践，并在各个领域中起着非常重要的作用。
金融工程(第5版) 课件第1章
(2) 马歇尔和班赛尔的评价
马歇尔和班赛尔在其《金融工程》一书中十分推崇这一定义，他们指出， 该定义中的“创新”和“创造”这两个词值得重视，它们具有三种涵义：
一是金融领域中思想的跃进，其创造性最高， 如创造出第一个零息债券、第一个 互换合约等； 二是指对已有的观念做出新的理解和应用，如将期货交易推广到以前没能涉及到 的领域，发展出众多 的期权及互换的变种等； 三 是指对已有的金融产品和手段进行重新组合，以适应某种特定的情况，如远期 互换、期货期权、互换期权的出现等。
（2）组合技术：组合技术主要是在同一类金融工具或产品之间进行搭配， 通过构造对冲头寸规避或抑制风险暴露，以满足不同风险管理者的需求。
（3）整合技术：整合技术主要是在不同种类的金融工具之间进行融合， 使其形成具有特殊作用的新型混合金融工具，以满足投资人或发行人的多 样化需求。
3. 三种技术的具体化
（1）分解技术
（美）马歇尔、班赛尔，宋逢明等译，《金融工程》，北京：清华大学出版社，1988。
(3) 芬纳蒂关于金融工程定义内涵 按照芬纳蒂关于金融工程定义的思路，金融工程可以划分为以下 三个方面的内容：
① 新型金融工具的设计和创造。 ② 创新性金融过程的设计和开发。
③ 针对企业整体金融问题的创造性解决方略。
（二）史密斯和史密森的定义
二、金融工程
1. 金融工程学科成立的标志
1991年“国际金融工程师学会”的成立，被认为是金融工程学科确 立的重要标志 。
该协会的宗旨是“界定和培育金融工程这一新兴专业”。
2 历史上金融学家关于金融工程的定义 (一) 芬纳蒂的定义及解释 （1）芬纳蒂的定义
美国金融学家约翰·芬纳蒂在1988年为金融工程作出了如下解释：
华东师大版一课一练·三年级英语(N版,第二学期)
C. What else can you see?
( ) 21. A. How many buses are there? B. How many vans are there?
C. How many cars are there?
( ) 22. A. There are some cars on the road.
Module 3 Unit 1 /59 Unit 2 /66 Unit 3 /73 Test for Module 3 /81
Module 4 Unit 1 /87 Unit 2 /94 Unit 3 /101 Test for Module 4 /107
Final Examination /112
( ) 40. Alice and Kitty are at home.
( ) 41. Alice and Kitty can’t make a spinner.
( ) 42. Alice and Kitty are good friends.
Exercise for reading and writing practice（读写练习）
III. Listen and choose（听录音，选出你听到的句子）
( ) 19. A. I can hear a ship.
B. He can hear a ship.
C. She can hear a sheep.
( ) 20. A. What can you see?
B. What do you see?
( ) 25. A. I can hear an aeroplane.
B. She can hear an aeroplane.
《货币金融学(第十三版)》英文版教学课件mishkin_econ13e_ppt_18
Federal Reserve System
Blank
Blank
Blank
Assets
Blank
Liabilities
Blank
Foreign Assets (International Reserves)
$1B negative $1 B
Monetary Base (reserves)
0
Government Bonds
18.2 Interpret the relationships among the current account, the capital account, and official reserve transactions balance.
18.3 Identify the mechanisms for maintaining a fixed exchange rate and assess the challenges faced by fixed exchange rate regimes.
• Capital Account – Net receipts from capital transactions
• Sum of these two is the official reserve transactions balance
Copyright © 2022, 2019, 2016 Pearson Education, Inc. All Rights Reserved
• Second, a current account deficit means that foreigners’ claim on U.S. assets is growing.
Copyright © 2022, 2019, 2016 Pearson Education, Inc. All Rights Reserved
ch13 Digital Signatures 密码编码学与网络安全：原理与实践 第四版英文课件
14
V1 = 10 mod 19 = 16 V2 = 43.34 = 5184 = 16 mod 19 since 16 = 16 signature is valid
Schnorr Digital Signatures
➢ also uses exponentiation in a finite (Galois)
➢ any user B can verify the signature by computing
m
V1 = a mod q V2 = yAS1 S1S2 mod q signature is valid if V1 = V2
ElGamal Signature Example
➢ use field GF(19) q=19 and a=10
Cryptography and Network Security
Chapter 13
Fifth Edition by William Stallings
Lecture slides by Lawrie Brown
Digital Signature Model
Digital Signature
➢ Alice computes her key:
A chooses xA=16
&
computes
16
yA=10
mod
19
=
4
➢ Alice signs message with hash m=14 as (3,4):
choosing random K=5 which has gcd(18,5)=1
➢ involve only sender & receiver ➢ assumed receiver has sender’s public-key ➢ digital signature made by sender signing
V1 = 10 mod 19 = 16 V2 = 43.34 = 5184 = 16 mod 19 since 16 = 16 signature is valid
Schnorr Digital Signatures
➢ also uses exponentiation in a finite (Galois)
➢ any user B can verify the signature by computing
m
V1 = a mod q V2 = yAS1 S1S2 mod q signature is valid if V1 = V2
ElGamal Signature Example
➢ use field GF(19) q=19 and a=10
Cryptography and Network Security
Chapter 13
Fifth Edition by William Stallings
Lecture slides by Lawrie Brown
Digital Signature Model
Digital Signature
➢ Alice computes her key:
A chooses xA=16
&
computes
16
yA=10
mod
19
=
4
➢ Alice signs message with hash m=14 as (3,4):
choosing random K=5 which has gcd(18,5)=1
➢ involve only sender & receiver ➢ assumed receiver has sender’s public-key ➢ digital signature made by sender signing
- 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)。
• Naked position (裸期权头寸策略) Take NO action • Covered position(抵补期权头寸策略) Buy 100,000 shares today Both strategies leave the FI exposed to significant risk
Option Price
f S
B A
Slope =
Stock Price
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
0
Theta
Out-of-the-Money
Time to Maturity
At-the-Money In-the-Money
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
13.4
Stop-Loss Strategy
This involves
13.2
Example
• A FI has SOLD for $300,000 a European call on 100,000 shares of a non-dividend paying stock: S0 = 49 X = 50 r = 5% = 20% = 13% T = 20 weeks • The Black-Scholes value of the option is $240,000 • How does the FI hedge its risk?
GammaXFra bibliotekStock Price •
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
13.12
Equation for Gamma
•
13.6
Delta Hedging
• This involves maintaining a delta neutral portfolio • The delta of a European call on a stock paying dividends at a rate q is N (d1 ) e qT • The delta of a European put is [ N (d1 ) 1] e qT • The hedge position must be frequently rebalanced • Delta hedging a written option involves a “BUY high, SELL low” trading rule
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
•
13.7
Delta Neutral Portfolio Example
•
13.14
Theta
• Theta () of a derivative (or a portfolio of derivatives) is the rate of change of the value with respect to the passage of time f • Figure 13.6 (p. 321) t
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
•
13.10
Delta for other Futures
13.1
The Greek Letters
Chapter 13
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
• The Gamma () for a European call or put paying a continuous dividend q is
N ' (d1 )e qT S 0 T
where
1 d12 / 2 N ' (d1 ) n(d1 ) e 2
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
…
48.130 0.183 12,100 46.630 0.007 (17,600) 48.120 0.000 (700)
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
– Fully covering the option as soon as it moves in-the-money – Staying naked the rest of the time
• This deceptively simple hedging strategy does NOT work well !!! • Transactions costs, discontinuity of prices, and the bid-ask bounce kills it
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
13.5
Delta
• Delta () is the rate of change of the option price with respect to the underlying • Figure 13.2 (p. 311)
(out-of-the-money)
Table 13.3 (p. 315)
Week 0 1 2 18 19 20 Stock Price Delta 49.000 0.522 49.750 0.568 52.000 0.705 … … Shares Purch. 52,200 4,600 13,700 … Cum. Cost of Cost Shares Incl. Purch. Interest 2,557.8 2,557.8 228.0 2,789.2 712.4 3,504.3 … … 582.4 1,109.6 (820.7) 290.0 (33.7) 256.6 Int. Cost 2.5 2.7 3.4 1.1 0.3 …
•
13.13
Gamma Addresses Delta Hedging Errors Caused By Curvature
• Figure 13.7 (p. 322)
C'' C' C
Call Price
S
S' Stock Price
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
•
13.11
Gamma
• Gamma () is the rate of change of delta () with respect to the price of the underlying 2 f 2 S S • Figure 13.9 (p. 325) [for a call or put]
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
13.3
Naked & Covered Positions
…
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
•
13.8
Delta Neutral Portfolio Example
(in-the-money)
Table 13.2 (p. 314)
Option Price
f S
B A
Slope =
Stock Price
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
0
Theta
Out-of-the-Money
Time to Maturity
At-the-Money In-the-Money
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
13.4
Stop-Loss Strategy
This involves
13.2
Example
• A FI has SOLD for $300,000 a European call on 100,000 shares of a non-dividend paying stock: S0 = 49 X = 50 r = 5% = 20% = 13% T = 20 weeks • The Black-Scholes value of the option is $240,000 • How does the FI hedge its risk?
GammaXFra bibliotekStock Price •
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
13.12
Equation for Gamma
•
13.6
Delta Hedging
• This involves maintaining a delta neutral portfolio • The delta of a European call on a stock paying dividends at a rate q is N (d1 ) e qT • The delta of a European put is [ N (d1 ) 1] e qT • The hedge position must be frequently rebalanced • Delta hedging a written option involves a “BUY high, SELL low” trading rule
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
•
13.7
Delta Neutral Portfolio Example
•
13.14
Theta
• Theta () of a derivative (or a portfolio of derivatives) is the rate of change of the value with respect to the passage of time f • Figure 13.6 (p. 321) t
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
•
13.10
Delta for other Futures
13.1
The Greek Letters
Chapter 13
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
• The Gamma () for a European call or put paying a continuous dividend q is
N ' (d1 )e qT S 0 T
where
1 d12 / 2 N ' (d1 ) n(d1 ) e 2
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
…
48.130 0.183 12,100 46.630 0.007 (17,600) 48.120 0.000 (700)
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
– Fully covering the option as soon as it moves in-the-money – Staying naked the rest of the time
• This deceptively simple hedging strategy does NOT work well !!! • Transactions costs, discontinuity of prices, and the bid-ask bounce kills it
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
13.5
Delta
• Delta () is the rate of change of the option price with respect to the underlying • Figure 13.2 (p. 311)
(out-of-the-money)
Table 13.3 (p. 315)
Week 0 1 2 18 19 20 Stock Price Delta 49.000 0.522 49.750 0.568 52.000 0.705 … … Shares Purch. 52,200 4,600 13,700 … Cum. Cost of Cost Shares Incl. Purch. Interest 2,557.8 2,557.8 228.0 2,789.2 712.4 3,504.3 … … 582.4 1,109.6 (820.7) 290.0 (33.7) 256.6 Int. Cost 2.5 2.7 3.4 1.1 0.3 …
•
13.13
Gamma Addresses Delta Hedging Errors Caused By Curvature
• Figure 13.7 (p. 322)
C'' C' C
Call Price
S
S' Stock Price
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
•
13.11
Gamma
• Gamma () is the rate of change of delta () with respect to the price of the underlying 2 f 2 S S • Figure 13.9 (p. 325) [for a call or put]
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
13.3
Naked & Covered Positions
…
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University
•
13.8
Delta Neutral Portfolio Example
(in-the-money)
Table 13.2 (p. 314)