期货期权及其衍生品配套课件Ch01
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期货期权及其衍生品配套(全34章)Ch01PPT课件
详细描述
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
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
期货期权及其衍生品配套课件(全34章)Ch09.ppt
Both are worth max(ST , K ) at the maturity of the options They must therefore be worth the same today. This means that
c + Ke -rT = p + S0
Options, Futures, and Other Derivatives, 7th International
C : American Call option price
P : American Put option price
ST :Stock price at option maturity
D : Present value of dividends during option’s life
r : Risk-free rate for maturity T with cont comp
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
7
Lower Bound for European Put Prices; No Dividends
(Equation 9.2, page 208)
p= 1 ?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
10
Early Exercise
4
Calls: An Arbitrage Opportunity?
c + Ke -rT = p + S0
Options, Futures, and Other Derivatives, 7th International
C : American Call option price
P : American Put option price
ST :Stock price at option maturity
D : Present value of dividends during option’s life
r : Risk-free rate for maturity T with cont comp
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
7
Lower Bound for European Put Prices; No Dividends
(Equation 9.2, page 208)
p= 1 ?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
10
Early Exercise
4
Calls: An Arbitrage Opportunity?
期货期权及其衍生品配套课件(全34章)Ch09.ppt
Variable c
p
CP
S0 K
–+
– +
–+
– +
T
? ? ++
r D
–++
–+ +
–++
–+ +
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
3
American vs European Options
Consider the following 2 portfolios: Portfolio A: European call on a stock + PV of the strike price in cash Portfolio C: European put on the stock + the stock
Edition, Copyright © John C. Hull 2008
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?
Properties of Stock Options
Chapter 9
Options, Futures, and Other Derivatives, 7th International Edition,
Copyright © John C. Hull 2008
期货期权及其衍生品配套课件(全34章ch22汇编
A company with an initial credit rating of Baa has a probability of 0.181% of defaulting by the end of the first year, 0.506% by the end of the second year, and so on
The corresponding Moody’s ratings are Aaa, Aa, A, Baa, Ba, B,Caa, Ca, and C
Bonds with ratings of BBB (or Baa) and above are considered to be “investment grade”
What are the default intensities and
unconditional default probabilities for a Caa
rate company in the third year?
Options, Futures, and Other Derivatives, 7th International
Aaa Aa A Baa Ba B Caa-C
1
23
0.000 0.000 0.000
0.008 0.019 0.042
0.021 0.095 0.220
0.181 0.506 0.930
1.205 3.219 5.568
5.236 11.296 17.043
19.476 30.494 39.717
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
The corresponding Moody’s ratings are Aaa, Aa, A, Baa, Ba, B,Caa, Ca, and C
Bonds with ratings of BBB (or Baa) and above are considered to be “investment grade”
What are the default intensities and
unconditional default probabilities for a Caa
rate company in the third year?
Options, Futures, and Other Derivatives, 7th International
Aaa Aa A Baa Ba B Caa-C
1
23
0.000 0.000 0.000
0.008 0.019 0.042
0.021 0.095 0.220
0.181 0.506 0.930
1.205 3.219 5.568
5.236 11.296 17.043
19.476 30.494 39.717
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
期货期权及其衍生品配套课件(全34章)Ch21.ppt
9
Example (Example 21.2, page 473)
Suppose
s
2 n
0.000002 0.13un21
0.86s
2 n1
The long-run variance rate is 0.0002 so that the long-run volatility per day is 1.4%
s2n
VL
un21
b
s2 n1
Since weights must sum to 1 b 1
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
8
GARCH (1,1) continued
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
3
Weighting Scheme
Instead of assigning equal weights to the observations we can set
In an ARCH(m) model we also assign some
weight to the long-run variani1 i ni
where
m
i 1 i 1
Options, Futures, and Other Derivatives, 7th International
s
2 n
u m
期货期权及其衍生品配套课件(全34章)Ch(25)
Interest Rate Futures
Chapter 6
Options, Futures, and Other Derivatives, 7th International Edition,
2021/8/5
Copyright © John C. Hull 2008
1
Day Count Conventions in the U.S. (Page 129)
Options, Futures, and Other Derivatives, 7th International
2021/8/5
Edition, Copyright © John C. Hull 2008
4
Example
Most recent settlement price = 90.00 Conversion factor of bond delivered = 1.3800 Accrued interest on bond =3.00 Price received for bond is 1.3800×90.00+3.00 = $127.20 per $100 of principal
Options, Futures, and Other Derivatives, 7th International
2021/8/5Edition Copyright © John C. Hull 2008
13
Forward Rates and Eurodollar Futures (Page 139-142)
Options, Futures, and Other Derivatives, 7th International
2021/8/5
Edition, Copyright © John C. Hull 2008
Chapter 6
Options, Futures, and Other Derivatives, 7th International Edition,
2021/8/5
Copyright © John C. Hull 2008
1
Day Count Conventions in the U.S. (Page 129)
Options, Futures, and Other Derivatives, 7th International
2021/8/5
Edition, Copyright © John C. Hull 2008
4
Example
Most recent settlement price = 90.00 Conversion factor of bond delivered = 1.3800 Accrued interest on bond =3.00 Price received for bond is 1.3800×90.00+3.00 = $127.20 per $100 of principal
Options, Futures, and Other Derivatives, 7th International
2021/8/5Edition Copyright © John C. Hull 2008
13
Forward Rates and Eurodollar Futures (Page 139-142)
Options, Futures, and Other Derivatives, 7th International
2021/8/5
Edition, Copyright © John C. Hull 2008
期货期权及其衍生品配套课件(全34章)Ch11.ppt
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
3
Setting Up a Riskless Portfolio
Consider the Portfolio: long D shares short 1 call option
4
Valuing the Portfolio
(Risk-Free Rate is 12%)
The riskless portfolio is: long 0.25 shares short 1 call option
The value of the portfolio in 3 months is 22 ´ 0.25 – 1 = 4.50
Stock price = $20
Stock Price = $22 Stock Price = $18
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
2
A Call Option (Figure 11.1, page 238)
Edition, Copyright © John C. Hull 2008
22D – 1
18D
Portfolio is riskless when 22D – 1 = 18D or
D = 0.25
Options, Futures, and Other Derivatives, 7th International
期货期权和其他衍生品英文课件 (1)
sample payoffs 4.Calculate mean payoff 5.Discount mean payoff at risk free rate to get an
estimate of the value of the option
Sampling Stock Price Movements
(continued)
When Dt is small a solution to the equations is
u es Dt d es Dt p ad
ud a e(rq) Dt
The Complete Tree
(Figure 21.2, page 452)
S0u4
S0u3
S0u2
S0u2
S0u
S0u
S0
S0
S0
S0d
S0d
S0d2
S0d3
S0d2
S0d4
Backwards Induction
We know the value of the option at the final nodes We work back through the tree using risk-neutral valuation to calculate the value of the option at each node, testing for early exercise when appropriate
per 1% change in volatility
Trees for Options on Indices, Currencies and Futures Contracts
As with Black-Scholes-Merton:
estimate of the value of the option
Sampling Stock Price Movements
(continued)
When Dt is small a solution to the equations is
u es Dt d es Dt p ad
ud a e(rq) Dt
The Complete Tree
(Figure 21.2, page 452)
S0u4
S0u3
S0u2
S0u2
S0u
S0u
S0
S0
S0
S0d
S0d
S0d2
S0d3
S0d2
S0d4
Backwards Induction
We know the value of the option at the final nodes We work back through the tree using risk-neutral valuation to calculate the value of the option at each node, testing for early exercise when appropriate
per 1% change in volatility
Trees for Options on Indices, Currencies and Futures Contracts
As with Black-Scholes-Merton:
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Introduction
Chapter 1
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
1
Size of OTC and Exchange-Traded Markets
This obligates the corporation to pay $2,048,900 for £1 million on January 20, 2019
What are the possible outcomes?
Options, Futures, and Other Derivatives, 7th International
17
Options
A call option is an option to buy a certain asset by a certain date for a certain price (the strike price) A put option is an option to sell a certain asset by a certain date for a certain price (the strike price)
16
2. Oil: Another Arbitrage
Opportunity?
Suppose that:
- The spot price of oil is US$95 - The quoted 1-year futures price of oil is
US$80
- The 1-year US$ interest rate is 5% per
Opportunity?
Suppose that:
- The spot price of gold is US$900 - The 1-year forward price of gold is US$900 - The 1-year US$ interest rate is 5% per
annum
(Figure 1.1, Page 3)
Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
2
Ways Derivatives are Used
To hedge risks
To speculate (take a view on the future direction of the market)
Sell £62,500 2.0500 US$/£ in March (CME)
Sell 1,000 bbl. of oil US$120/bbl. in April (NYMEX)
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
The party that has agreed to sell has what is termed a short position
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
15
1. Oil: An Arbitrage Opportunity?
Suppose that:
- The spot price of oil is US$95 - The quoted 1-year futures price of oil is
US$125
- The 1-year US$ interest rate is 5% per
To lock in an arbitrage profit
To change the nature of a liability
To change the nature of an investment without incurring the costs of selling one portfolio and buying another
Edition, Copyright © John C. Hull 2019
9
Futures Contracts (page 6)
Agreement to buy or sell an asset for a certain price at a certain time Similar to forward contract Whereas a forward contract is traded OTC, a futures contract is traded on an exchange
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
10
Exchanges Trading Futures
Chicago Board of Trade Chicago Mercantile Exchange LIFFE (London) Eurex (Europe) BM&F (Sao Paulo, Brazil) TIFFE (Tokyo) and many more (see list at end of book)
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
5
Terminology
The party that has agreed to buy has what is termed a long position
Edition, Copyright © John C. Hull 2019
8
Profit from a Short Forward Position
Profit
Price of Underlying
K
at Maturity, ST
Options, Futures, and Other Derivatives, 7th International
annum
- The storage costs of oil are 2% per
annum
Is there an arbitrage opportunity?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
annum
Is there an arbitrage opFra bibliotekortunity?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
13
2. Gold: Another Arbitrage
If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then
F = S (1+r )T
where r is the 1-year (domestic currency) risk-free rate of interest.
Edition, Copyright © John C. Hull 2019
7
Profit from a Long Forward Position
Profit
Price of Underlying
K
at Maturity, ST
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
4
Forward Price
The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) The forward price may be different for contracts of different maturities
In our examples, S = 900, T = 1, and r =0.05 so that
F = 900(1+0.05) = 945
Options, Futures, and Other Derivatives, 7th International
Chapter 1
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
1
Size of OTC and Exchange-Traded Markets
This obligates the corporation to pay $2,048,900 for £1 million on January 20, 2019
What are the possible outcomes?
Options, Futures, and Other Derivatives, 7th International
17
Options
A call option is an option to buy a certain asset by a certain date for a certain price (the strike price) A put option is an option to sell a certain asset by a certain date for a certain price (the strike price)
16
2. Oil: Another Arbitrage
Opportunity?
Suppose that:
- The spot price of oil is US$95 - The quoted 1-year futures price of oil is
US$80
- The 1-year US$ interest rate is 5% per
Opportunity?
Suppose that:
- The spot price of gold is US$900 - The 1-year forward price of gold is US$900 - The 1-year US$ interest rate is 5% per
annum
(Figure 1.1, Page 3)
Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
2
Ways Derivatives are Used
To hedge risks
To speculate (take a view on the future direction of the market)
Sell £62,500 2.0500 US$/£ in March (CME)
Sell 1,000 bbl. of oil US$120/bbl. in April (NYMEX)
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
The party that has agreed to sell has what is termed a short position
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
15
1. Oil: An Arbitrage Opportunity?
Suppose that:
- The spot price of oil is US$95 - The quoted 1-year futures price of oil is
US$125
- The 1-year US$ interest rate is 5% per
To lock in an arbitrage profit
To change the nature of a liability
To change the nature of an investment without incurring the costs of selling one portfolio and buying another
Edition, Copyright © John C. Hull 2019
9
Futures Contracts (page 6)
Agreement to buy or sell an asset for a certain price at a certain time Similar to forward contract Whereas a forward contract is traded OTC, a futures contract is traded on an exchange
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
10
Exchanges Trading Futures
Chicago Board of Trade Chicago Mercantile Exchange LIFFE (London) Eurex (Europe) BM&F (Sao Paulo, Brazil) TIFFE (Tokyo) and many more (see list at end of book)
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
5
Terminology
The party that has agreed to buy has what is termed a long position
Edition, Copyright © John C. Hull 2019
8
Profit from a Short Forward Position
Profit
Price of Underlying
K
at Maturity, ST
Options, Futures, and Other Derivatives, 7th International
annum
- The storage costs of oil are 2% per
annum
Is there an arbitrage opportunity?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
annum
Is there an arbitrage opFra bibliotekortunity?
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
13
2. Gold: Another Arbitrage
If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then
F = S (1+r )T
where r is the 1-year (domestic currency) risk-free rate of interest.
Edition, Copyright © John C. Hull 2019
7
Profit from a Long Forward Position
Profit
Price of Underlying
K
at Maturity, ST
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
4
Forward Price
The forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero) The forward price may be different for contracts of different maturities
In our examples, S = 900, T = 1, and r =0.05 so that
F = 900(1+0.05) = 945
Options, Futures, and Other Derivatives, 7th International