期货期权及其衍生品配套课件Ch27

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十一讲期货期权与其他衍生工具市场PPT学习教案

仓(Open) 平仓：买入后卖出, 或卖出后买入结算原先所做的
新单单号：系统为委托单或成交单分配的唯一标识
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期货与期权（12）
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期货与期权（13）
期货交割价格的合成：机会成本定价或套利定价。 100盎司的黄金，即期价格：每盎司$400。一位买家想在三个月后买，价格是多少？ 100盎司黄金三个月的储藏和保险的金额：$5+$10=$15；放弃的三个月的利息：40000@2%=$800; $40000+$800+$15=$40815 每盎司黄金$408.15。在即期价格和期货价格间的价差反映了利息、储存和
机构、个人，只要存在与利率、汇率和价格波动相关的风险暴露，都可能是期货市场的潜在保值者；同时投机者也不断增多。
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期货与期权（3）
期货合约的买方：同意按既定价格在未来购买某种基础商品的一方，在交易中被称为多头（long position）或称为做多（long futures）。
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期货与期权（11）
买价：某商品当前最高申报买入价卖价：某商品当前最低申报卖出价涨跌幅：某商品当日收盘价与昨日结算价之间的价差涨停板额：某商品当日可输入的最高限价(等于昨结
算价+最大变动幅度) 跌停板额：某商品当日可输入的最低限价(等于昨结
算价—最大变幅) 空盘量：当前某商品未平仓合约总量开仓：只做了买入卖出双向操作中的一项, 即开新
头寸进行清算。平仓：轧平头寸。为了达到平仓的目的，期货合约的交易者必须在合约到期
前对同样的合约做一笔相反的交易以冲销手中的头寸。合约的买方需要卖出同等数量的相同的期货合约，而卖方则要买入一笔同等数量的相同的合约。实物交割：即期货合约的买方按既定价格买入某种基础工具，卖方要按既定的价格卖出基础工具。

期权期货及其他衍生品ppt课件

8
案例 1 ：美式看跌期权的二叉树定价
假设标的资产为不付红利股票，其当前市场价为 50 元,波动率为每年 40% ，无风险连续复利年利率为 10% ，该股票 5 个月期的美式看跌期权协议价格为 50 元，求该期权的价值。
9
案例 1 ：美式看跌期权的二叉树定价 (cont.)
为了构造二叉树，我们把期权有效期分为五段，每段一个月(等于 0.0833 年)。可以算出
10
案例 1 ：美式看跌期权的二叉树定价 (cont.)
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二Байду номын сангаас树定价的一般过程：以美式看跌期权为例
把期权有效期划分为 N 个长度为 ∆t 的小区间和分别为节点 (i, j) 处的标的资
产价格与期权价值：
其中j=0,1,2,… ..N
当时间区间划分趋于无穷大，可以求出美式看跌期权的准确价值。一般将时间区间分成 30 步就可得到较为理想的结果。
20
模拟运算次数的确定
如果对估计值要求 95% 的置信度，则期权价值应满足
其中， M 为进行运算的次数， p 为均值， ω 为标准差。
21
主要优点和主要缺点
主要优点：
◦ 应用简单，无需深刻理解定价模型 ◦ 适用情形广泛
欧式衍生产品回报路径依赖回报取决于多个标的资产
主要缺点：
◦ 难以处理提前执行的情形 ◦ 为了达到一定的精确度，一般需要大量的模拟运
24
14
蒙特卡罗模拟
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随机路径
在风险中性世界中，为了模拟路径
我们把期权的有效期分为 N 个长度为 ∆t 的时间段，则上式的近似方程为：
或
16
随机路径 (cont.)

25_期权期货及其他衍生品第一章课件

15.00
Oct Call
4.650
Jan Call
4.950
Apr Call
5.150
Oct Put
0.025
Jan Put

17.50 2.300 2.775 3.150 0.125 0.475 0.725
20.00 0.575 1.175 1.650 0.875 1.375 1.700
5
远期价格(forward price)
• 远期价格(forward price)定义为使得远期合约价值为零的交割价格。
为什么是合约价值为零情况下的交割价格？如果市场出现合约价值不是零的交割时，会发
生什么呢？
6
1. 黄金市场: 是否有套利的机会？
假定: 黄金的现货价格是900美元每盎司一年期黄金远期价格是1020美元每盎司一年期美元利率是5%
17
期权 vs 期货/远期
• 期货/远期合约赋予持有者以一定的价格购买或卖出某种资产
• 期权合约给予持有者以一定价格购买或卖出某种资产的权利
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交易者的类型
•对冲者(hedgers) • 投机者(speculators) • 套利者(arbitrageurs)
衍生品交易过程中的巨额亏损有时是因为有些对冲交易者和套利交易者转变为投机交易者 (比如英国巴林银行的破产)
• 与远期合约不同的是：1)场内交易；2)合约标准化；3)交割日期。
• 期货价格取决供需双方
11
全球主要期货交易所
• Chicago Board of Trade • Chicago Mercantile Exchange • LIFFE (London) • Eurex (Europe) • BM&F (Sao Paulo, Brazil) • TIFFE (Tokyo) • 其它的列在课本后面

期货期权及其衍生品配套课件(全34章)Ch27.ppt

d ?1 ƒ1
μ1
dt
σ1
dz
d?2 ƒ2
μ2
dt σ2
dz
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
2
Forming a Riskless Portfolio
This gives: μ1σ2 μ2σ1 r σ2 r σ1
or μ1 r μ2 r
σ1
σ2
This shows that (m – r )/s is the same for all derivatives dependent on the same underlying variable,
We refer to (m – r )/s as the market price of risk for and denote it by l
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2008
4
Extension of the Analysis to Several Underlying Variables
(Equations 27.12 and 27.13, page 619)
If f dependson severalunderlyingvariables
with
d?
ƒ
μ
dt
n i 1
7
The Equivalent Martingale Measure Result (Page 620-621)

期货期权和其他衍生品英文课件 (2)

Girsanov’s Theorem
Volthe real world and the risk-neutral world We can therefore measure volatility in the real world and use it to build a tree for the an asset in the risk-neutral world
Option is American (Figure 13.8, page 285)
72 0
60
50 5.0894
The American feature increases the value at node C from 9.4636 to 12.0000.
1.4147
48
4
40
C
12.0
32
20
Assets Other than Non-Dividend Paying Stocks
For options on stock indices, currencies and futures the basic procedure for constructing the tree is the same except for the calculation of p
B
20
1.7433
19.8
0.9497 A
0.0
18
0.0
16.2
0.0
Value at node B
= e–0.04×0.25(0.5503×3.2 + 0.4497×0) = 1.7433
Value at node A
= e–0.04×0.25(0.5503×1.7433 + 0.4497×0) = 0.9497

期权,期货及其衍生品第27弹共24页文档

= ( 1 2 ƒ1 ƒ 2 2 1 ƒ1 ƒ 2 ) t
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2012
3
Market Price of Risk (Page 632)
Consider a variable (not necessaril y the price
of a traded security) that follows the process
d m dt s dz Imagine two derivative s dependent on
Sincetheportfoliosriskles:s=rt
Thisgives: 12 21 r 2 r 1
or 1 r 2 r
σ1
σ2
This shows that ( – r )/ is the same for all
derivatives dependent on the same underlying
s(t)=EA[s(T)]
Options, Futures, and Other Derivatives, 8th Edition,
Copyright © John C. Hull 2012
17
Extension to Several Independent Factors
(Page 640)
In the traditiona l risk - neutral world
Options, Futures, and Other Derivatives, 8th Edition,

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Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
11
Money Market Account continued
T
Since
g0
= 1 and
gT
=
e
rdt
Edition, Copyright © John C. Hull 2019
12
Zero-Coupon Bond Maturing at time T as Numeraire
The equation
f0 g0
E g
fT gT
becomes
f0 P (0,T )ET [ fT ]
w here P ( 0,T ) is the zero - coupon bond price
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
4
Extension of the Analysis to Several Underlying Variables
Martingales and Measures
Chapter 27
Options, Futures, and Other Derivatives, 7th International Edition,
Copyright © John C. Hull 2019
1
Derivatives Dependent on a Single Underlying Variable
Options, Futures, and Other Derivatives, 7th International
ቤተ መጻሕፍቲ ባይዱ
Edition, Copyright © John C. Hull 2019
15
Annuity Factor as the Numeraire
The equation
f0 g0
E g
The process for the value of the account is
dg=rg dt
This has zero volatility. Using the money market account as the numeraire leads to the traditional risk-neutral world where l=0
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
3
Market Price of Risk (Page 616)
Sincteheportfoilsioriskle:ss =rt
and E T denotes expectatio ns in a w orld that is FRN w rt the bond price
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
8
Forward Risk Neutrality
We will refer to a world where the market price of risk is the volatility of g as a world that is forward risk neutral with respect to g.
If Eg denotes a world that is FRN wrt g
f0 g0
E
g
f
T
gT
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
9
(t )dz i
dg
(t)
r
(t
)
m i 1
l
i
s
g
,i
(
t
)
g
(
t
)
dt
m i 1
s g ,i (t ) g (t )dz i
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
10
Money Market Account as the Numeraire
The money market account is an account that starts at $1 and is always invested at the shortterm risk-free interest rate
fT gT
becomes
f0
A
(0
)
E
A
A
fT (T
)
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
16
Annuity Factors and Swap Rates
Edition, Copyright © John C. Hull 2019
17
Extension to Several Independent Factors
(Page 625)
In the traditiona l risk - neutral world
m
df (t ) r (t ) f (t )dt s f ,i (t ) f (t )dz i i 1
d ?1 ƒ1
μ1
dt
σ1
dz
d?2 ƒ2
μ2
dt
σ2
dz
Options, Futures, and Other Derivatives, 7th International
Edition, Copyright © John C. Hull 2019
2
Forming a Riskless Portfolio
T higsive:sμ1σ2 μ2σ1 rσ2 rσ1
or μ1r μ2 r
σ1
σ2
This shows that (m – r )/s is the same for all derivatives dependent on the same underlying
variable,
We refer to (m – r )/s as the market price of risk for and denote it by l
Edition, Copyright © John C. Hull 2019
14
Interest Rates
In a world that is FRN wrt P(0,T2) the expected value of an interest rate lasting between times T1 and T2 is the forward interest rate
(Equations 27.12 and 27.13, page 619)
If f depends on several underlying
with
d?
ƒ
μ dt
n
σi
i 1
dz i
then
n
μ r λ iσ i i 1
variables
Options, Futures, and Other Derivatives, 7th International
We can set up a riskless portfolio , consisting of
+ σ 2 ƒ2 of the 1st derivative and σ1ƒ1 of the 2nd derivative
(σ 2 ƒ2 ) ƒ1 (σ 1ƒ1 ) ƒ2
= ( μ1σ 2 ƒ1ƒ2 μ 2 σ 1ƒ1ƒ2 ) t
0
,
the
equation
f0 g0
E g
fT gT
becomes
f0
Eˆ
e
T
rdt
0
fT
where Eˆ denotes expectatio ns in the
traditiona l risk - neutral world
Options, Futures, and Other Derivatives, 7th International
13
Forward Prices
In a world that is FRN wrt P(0,T), the expected value of a security at time T is its forward price
Options, Futures, and Other Derivatives, 7th International