Hull经典衍生品教科书第9版官方第25章精品PPT课件
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Hull经典衍生品教科书第9版官方PPT,第29章
Both the bond price and the strike price should be cash prices not quoted prices
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 5
Forward Bond and Forward Yield
Approximate duration relation between forward bond price, FB, and forward bond yield, yF
FB FB y F D y F or Dy F FB FB yF
where D is the (modified) duration of the forward bond at option maturity
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
Chapter 29 Interest Rate Derivatives: The Standard Market Models
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1ቤተ መጻሕፍቲ ባይዱ
The Complications in Valuing Interest Rate Derivatives (page 673)
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
Hull经典衍生品教科书第官方, ppt课件
Chapter 6 Interest Rate Futures
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
1
Day Count Convention
• Defines:
• the period of time to which the interest rate applies
• day count is Actual/Actual in period? • day count is 30/360?
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
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Treቤተ መጻሕፍቲ ባይዱsury Bill Prices in the US
John C. Hull 2014
2
Day Count Conventions in the U.S. (Page 132)
Treasury Bonds: Actual/Actual (in period)
Corporate Bonds: 30/360
Money Market Instruments:
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4
Examples continued
• T-Bill: 8% Actual/360:
• 8% is earned in 360 days. Accrual calculated by dividing the actual number of days in the period by 360. How much interest is earned between March 1 and April 1?
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
1
Day Count Convention
• Defines:
• the period of time to which the interest rate applies
• day count is Actual/Actual in period? • day count is 30/360?
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
6
Treቤተ መጻሕፍቲ ባይዱsury Bill Prices in the US
John C. Hull 2014
2
Day Count Conventions in the U.S. (Page 132)
Treasury Bonds: Actual/Actual (in period)
Corporate Bonds: 30/360
Money Market Instruments:
John C. Hull 2014
4
Examples continued
• T-Bill: 8% Actual/360:
• 8% is earned in 360 days. Accrual calculated by dividing the actual number of days in the period by 360. How much interest is earned between March 1 and April 1?
Hull经典衍生品教科书第9版官方PPT,第30章
Chapter 30 Convexity, Timing, and Timing, and Quanto Adjustments
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1
Forward Yields and Forward Prices
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
2
Relationship Between Bond Yields and Prices (Figure 30.1, page 694)
We define the forward yield on a bond as the yield calculated from the forward bond price There is a non-linear relation between bond yields and bond prices It follows that when the forward bond price equals the expected future bond price, the forward yield does not necessarily equal the expected future yield
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
7
Timing Adjustments (Equation 30.4, page
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
1
Forward Yields and Forward Prices
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
2
Relationship Between Bond Yields and Prices (Figure 30.1, page 694)
We define the forward yield on a bond as the yield calculated from the forward bond price There is a non-linear relation between bond yields and bond prices It follows that when the forward bond price equals the expected future bond price, the forward yield does not necessarily equal the expected future yield
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
7
Timing Adjustments (Equation 30.4, page
Hull经典衍生品教科书第9版官方第19章精品PPT课件
Buy 100,000 shares today
What are the risks associated with these strategies?
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
5
Delta (See Figure 19.2, page 403)
Delta (D) is the rate of change of the option price with respect to the underlying
short 1000 options buy 600 shares
Gain/loss on the option position is offset by loss/gain on stock position Delta changes as stock price changes and time passes Hedge position must therefore be rebalanced
Chapter 19 The Greek Letters
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
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Example
A bank has sold for $300,000 a European call option on 100,000 shares of a non-dividend paying stock S0 = 49, K = 50, r = 5%, s = 20%, T = 20 weeks, m = 13% The Black-Scholes-Merton value of the option is $240,000 How does the bank hedge its risk to lock in a $60,000 profit?
What are the risks associated with these strategies?
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
5
Delta (See Figure 19.2, page 403)
Delta (D) is the rate of change of the option price with respect to the underlying
short 1000 options buy 600 shares
Gain/loss on the option position is offset by loss/gain on stock position Delta changes as stock price changes and time passes Hedge position must therefore be rebalanced
Chapter 19 The Greek Letters
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
1
Example
A bank has sold for $300,000 a European call option on 100,000 shares of a non-dividend paying stock S0 = 49, K = 50, r = 5%, s = 20%, T = 20 weeks, m = 13% The Black-Scholes-Merton value of the option is $240,000 How does the bank hedge its risk to lock in a $60,000 profit?
Hull经典衍生品教科书第9版官方PPT,第3章
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 14
Example
S&P 500 futures price is 1,000 Value of Portfolio is $5 million Beta of portfolio is 1.5 What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
4
Basis Risk
Basis is usually defined as the spot price minus the futures price Basis risk arises because of the uncertainty about the basis when the hedge is closed out
Optimal hedge ratio is
ˆS s ˆ ˆ hr ˆF s
where varis ˆF s
Correlation between percentage daily changes for spot and futures
Optimal number of contracts if adjustment for daily settlement
h *Q A QF
ˆ hV A VF
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
Example
S&P 500 futures price is 1,000 Value of Portfolio is $5 million Beta of portfolio is 1.5 What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
4
Basis Risk
Basis is usually defined as the spot price minus the futures price Basis risk arises because of the uncertainty about the basis when the hedge is closed out
Optimal hedge ratio is
ˆS s ˆ ˆ hr ˆF s
where varis ˆF s
Correlation between percentage daily changes for spot and futures
Optimal number of contracts if adjustment for daily settlement
h *Q A QF
ˆ hV A VF
Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014
期权、期货及其他衍生产品第9版-赫尔】Ch(9)幻灯片PPT
Options, Futures, and Other Derivatives, 9th Edition, Copyright ©
John C. Hull 2014
4
Historical Simulation to Calculate the One-Day VaR
Create a database of the daily movements in all market variables. The first simulation trial assumes that the percentage changes in all market variables are as on the first day The second simulation trial assumes that the percentage changes in all market variables are as on the second day and so on
Let vi be the value of a variable on day i
There are 500 simulation trials
The ith trial assumes that the value of the market
variable tomorrow is
v500
vi vi1
期权、期货及其他衍生产品第9 版-赫尔】Ch(9)幻灯片PPT
本PPT课件仅供大家学习使用 请学习完及时删除处理 谢谢！
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
[考研专业课课件] 赫尔《期货、期权及其他衍生产品》 课件 第25章 特种期权
![[考研专业课课件] 赫尔《期货、期权及其他衍生产品》 课件 第25章 特种期权](https://img.taocdn.com/s3/m/3d5b566f1711cc7931b71666.png)
c——0时刻的期限为T2-T1的平值期权的价格
欧式平价期权的价格与资产价格成比例。因
此，在T1时刻，远期开始期权价格为cS1/S0。采 用风险中性定价，0时刻的远期开始期权价格为
e
rT1
S1 ˆ E c S0
。
ˆ ——风险中性世界里的期望值。 E
( r q )T1 ˆ E S S e 因为c和S0为已知， 。 1 0
其中
（25-1）
d1
ln( S0 / K 2 ) (r q 2 / 2) / T
T
d 2 d1 T
这个公式所给的价格比通常的布莱克-斯科尔 斯-默顿公式所给执行价格为K2的普通看涨期权价
rT 格高出 ( K2 K1 )e N (d2 ) 。当期权被行使时，
qT1 ce 所以，远期开始欧式价格为 。
对于无股息股票，q=0，一个远期开始期权的
价格与一个一般的具有相等期限的平值期权价格 相等。
25．5 棘轮期权
棘轮期权[cliquet option或ratchet option，有时也称做执行价格调整期权（strike reset）]：一系列由某种方式确定执行价格的看 涨或看跌期权。假设调整日期为时刻τ，2τ， …，（n-1）τ，棘轮期权期限为nτ。
一种简单的棘轮期权：第一个期权的有效时
间是时间0与τ之间，执行价格为K（也许是资产 的初始价格）；第二个期权在时刻2τ提供收益， 其执行价格为资产在τ时刻的价格；第三个期权 在时刻3τ提供收益，其执行价格为资产在2τ时 刻的价格等。这是个普通期权加上n-1个远期开始 期权，而这些远期开始。
25．6 复合期权
25．3 缺口期权
缺口期权：一种欧式期权，当ST≥K2时，其收 益为当ST-K1。 缺口期权与具有执行价格K2的普通看涨期权 之间的区别： 当ST≥K2时，收益增加了K2-K1 当K2>K1时，这个数量为正，K1>K2时为负。
Hull衍生品教科书第版官方PPT
16
Control Variate Technique
• Value American option, fA • Value European option using same tree,
fE • Value European option using Black-
Scholes –Merton, fBS • Option price =fA+(fBS – fE)
a e0.11/12 1.0084 u e0.4 1/12 1.1224 d 1 0.8909
u p 1.0084 0.8909 0.5073
1.1224 0.8909
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
d es Dt
p ad ud
a e(r q) Dt
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
6
The Complete Tree
(Figure 21.2, page 453)
u e(r qs2 / 2)Dt s Dt d e(r qs2 / 2)Dt s Dt
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
18
Trinomial Tree (Page 467)
As with Black-Scholes-Merton:
• For options on stock indices, q equals the dividend yield on the index
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for the first time and S0 < H
f QS H a (a > 0) satisfies the boundary conditions.
It satisfies the differential equation
f t
(r q)S
f S
1 2S 2 2
2 f S 2
rf
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
3
Perpetual American Options
Consider first a derivative that pays off Q when S = H
Gap call S0 N (d1) K1N (d2 ) Gap put K1erT N (d2 ) S0eqT N (d1)
d1 ln(S0
K2 ) (r q 2 T
2 )Td2 d1 TOptions, Futures, and Other Derivatives, 9th Edition,
swaps
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
2
Packages (page 598-599)
Portfolios of standard options Examples from Chapter 11: bull spreads, bear spreads, straddles, etc Often structured to have zero cost One popular package is a range forward contract (see Chapter 17)
Chapter 26 Exotic Options
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
1
Types of Exotics
Packages
Barrier options
Perpetual American calls and puts Nonstandard American options Gap options Forward start options Cliquet options Compound options
when
(r q)a 1 a(a 1)2 r 2
This has solutions a1>0 and a2<0
The value of the derivative is therefore
QS H a1
Options, Futures, and Other Derivatives, 9th Edition,
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
6
Gap Options
Gap call pays ST − K1 when ST > K2 Gap put pays off K1 − ST when ST < K2 Can be valued with a small modification to BSM
Binary options Lookback options Shout options Asian options Options to exchange one asset for another Options involving several assets
Chooser options
Volatility and Variance
S K
a2
Options, Futures, and Other Derivatives, 9th Edition,
Copyright © John C. Hull 2014
5
Non-Standard American Options
(page 600)
Exercisable only on specific dates (Bermudans) Early exercise allowed during only part of life (initial “lock out” period) Strike price changes over the life (warrants, convertibles)
This is maximized when H K a1 (a1 1)
The value of the perpetual call is therefore
K a1 1
a1 1 a1
S K
a1
The value of a perpetual put is similarly
K a2 1
a2 1 a2
Copyright © John C. Hull 2014
7
Forward Start Options (page 602)
Option starts at a future time, T1 Implicit in employee stock option plans Often structured so that strike price equals asset price at time T1 Value is then eqT1 times the value of similar option starting today
Copyright © John C. Hull 2014
4
Perpetual American Options continued
Consider next a perpetual American call option with strike price K
If it is exercised when S=H the value is (H K )S H a1