Derivatives

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导数教学PPT(英文)(derivatives)

The Constant Multiple Rule
Brown University. “Basic Derivative Rules” Brown University Calculus Review. 6 August 2008 5:57 PM. Web. 9 Sept. 2014.
The Sum&Difference t wo funct ionsis t hesum (or difference ) of Rule
1.If you see a rational function with an x value on the numerator as well as on the denominator, a mental check should go off in your head: USE THE QUOTIENT RULE!
*When Do We Use The Quotient Rule?!*
This is probably the most obvious clue that can lead you to use the quotient rule. 2.You use the quotient rule to find the derivative of a rational expression. 3.WARNING! Although the quotient rule is effective in its use, it can be very lengthy. We suggest that you make sure the problem you are solving for has an x value on both the numerator and denominator, if only a number is present on the denominator, you can discard using the quotient rule and move on to use the power rule. * It could save you from too much mental exhaustion* : )

Convertibles, Warrants, and Derivatives

– Convertibles may also suffer from the attachment of a call provision
1-7
Advantages to the Corporation
• Interest rate paid on convertible issues is lower
• Call option provision is used to force conversion when it needs to shift outstanding debt to common stock
– Value of convertible bonds might go up significantly
• While a few firms that sell convertible bonds may be high quality firms, most are small companies with low credit ratings and high risk
1-9
Forcing Conversion
1-8
Disadvantages to the Corporation
• Size of convertible bond market is small compared to markets for nonconvertible corporate bonds and commoarrants
• Intrinsic value of a warrant: I = (M – E) X N
• Where • I = Intrinsic value of a warrant • M = Market value of a common stock (stock price) • E = Exercise price of a warrant • N = Number of shares each warrant entitles the holder to purchase

衍生品证券Derivatives_Chapter 1

Buying and Short-Selling Financial Assets
2
What are Derivatives?
A derivative security is a financial instrument whose value derives from that of some other underlying asset or assets whose price are taken as given. Remark: The value of a derivative is in a relative sense. No need to inquire into the deeper economic forces that determine the prices of the underlying assets.
Regulatory arbitrage
• To circumvent regulations
6
Three Different Perspectives
End users • Corporations • Investment managers • Investors Intermediaries • Market-makers • Traders
Figure 1.4 Millions of futures contracts traded annually at the Chicago Board of Trade (CBT), Chicago Mercantile Exchange (CME), and the New York Mercantile Exchange (NYMEX), 1970–2006. The CME and CBT merged in 2007.

衍生品证券Derivatives_Chapter 5

Payments, receipts, and their timing
4
Pricing Prepaid Forwards
If we can price the prepaid forward (FP), then we can calculate the price for a forward contract
E0 (ST ) S0eaT
• Combining the two,
FP 0,T

S0eaT eaT
S0
7
Pricing Prepaid Forwards (cont’d)
Pricing by arbitrage
• Arbitrage: a situation in which one can generate positive
i1
12
Pricing Prepaid Forwards (cont’d)
Example 5.2: continuous dividend • The index is $125 and the dividend yield is 3%
continuously compounded. How much does a 1-year prepaid forward cost?
Present value of 1 share at time T is S0e-δT.
11
Pricing Prepaid Forwards (cont’d)
Example 5.1: fixed discrete dividend
• XYZ stock costs $100 today and is expected to pay a
pricingprepaidforwardscontd13fp01?125e?003?12131pricingforwardsonstockforwardpriceisthefuturevalueoftheprepaidforward?nodividendsrtpttttessfvffvf00000000???14?discretedividendscontinuousdividends?????nitttrrttiideesf100trtesf00???pricingforwardsonstockcontdforwardpremium

Derivatives_Chapter 12

C(F0PT ( S ) ,F0PT ( K ) ,s ,T) = F0PT ( S ) N(d1) F0PT ( K ) N(d2) , , , ,
where
d1 ln F0P,T (S)/F0P,T (K) 1 s 2T 2

s T
P F0,T ( K ) = Ke-rT
d 2 d1 σ T
rate r = 8%
• The option expires in one year T = 1 • XYZ does not pay dividends δ = 0
5
Using Binomial Pricing Model
Consider one year as one period, we found that the option price is $7.8391. (Refer to slides 10-21, 10-22, and 10-23.) Dividing one year into three periods, we found that the option price is $7.074. (Refer to slides 10-30, 10-31, and 10-32.) Using different number n of periods, we have
Just like in Chapter 10 that we adjusted the binomial model to price options on different underlying assets.
14
Applying BS to Other Assets (cont’d)
Call Options:
ST K ; cT 0;

Derivatives_Chapter 3

• Used to insure short positions (caps)
• Buying call options
• Written against asset positions (selling insurance)
• Covered call • Covered put
4
Insuring a Long Position: Floors
2
Long / Short Call / Put OptStrategies
Insurance strategies using options:
• Used to insure long positions (floors)
• Buying put options
• Call (K, t) and Put (K, t) denote the premiums of options with strike price K and time t until expiration • PV (F0,t ) is the present value of the forward price
18
Put-Call Parity
The net cost of buying the index using options (synthetic forward contract) must equal the net cost of buying the index using a forward contract Call (K, t) – Put (K, t) = PV (F0,t – K)
22
Bull Spreads (cont’d)
A bull spread is to buy a call/put and sell an otherwise identical call/put with a higher strike price Bull spread using call options: • Long a call with no downside risk, and • Short a call with higher strike price to eliminate

Derivatives_Chapter 8

• Assume interest rates are unchanged
• The new swap price will be $22.483, $2 higher than the old one (check and understand why exactly $2)
• PV of the differences = 2/1.06 + 2/(1.0652) = $3.65
100,000 barrels are the notional amount of the swap, used to determine the magnitude of the payments when the swap is settled financially 10
Understanding Swaps
Strategy 1: Long forward contracts for 100,000 barrels in each of the next 2 years
• IP pays $20 in year one and $21 in year two for oil
Strategy 2: Prepaid swap
5
A Commodity Swap (cont’d)
Strategy 3: Swap
• Defer payments until the oil is delivered, while still fixing the total price • A swap usually calls for equal payment in each year
• Swap settlement; swap counterparty; market value of a swap; computing swap price (rate).

Derivatives与Options(英文版)

(d1)=
Ps
v2
ln + ( r + ) t
S
2
vt
(d2) = d1 - v t
Call Option
Example
What is the price of a call option given the following?.
P = 36
r = 10%
v = .40
S = 40
t = 90 days / 365
P = 36
r = 10%
v = .40
S = 40
t = 90 days / 365
OC = Ps[N(d1)] - S[N(d2)]e-rt OC = 36[.3794] - 40[.3065]e - (.10)(.2466) OC = $ 1.70
Put - Call Parity
Put Price = Oc + S - P - Carrying Cost + Div. Carrying cost = r x S x t
+ 6
P /L
-3
2 73 0 3 6
P s
Option Strategies
Short Call Sold Call @ Oc = 3 S=27 Ps=30
+ 3
P /L
-6
2 73 0 3 6
P s
Derivatives & Options
Historical Topics (Internal to the Corp) 1 - Capital Budgeting (Investment) 2 - Capital Structure (Financing)

Derivatives_Chapter 7

• pay if the reference rate is below the FRA rate • Settled either at the initiation or maturity of the borrowing or lending transaction
9
FRA Settlement: Settle at Maturity
10
FRA Settlement: Settle at Initiation
Settle at the time of borrowing, on date 120 (June), the payment to the borrower is
(rquarterly - rFRA ) Notional principal 1 rquarterly
13
Replication of FRAs (cont’d)
Table Example of synthetic FRA. The transactions in this table are exactly those in previous table, except that all bonds are sold at time t.
(rquarterly rFRA ) notional principal
• If the borrowing rate in June is 1.5%, the borrower shall pay 100m×(1.8% – 1.5%) = $300,000 to the contract’s counterparty • If the borrowing rate in June is 2.0%, the borrower will receive 100m ×(2.0% – 1.8%) = $200,000

导数英文版知识点总结

导数英文版知识点总结IntroductionThe concept of derivatives is a fundamental concept in calculus and mathematics. It is a powerful tool used to analyze the behavior of functions, solve problems in various fields such as physics, engineering, and economics, and has wide applications in real-life situations. In this article, we will summarize the key knowledge points of derivatives, including the definition of derivatives, the rules for finding derivatives, applications of derivatives, and some important theorems related to derivatives.Definition of DerivativesThe derivative of a function at a point is defined as the limit of the average rate of change of the function over a small interval around the point, as the interval becomes infinitesimally small. Mathematically, the derivative of a function f(x) at a point x=a, denoted by f'(a) ordf/dx|a, is defined as:\[ f'(a) = \lim _{h \to 0} \frac{f(a + h) - f(a)}{h} \]The derivative measures the rate at which the function changes at a specific point, or the slope of the tangent line to the function at that point.Rules for Finding DerivativesThere are several rules and formulas for finding derivatives of different types of functions. The basic rules for finding derivatives are as follows:1. Power Rule: The derivative of a power function f(x) = x^n, where n is a constant, is given by f'(x) = nx^(n-1).2. Constant Rule: The derivative of a constant function f(x) = c, where c is a constant, is zero.3. Sum and Difference Rule: The derivative of the sum or difference of two functions is the sum or difference of their derivatives.4. Product Rule: The derivative of the product of two functions u(x) and v(x) is given by (uv)' = u'v + uv'.5. Quotient Rule: The derivative of the quotient of two functions u(x) and v(x) is given by (u/v)' = (u'v - uv')/v^2.6. Chain Rule: If y = f(g(x)), then the derivative of y with respect to x is given by dy/dx =f'(g(x))g'(x).These rules are fundamental for finding derivatives of algebraic, trigonometric, exponential, and logarithmic functions.Applications of DerivativesDerivatives have wide applications in various fields, including physics, engineering, economics, and biology. Some common applications of derivatives are:1. Optimization Problems: Derivatives are used to find the maximum or minimum values ofa function, such as the maximum profit, minimum cost, maximum area, or minimum distance.2. Rate of Change: Derivatives are used to measure the rate of change of a quantity over time, such as the velocity of an object, the growth of a population, or the rate of decay of a radioactive substance.3. Tangent Lines and Linear Approximations: Derivatives are used to find the equation of the tangent line to a curve at a specific point, and to approximate the value of a function near that point.4. Related Rates: Derivatives are used to solve problems involving the rates of change of two or more related quantities, such as the changing area of a rectangle, the changing volume ofa cone, or the changing distance between two moving objects.5. Newton's Laws of Motion: Derivatives are used to describe the motion of objects in terms of position, velocity, and acceleration, and to analyze the forces acting on the objects. Important Theorems Related to DerivativesThere are several important theorems related to derivatives that are widely used in calculus and mathematical analysis. Some of the key theorems are:1. Mean Value Theorem: If a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a).2. Rolle's Theorem: If a function f(x) is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one point c in (a, b) such that f'(c) = 0.3. Cauchy's Mean Value Theorem: If two functions u(x) and v(x) are continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that (u(b) - u(a))v'(c) = (v(b) - v(a))u'(c).4. Fermat's Theorem: If a function f(x) has a local maximum or minimum at a point c, andf'(c) exists, then f'(c) = 0.5. L'Hôpital's Rule: If the limit of a quotient of two functions is of the form 0/0 or ∞/∞, then the limit of the quotient of their derivatives is equal to the limit of the original quotient, provided the limit of the derivative exists.ConclusionThe concept of derivatives is a fundamental concept in calculus, and it plays a crucial role in analyzing the behavior of functions, solving problems in various fields, and making predictions about real-life situations. This article has summarized the key knowledge points of derivatives, including the definition of derivatives, the rules for finding derivatives, applications of derivatives, and important theorems related to derivatives. A thorough understanding of these knowledge points is essential for mastering the techniques of finding derivatives and applying them to solve real-world problems.。

CFA衍生工具(Derivatives)考点解析20200129

CFA衍生工具(Derivatives)考点解析对于很多想参加CFA考试的同学来说，对于CFA的考试内容还不是很了解。

我就为大家分享一下CFA考试的考试科目：1、道德与职业行为标准(Ethics and Professional Standards)2、定量分析(Quantitative)3、经济学(Economics)4、财务报表分析(Financial Statement Analysis)5、公司理财(Corporate Finance)6、权益投资(Equity Investments)7、固定收益投资(Fixed Income)8、衍生工具(Derivatives)9、其他类投资（Alternative Investments）10、投资组合管理(Portfolio Management)Derivatives（金融衍生品）很多CFA考生都认为一级里的Derivatives（金融衍生品）非常难，碰到这个章节就觉得十分头疼。

好在这个部分在考试中占比仅为5%，有些考生甚至采取了丢车保帅的做法。

提醒大家，不必对此产生畏难情绪。

CFA一级考试金融衍生品科目考试以前有一些计算，但现在以定性题目为主，要求考生能理解其中原由，难度有所下降。

随着国内逐渐开放衍生品市场，越来越需要有衍生品专业知识的人才。

这部分的衍生品主要介绍衍生品的一些基本知识，包括衍生品的种类及市场区分，4大类衍生品的基本定价原理，以及简单期权策略。

CFA一级考试的Derivatives（金融衍生品）具体的内容知识点包含1个study session，3个reading。

其中，Reading 57对衍生品市场进行了区别，并对4大类衍生品进行了基本定义；Reading 58讲衍生品的定价和估值的基本原理，并对4大类衍生品的基本定价做了介绍；Reading 59对期权做了进一步分析，介绍两种期权及两种期权策略的应用。

从CFA考试的重要度来看，Reading 58、Reading 59是最重要的，Reading 57其次，其他Reading重要性不大。

CFA一级典型例题 Derivatives 衍生品

Derivatives1. In contrast to over-the-counter options, futures contracts:A. are not exposed to default risk.B. are private, customized transactions.C. represent a right rather than a commitment.Answer: AA is correct. Over-the counter options are exposed to default risk but futures contracts are standardized transactions that take place on futures exchanges and are not exposed to default risk.2. Which of the following best describes how derivatives are priced?A. A hedge portfolio is used that eliminated arbitrage opportunities.B. The payoff of the underlying is adjusted downward by the derivative value.C. The expected future payoff of the derivative is discounted at the risk-free rate plus a risk premium. Answer: AA is correct. A hedge portfolio is formed that eliminated arbitrage opportunities and implies a unique price for the derivative. The other answers are incorrect because the underlying payoff if not adjusted by the derivative value and the discount rate of the derivative does not include a risk premium.3. Which of the following factors does not affect the forward price?A. The cost of holding the underlying.B. Dividends or interest paid by the underlying.C. Whether the investor is risk averse, risk seeking, or risk neutral.Answer: CC is correct. The costs of holding the underlying, known as carrying costs, and the dividends and interest paid by the underlying are extremely relevant to the forward price. How the investor feels about risk is irrelevant, because the forward price is determined by arbitrage.4. Which of the following best describes the forward rate of an FRA?A. The spot rate implied by the term structureB. The forward rate implied by the term structureC. The rate on a zero-coupon bond of maturity equal to that of the forward contractAnswer: BFRAs are based on Libor, and they represent forward rates, not spot rates. Spot rates are needed to determine forward rates, but they are not equal to forward rates. The rate on a zero-coupon bond of maturity equal to that of the forward contract describes a spot rate.-1-5. Which of the following conditions will not make futures and forward prices equivalent?A. Interest rates are known.B. Futures prices are uncorrelated with interest rates.C. The volatility of the forward price is different from the volatility of the futures price.Answer: CC is correct. Known interest rates and the condition that futures prices are uncorrelated with forward prices will make forward and futures prices equivalent. The volatility of forward and futures prices has no relationship to any difference.6. Based on put-call parity for European options, a synthetic put is most likely equivalent to a:A. long call, short underlying asset, long bond.B. long call, long underlying asset, short bond.C. short call, long underlying asset, short bond.Answer: AA is correct. A Synthetic Put is equivalent to a Long Call + Short Underlying + Long Bond.7. Which statement best describes option price sensitivities? The value of a:A. call option increases as interest rates rise.B. put option increases as volatility decreases.C. put option decreases as interest rates decline.Answer: AA is correct. Call options increase in value as interest rates rise.8. Which of the following best describes the binomial option pricing formula?A. The expected payoff is discounted at the risk-free rate plus a risk premium.B. The spot price is compounded at the risk-free rate minus the volatility premium.C. The expected payoff based on risk-neutral probabilities is discounted at the risk-free rate. Answer: CC is correct. Risk-neutral probabilities are sued, and discounting is at the risk-free rate. There is no risk premium incorporated into option pricing because of the use of arbitrage.9. With respect to American calls, which of the following statements is most accurate?A. American calls should be exercised early if the underlying has reached its expected maximum price.B. American calls should be exercised early if the underlying has a lower expected return than therisk-free rate.C. American calls should be exercised early if there is a dividend or other cash payment on the-2-underlying.Answer: CC is correct. Cash payments on the underlying are the only reason to exercise American calls early. Interest rates, the expected return on the underlying, and any notion of a maximum price is irrelevant. But note that a dividend does not mean that early exercise should automatically be conducted. A dividend is only a necessary condition to justify early exercise for calls.10. An investor purchases ABC stock at $71 per share and executes a protective put strategy. The put option used in the strategy has a strike price of $66, expires in two months, and is purchased for $1.45. At expiration, the protective put strategy breaks even when the price of ABC is closest to:A. $64.55.B. $67.45.C. $72.45.Answer: CC is correct because to break even, the underlying stock must be at least as high as the amount expended up front to establish the position. To establish the protective put, the investor would have spent $71 + $1.45 = $72.45.-3-。

Derivatives_Chapter 2

Payoff
Payoff
Spot price
Spot price
8
Forward vs. Outright Purchase
Outright purchase: • Invest $1,000 in index and own the index. Forward: • Invest zero, sign the contract • Invest $1,020 at expiration and own the index. Same outcome: own the index at expiration.
1
Chapter Outline
Basic derivatives contracts
• Forward contracts • Call options • Put options
Types of positions
• Long / Short position
Graphical representation
In six months at contract expiration,
• If the spot price is higher than $1,000, the option will be exercised.
• If the spot price is lower than $1,000, the option buyer will walk away and do nothing. • Payoff for buyer = Max [0, spot price – strike price]
Futures contracts are the same as forwards in principle except for some institutional and pricing d High of the day The open price Expiration month

derivatives加拿大著名咨询公司在建设银行的讲座5资料

Sell the bond forward for sale in six months at a price of $100 per $100 of face value. If interest rates rise as predicted, purchase the bond in the market for $912,894.79 and deliver under the forward contract. Collect $1,000,000. Profit on the forward exactly offsets the loss on the bond portfolio. If rates fall instead of rise, you will incur a loss, as you will have to deliver the bond at a price below its market price.
Derivatives
10
Comparing Futures & Forwards
Forward
Standardized Exchange-traded Marked-to-market Profits & losses settled daily Margin required Existence of clearinghouse No No No No No No
Derivatives
Lecture #5
Derivatives
Definition: A derivative security is a security whose market value is determined by the value of another, underlying security Functions

2.Ceres官方教程-非线性最小二乘～Derivatives（导数）

2.Ceres官⽅教程-⾮线性最⼩⼆乘～Derivatives（导数）像⼤多数优化软件包⼀样，Ceres求解器依赖其能够在任意参数值下评估⽬标函数中每⼀项的值和导数。

正确⽽⾼效地做到这⼀点是取得好结果的关键。

Ceres提供了⼀系列解决⽅案，其中⼀个就是在Hello World中⽤到的Automatic Differentiation (⾃动微分算法)。

我们将探讨另外两种可能性，即解析法（Analytic）和数值法（Numeric ）求导。

1.Numeric Derivatives(数值法求导)在某些情况下，只定义⼀个仿函数是不⾏的，例如，当残差的求值涉及调⽤您⽆法控制的库函数时。

在这种情况下，可以使⽤数值微分法。

⽤户定义⼀个仿函数(functor)来计算残差值，并且构建⼀个数值微分代价函数(NumericDiffCostFunction)。

⽐如对于 f(x)=10−x 对应函数体如下：struct NumericDiffCostFunctor {bool operator()(const double* const x, double* residual) const {residual[0] = 10.0 - x[0];return true;}};/*对⽐Hello world中的Functor的定义可以发现，这次没⽤模板类。

*/然后继续添加ProblemCostFunction* cost_function =new NumericDiffCostFunction<NumericDiffCostFunctor, ceres::CENTRAL, 1, 1>(new NumericDiffCostFunctor);problem.AddResidualBlock(cost_function, nullptr, &x);对⽐在Hello World中使⽤automatic算法CostFunction* cost_function =new AutoDiffCostFunction<CostFunctor, 1, 1>(new CostFunctor);problem.AddResidualBlock(cost_function, nullptr, &x);⼀般来说，Ceres官⽅更加推荐⾃动微分算法，因为C++模板类使⾃动算法有更⾼的效率。

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Derivatives——Derivatives market and
instruments
1、衍生品简单定义
Y=f（x），利用未来价格的不确定性避险或者投机赚钱的方法
四大衍生品中，只有期权的权利义务是不对等的，所以要收取高额期权费
2、名义本金和市场容量
特别需要注意的是，名义本金是合同约定的，一个假设金额
市场容量是指合约标的都是市场中的实际金融资产，合约标的物的总市值不能超出市场
3、衍生品分类
根据合约分类，远期合约协议和不确定的追索权利
根据交易场所分类，交易场所交易和OTC 其中，交易场所为标准化合约、有清算所作为交易媒介、受政策监管；OTC正相反
4、衍生品市场优劣势
优势：价格发现；通过对冲和投机进行风险控制；交易成本低
劣势：杠杆风险太大；产品复杂；不确定性因素太多类似赌博
5、套利
同一资产在市场上有两种价格，就会形成套利
套利包括两种形式：一种是迅速实现盈利并且无负债，另一种是收益率大于无风险收益率
一价定律：有着同样未来现金流的两种资产，价格理应相同
如果收益为固定payoff，一定属于无风险收益
套利是消除定价错误，套利者是价格发现的主要功臣
6、总结
OTC交易量大于场内交易量
金融资产交易量大于大宗商品交易量
7、远期合约
分类：商品远期合约、金融远期合约
目的：套利保值合约、投机获利
每一方都有违约风险，属于零和游戏8、远期合约的使用者
END USER风险回避
Dealer保持敞口，挣得买卖差价，提高市
场流动性
9、远期合约结清
到期结清：实物+现金结清、现金差价结清
提前结清：制定一个期限与剩余时间相同
的反向远期合约，锁定G/L；如果是与第
三方签约的话，有一份合同有违约风险，
如果与原合作方签约，没有违约风险
10、权益类远期合约
标的是股票、资产组合和股指
可以选用实物交割（股票）或者现金交割，
股指必须使用现金交割
一般来讲，股利分红不参加权益合约收益
计算，因为股利发放的不确定性远小于价
格波动
如果选用总收益的绝对值作为标的的话，
就不存在上述情况了
11、债券类远期合约
与权益类远期合约不同的是，债券有到期
时间，所以成熟期要在到期日之前
T-bill报价方法：100倍的年华贴现率
Coupon债券的报价方法：预期收益率报
价
12、远期利率合约
LIBOR是基于大额欧洲美元定期存款的同
业流动拆借利率，标的是美元单利利率，
按360天年化
FRA就是几月LIBOR的远期变化合约
FRA3*6表示：3月后购买1份90天的
libor
一般libor的天数为30天60天90天和
120天，45天的叫off-the-run
与T-bill远期的区别：一种为净增率，一
种为贴现率
13、远期利率合约的交割
现金交割，实际上并没有借入libor贷款
Libor上升，买方获利
计算方式：本金形成的利息差进行贴现，
本金*期间利率差/（1+期间实际利率）360
14、远期汇率合约
现金交割或者事物交割
本金*汇率差
15、期货合约
期货合约可以现金交割或者实物交割
在即期期货合约是没有价值的
16、标准化期货合约
标准化期货合约包括商品的数量质量，以
及交割的时间和方式
清算中心作为中间媒介，杜绝违约风险，
允许交易方在期货合约到期日执行反向头
寸
17、期货合约风险控制方法
存入保证金
每日价格有上下线：涨跌停限制
逐日盯市制度:MM门槛低，此外给出一定
的时间缓冲，来补充保证金
18、margin的比较
股票margin回到MM，相当于首付
期货margin回到IM，相当月保证金
19、期货价格
期货价格是公开竞价形成的期货合约标的
物价格，有供需决定
交割价格是休市后的平均价格，用来确定
保证金额度
期货价格和现实价格之间的差额叫做基差
基差在合约到期的时候逐步收敛
20、期货交割
到期日交割：合同约定的实物交割和现金
支付
提前交割：抛售或者抵消交易；场外交易
在清算所备案
21、卖方决定权
期货的交割日和最后交易日之间跨度较长，
在此交割期间，卖方有权利决定何时何地
何方式进行交割
22、利率期货——90天国库券期货
现金交割
实际期货价格是100—100倍的90天利率
每100万美元的期货合同，期货价格每上
升1个bp代表25美元净增
23、利率期货——90天欧洲美元期货
现金交割
与国库券期货不同的是，期货价格非折现率，而是净增率
买期货类似于贷款，卖方类似于借款
每100万美元的期货合同，期货价格每上升1个bp代表25美元净增
24、国债期货
实物交割
标的物是coupon6%、15年的虚拟债券，但实际交割时用的是不同剩余期限，不同利率的实物票据，因此转换因可用来进行修正，但不可避免仍然部分交割损失
无论如何，卖方选择最便宜交割债券法
报价方式98 16/32
25、股指期货
现金交割
标的物是标普指数，乘数是250
26、汇率期货
现金交割+实物交割
用每单位多少美元进行计量
28、各代表性衍生品对比
29、期权
美式期权优于欧式期权，因为美式期权可以提前执行
30、Inthemoney：s>x Atthemoney：s=x Outthemoney：s<x
31、买方期权的内在价值：max（0，s-x）卖方期权的内在价值：max（0，x-s）
期权价格=内在价值+时间价值
32、利率期权有cap有floor
利率期权和FRA的区别相同点：没有标的实物，现金交割
不同点：利率期权可以提前交割；利率期
权选择在贷款结束后判定；贷款获利需要
折现
33、
买方看涨+卖方看跌=FRA
买方的cap+卖方put=swap
34、
35、认沽认购等价关系
指买权和卖权之间的必然联系，如果联系
不成立，则存在套利机会
C+k’=s+p
C+k’受托买权
S+p保护性卖权
如果标的资产在期权期限内有现金流，则
要在s中减去
因此，美式期权无论在何种情况下都比欧
式期权灵活，如果提前执行，价格都大于
欧式
36、互换
以机构互换为主
违约风险大
量巨大
不受监管
37、结清方式
协定终止
反向交易对冲，比如swaption
出售给第三方
38、利率互换
利息netting
Net PMT=本金*（固定利率-浮动利率）*
期限/360
39、汇率互换
期初换本金
期中不netting
期末换本金
40、权益互换
贷款和发股之间的互换
如果股指下跌，股指现对应放要双重付息
41、有担保买权s-c
最大x-（s-c）最小s-c
42、有担保卖权s+p
最大无限最小（s+p）
-x。