23-1
第 23章期货与互换的详细分析
Futures and Swaps,A
Closer Look
23-2
期货与互换
Futures and Swaps
23.1 外汇期货
23.2 股票指数期货
23.3 利率期货
23.4 商品期货的定价
23.5 互换
23-3
期货市场 Futures markets
– 芝加哥商品交易所 ( 国际货币市场 )
Chicago Mercantile (International Monetary Market)
– 伦敦国际金融期货交易所
London International Financial Futures Exchange
– 中美洲商品交易所
MidAmerica Commodity Exchange
活跃的远期市场
Active forward market
期货市场和远期市场的差异
Differences between futures and forward markets
外汇期货
Foreign Exchange Futures
23-4
利率平价理论 Interest rate parity theorem
用美元和英镑来举例 Developed using the US Dollar
and British Pound
T
UK
US
r
rEF
1
1
00
where
F0,是远期价格 is the forward price
E0,为当前两种货币的汇率 is the current exchange rate
外汇期货定价
Pricing on Foreign Exchange Futures
23-5
定价举例
Text Pricing Example
rus = 5% ruk = 6% E0 = $1.60 per pound
T = 1 yr
5 85.1$
06.1
05.160.1$ 1
0
F
当 r us小于 r uk时,F0肯定小于 E0，由 F0比 E0得到的美元升值程度正好可以与两国利率之间 的差额抵消。当然，如果情况相反结论依然成立：当 r us大于 r uk时,F0肯定大于 E0。
When rus is less than ruk,F0 must be less than E0,The appreciation of the dollar
embodied in the ratio of F0 to E0 exactly compensates for the difference in
interest rates available in the two countries,Of course,the argument also works in
reverse,If rus is greater than ruk,then F0 is greater than E0.
23-6
外汇期货
Foreign Exchange Futures
23-7
汇率风险套期保值
Hedging Foreign Exchange Risk
23-8
汇率风险套期保值
Hedging Foreign Exchange Risk
23-9
汇率风险套期保值
Hedging Foreign Exchange Risk
套利的净所得是无风险的，它等于 E0(1＋ rUS)-F0(1＋ r UK)。如果这个值是正的
，就在英国借款，在美国贷款，然后建立期货多头头寸以消除汇率风险。如果这个值是负的，就在美国借款，在英国贷款，然后建立英镑期货的空头头寸。
当价格正好相符没有套利机会时，这个表达式一定等于零。如果它为正，投资者会攫取套利收益；如果它为负，投资者反向操作还是能获得套利收益。把这个表达式整理一下得到：
The net proceeds to the arbitrage portfolio are risk-free and given by E0(1+rUS)-
F0(1+rUK),If this value is positive,borrow in the United Kingdom,lend in the United
States,and enter a long futures position to eliminate foreign exchange risk,If the
value is negative,borrow in the United States,lend in the United Kingdom,and take a
short position in pound futures,When prices preclude arbitrage opportunities,the
expression must equal zero,Rearranging this expression gives us the relationship
23-10
对本国和国际股票都有效
Available on both domestic and international
stocks.
与直接购买股票相比的优点
Advantages over direct stock purchase:
– 更低的交易成本
lower transaction costs
– 有利市场时机和重组的选择
better for timing or allocation strategies
– 减少资产组合的时间
takes less time to acquire the portfolio
股票指数期货
Stock Index Contracts
23-11
用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
综合股购买 Synthetic stock purchase:
– 购买股指而不是实际的股票
Purchase of the stock index instead of actual
shares of stock.
国库券加股指期货综合头寸的建立可得到比仅投资股指期货的双倍收入
Creation of a synthetic T-bill plus index futures
that duplicates the payoff of the stock index
contract.
23-12
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
23-13
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
23-14
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
例如,假如一机构投资者想在市场上进行为期一个月的 4500 万美元的投资,为了使交易费用最省,他决定购买标准普尔 500指数期货合约而不是真正持有股票 。 如果现在的标准普尔 500股指为 900点,1月期的期货价格是 909点,国库券的月利率是 1%，
则该投资者需要买入 200份合约 (每份合约相当于价值为 250美元
× 900＝ 225 000美元的股票,而 45000000 美元 /225000美元＝
200)。 这样他就有了 50000美元乘以标准普尔 500指数的多头头寸 (200份合约乘以合约的指数单价 250美元 )。 为了支付期货价格,该投资者在国库券上的投资额必须等于 50000美元乘以期货价格的现值,即 50000 美元 × (909/1.01)＝ 45000000美元市值的国库券 。 注意,在国库券上这 4500万美元的支出恰好等于直接购买股票所需的资金数额 (国库券的面值是 50000美元 × 909＝ 45
450 000美元 )。
23-15
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
那么到了到期日，该综合股票头寸的价值是多少呢？与以往一样，我们设 ST为到期日股指价值,F0为原期货价格：
合约到期日的总收入的确与股指价值成比例，也就是说，除了期中的红利分配与税务处理这两点外，
采取这种证券资产组合策略与持有指数股票资产组合本身没什么区别。
23-16
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
For example,suppose that an institutional investor wants to
invest $135 million in the market for one month and,to
minimize trading costs,chooses to buy the S&P 500 futures
contracts as a substitute for actual stock holdings,If the index is
now at 1,350,the one- month delivery futures price is 1,363.50,
and the T-bill rate is 1% per month,it would buy 400 contracts,
(Each contract controls $250－＞ 1,350－＞ $337,500 worth of
stock,and $135million/$337,500＝ 400.) The institution thus has
a long position on 100,000 times the S&P 500 index (400
contracts times the contract multiplier of 250),To cover
payment of the futures price,it must invest 100,000 times the
present value of the futures price in T- bills,This equals
100,000Ｘ１,363.50/1.01)＝ $135 million market value of bills,
Notice that the $135 million outlay in bills is precisely equal to
the amount that would have been needed to buy the stock
directly,(The face value of the bills will be 100,000Ｘ 1,363.50＝
$136.35 million.)
23-17
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
This is an artificial,or synthetic,stock position,What is the
value of this portfolio at the maturity date? Call ST the
value of the stock index on the maturity date T,and as
usual,let F0 be the original futures price:
The total payoff on the contract maturity date is exactly proportional to the
value of the stock index,In other words,adopting this portfolio strategy is
equivalent to holding the stock index itself,aside from the issue of interim dividend
distributions and tax treatment,
23-18
股指期货定价
Pricing on Stock Index Contracts
现货与期货价格之间的平价关系是 ;
The spot-futures price parity that was developed in
Chapter 22 is given as;
F0＝ S0(1＋ r f – d ) T
实证研究已经证实期货价格与现货价格密切相关,
Empirical investigations have shown that the actual
pricing relationship on index contracts follows the
spot-futures relationship.
d:为年红利率 dividend rate,
23-19
寻找股票和股指间的价格差
Exploiting mispricing between underlying stocks
and the futures index contract.
期货价太高 -卖空股指期货买股指股票
Futures Price too high - short the future and buy
the underlying stocks.
期货价太低 -买股指期货卖空股指股票 Futures
price too low - long the future and short sell the
underlying stocks.
指数套利
Index Arbitrage
23-20
实际上指数套利很难进行
This is difficult to implement in practice.
Transactions costs are often too large.
Trades cannot be done simultaneously.
程序交易的发展
Development of Program Trading
Used by arbitrageurs to perform index arbitrage.
Permits acquisition of securities quickly.
三重魔力日
Triple-witching hour
Evidence that index arbitrage impacts volatility.
指数套利和程序交易
Index Arbitrage and Program Trading
23-21
对冲系统风险
Hedging Systematic Risk
为保护股票市场价格的下降,买空相应数量的股指期货,
To protect against a decline in level stock prices,
short the appropriate number of futures index
contracts.
用股指期货可低成本和更快速
Less costly and quicker to use the index
contracts.
使用资产组合 β来决定对冲率
Use the beta for the portfolio to determine the
hedge ratio.
23-22
对冲系统风险,举例
Hedging Systematic Risk,Text Example
Portfolio Beta =,8 S&P 500 = 1,000
Decrease = 2.5% S&P falls to 975
投资组合价值 Portfolio Value = $30 million
Project loss if market declines by 2.5% = (.8) (2.5) = 2%
2% of $30 million = $600,000
Each S&P500 index contract will change $6,250 for a 2.5%
change in the index
23-23
对冲率,举例
Hedge Ratio,Text Example
H =
=
投资组合的变化 Change in the portfolio value
一个期货合约的利润 Profit on one futures contract
$600,000
$6,250
= 96 合约 (空头 ) contracts short
23-24
利率期货
Interest Rate Futures
本国利率合约
Domestic interest rate contracts
– 国库券,票据和债券 T-bills,notes and bonds
– 市政债券 municipal bonds
国际合约 International contracts
– 欧洲美元 Eurodollar
对冲 Hedging
– 承销商 Underwriters
– 公司发行债务 Firms issuing debt
23-25
利率套期保值的运用
Uses of Interest Rate Hedges
拥有固定收益资产组合的投资者保护利率的上升
Owners of fixed-income portfolios protecting
against a rise in rates.
计划发行债券的公司保护利率上升 Corporations
planning to issue debt securities protecting
against a rise in rates.
投资者锁定计划未来投资的收益率（对冲利率的下降）
Investor hedging against a decline in rates for a
planned future investment.
23-26
对冲利率风险
Hedging Interest Rate Risk,Text Example
组合价值 Portfolio value = $10 million
定义的久期 Modified duration = 9 years
如果利率上升 10个基点 If rates rise by 10 basis points (.1%)
价值变化 Change in value = ( 9 ) (,1%) =,9% or $90,000
基点现值 Present value of a basis point (PVBP) = $90,000 / 10
= $9,000
23-27
对冲率,举例
Hedge Ratio,Text Example
H =
=
投资组合的 PVBP for the portfolio
对冲工具的 PVBP for the hedge vehicle
$9,000
$90
= 100 contracts
23-28
商品期货定价
Commodity Futures Pricing
股票定价原理也可运用到商品期货定价
General principles that apply to stock apply to commodities.
商品有持有成本 Carrying costs are more for commodities.
CrPF f )1(00
Where; F0 = futures price P0 = cash price of the asset
C = Carrying cost c = C/P0
)1(00 crPF f
23-29
商品期货定价
Commodity Futures Pricing
因为市场价格不允许存在套利机会，所以这种净投资为零的无风险策略的最终现金流应该为零。如果现金流为正，按照这种方法不需任何投资就可获得可靠的收益。如果现金流为负
，采取相反的步骤仍可获利。实际上，反向操作需要卖空商品
，这是不常见的,不过只要卖空合理地考虑了存储成本就仍是可行的 。
23-30
商品期货定价
Commodity Futures Pricing
Because market prices should not allow for arbitrage opportunities,the terminal
cash flow of this zero net investment,risk-free strategy should be zero,If the
cash flow were positive,this strategy would yield guaranteed profits for no in-
vestment,If the cash flow were negative,the reverse of this strategy also would
yield prof- its,In practice,the reverse strategy would involve a short sale of the
commodity,This is unusual but may be done as long as the short sale contract
appropriately accounts for storage costs
23-31
利率互换 Interest rate swap
汇率互换 Foreign exchange swap
信用风险互换 Credit risk on swaps
互换的其它类型 Swap Variations
– 利率上限合约 Interest rate cap
– 利率下限合约 Interest rate floor
– 利率双限合约 Collars
– 互换期权 Swaptions
互换
Swaps
23-32
互换是一系列的期货合约
Swaps are essentially a series of forward contracts.
互换和期货合约的不同是：互换在每个周期内有相同的收支而与此同时期货合约在不同的周期有不同的收支．
One difference is that the swap is usually structured
with the same payment each period while the forward
rate would be different each period.
互换定价
Pricing on Swap Contracts
23-33
用汇率互换作为例子,互换定价将被由下式定义
Using a foreign exchange swap as an example,the swap pricing
would be described by the following formula.
其中 y1与 y2分别是用来对一年期与二年期美元现金流进行贴现的收益率，该收益 率可以从收益曲线上得到。
where y1 and y2 are the appropriate yields from the yield
curve for discounting dollar cash flows of one- and two-year
maturities,respectively,
2
2
*
1
*
2
2
2
1
1
)1()1()1()1( y
F
y
F
y
F
y
F
互换定价
Pricing on Swap Contracts
23-34
各种股票市场指数的期货合约都采用现金结算。把这些合约与国库券结合可以构造综合股票头寸，对市场时机决定者来说，
这是一种非常有价值的工具。同样，股票指数期货合约也可以被套利者用来从市场的非平价关系中套利。
Futures contracts calling for cash settlement are traded on
various stock market indexes,The contracts may be mixed
with Treasury bills to construct artificial equity positions,
which makes them potentially valuable tools for market
timers,Market index contracts are used also by arbitrageurs
who attempt to profit from violations of the parity relationship.
Summary
23-35
外汇期货合约有好多品种，其中还包括欧洲货币指数。外汇期货的利率平价关系为：
Foreign exchange futures trade on several foreign currencies,as
well as on a European currency index,The interest rate parity
relationship for foreign exchange futures is
Summary
其中汇率是用每单位外币的美元数标价的。如果期货价格偏离了这个价值就意味 着存在套利机会。不过，实证研究表明，通常平价关系都是满足的。
with exchange rates quoted as dollars per foreign currency,Deviations of
the futures price from this value imply arbitrage opportunity,Empirical
evidence,however,suggests that generally the parity relationship is
satisfied.
23-36
对冲要求投资者购买那种能抵消其投资组合特殊来源风险的敏感性资产．一个对冲头寸要求对冲工具能带来与要保护的头寸相反方向的收入。
Hedging requires investors to purchase assets that
will offset the sensitivity of their portfolios to
particular sources of risk,A hedged position requires
that the hedging vehicle provide profits that vary
inversely with the value of the position to be
protected.
Summary
23-37
由于存在着标的商品的储存成本，所以商品期货的定价比较复杂。当投资者愿意储存商品时，用储存成本扣除便利收益，可以得到如下期货定价方程：
F0＝ P0(1＋ rf＋ c)
非利息的净储存成本 c，就相当于一种“负红利”。
Commodity futures pricing is complicated by costs for storage
of the underlying commodity,When the asset is willingly stored
by investors,then the storage costs net of convenience yield
enter the futures pricing equation as follows:
F0＝ P0(1＋ r f＋ c)
The non–interest net carrying costs,c,play the role of a
“negative dividend” in this context.
Summary
23-38
当商品不是出于投资目的而储存起来时，正确的期货价格应该根据一般的风险补偿原则确定，即
When commodities are not stored for investment purposes,
the correct futures price must be determined using general
risk–return principles,In this event,
Summary
合理的期货均衡价格与无套利预期是彼此一致的。
The equilibrium (risk–return) and the no-arbitrage
predictions of the proper futures price are consistent with
one another for stored commodities.
23-39
可以把一系列现金流进行交换的互换看作是远期合约的资产组合 。 每次交换都可以看作是一个单独的远期协议 。 不过,
与把每次交换都单独定价不同的是,互换把一个,远期价格
” 用于所有的交换 。 因此,互换的价格应该是每次交换都单独定价得到的远期价格的平均值 。
Summary
Swaps,which call for the exchange of a series of cash
flows,may be viewed as portfolios of forward contracts,
Each transaction may be viewed as a separate forward
agreement,However,instead of pricing each exchange
independently,the swap sets one,forward price” that
applies to all of the transactions,Therefore,the swap price
will be an average of the forward prices that would prevail
if each exchange were priced separately.
第 23章期货与互换的详细分析
Futures and Swaps,A
Closer Look
23-2
期货与互换
Futures and Swaps
23.1 外汇期货
23.2 股票指数期货
23.3 利率期货
23.4 商品期货的定价
23.5 互换
23-3
期货市场 Futures markets
– 芝加哥商品交易所 ( 国际货币市场 )
Chicago Mercantile (International Monetary Market)
– 伦敦国际金融期货交易所
London International Financial Futures Exchange
– 中美洲商品交易所
MidAmerica Commodity Exchange
活跃的远期市场
Active forward market
期货市场和远期市场的差异
Differences between futures and forward markets
外汇期货
Foreign Exchange Futures
23-4
利率平价理论 Interest rate parity theorem
用美元和英镑来举例 Developed using the US Dollar
and British Pound
T
UK
US
r
rEF
1
1
00
where
F0,是远期价格 is the forward price
E0,为当前两种货币的汇率 is the current exchange rate
外汇期货定价
Pricing on Foreign Exchange Futures
23-5
定价举例
Text Pricing Example
rus = 5% ruk = 6% E0 = $1.60 per pound
T = 1 yr
5 85.1$
06.1
05.160.1$ 1
0
F
当 r us小于 r uk时,F0肯定小于 E0，由 F0比 E0得到的美元升值程度正好可以与两国利率之间 的差额抵消。当然，如果情况相反结论依然成立：当 r us大于 r uk时,F0肯定大于 E0。
When rus is less than ruk,F0 must be less than E0,The appreciation of the dollar
embodied in the ratio of F0 to E0 exactly compensates for the difference in
interest rates available in the two countries,Of course,the argument also works in
reverse,If rus is greater than ruk,then F0 is greater than E0.
23-6
外汇期货
Foreign Exchange Futures
23-7
汇率风险套期保值
Hedging Foreign Exchange Risk
23-8
汇率风险套期保值
Hedging Foreign Exchange Risk
23-9
汇率风险套期保值
Hedging Foreign Exchange Risk
套利的净所得是无风险的，它等于 E0(1＋ rUS)-F0(1＋ r UK)。如果这个值是正的
，就在英国借款，在美国贷款，然后建立期货多头头寸以消除汇率风险。如果这个值是负的，就在美国借款，在英国贷款，然后建立英镑期货的空头头寸。
当价格正好相符没有套利机会时，这个表达式一定等于零。如果它为正，投资者会攫取套利收益；如果它为负，投资者反向操作还是能获得套利收益。把这个表达式整理一下得到：
The net proceeds to the arbitrage portfolio are risk-free and given by E0(1+rUS)-
F0(1+rUK),If this value is positive,borrow in the United Kingdom,lend in the United
States,and enter a long futures position to eliminate foreign exchange risk,If the
value is negative,borrow in the United States,lend in the United Kingdom,and take a
short position in pound futures,When prices preclude arbitrage opportunities,the
expression must equal zero,Rearranging this expression gives us the relationship
23-10
对本国和国际股票都有效
Available on both domestic and international
stocks.
与直接购买股票相比的优点
Advantages over direct stock purchase:
– 更低的交易成本
lower transaction costs
– 有利市场时机和重组的选择
better for timing or allocation strategies
– 减少资产组合的时间
takes less time to acquire the portfolio
股票指数期货
Stock Index Contracts
23-11
用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
综合股购买 Synthetic stock purchase:
– 购买股指而不是实际的股票
Purchase of the stock index instead of actual
shares of stock.
国库券加股指期货综合头寸的建立可得到比仅投资股指期货的双倍收入
Creation of a synthetic T-bill plus index futures
that duplicates the payoff of the stock index
contract.
23-12
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
23-13
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
23-14
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
例如,假如一机构投资者想在市场上进行为期一个月的 4500 万美元的投资,为了使交易费用最省,他决定购买标准普尔 500指数期货合约而不是真正持有股票 。 如果现在的标准普尔 500股指为 900点,1月期的期货价格是 909点,国库券的月利率是 1%，
则该投资者需要买入 200份合约 (每份合约相当于价值为 250美元
× 900＝ 225 000美元的股票,而 45000000 美元 /225000美元＝
200)。 这样他就有了 50000美元乘以标准普尔 500指数的多头头寸 (200份合约乘以合约的指数单价 250美元 )。 为了支付期货价格,该投资者在国库券上的投资额必须等于 50000美元乘以期货价格的现值,即 50000 美元 × (909/1.01)＝ 45000000美元市值的国库券 。 注意,在国库券上这 4500万美元的支出恰好等于直接购买股票所需的资金数额 (国库券的面值是 50000美元 × 909＝ 45
450 000美元 )。
23-15
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
那么到了到期日，该综合股票头寸的价值是多少呢？与以往一样，我们设 ST为到期日股指价值,F0为原期货价格：
合约到期日的总收入的确与股指价值成比例，也就是说，除了期中的红利分配与税务处理这两点外，
采取这种证券资产组合策略与持有指数股票资产组合本身没什么区别。
23-16
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
For example,suppose that an institutional investor wants to
invest $135 million in the market for one month and,to
minimize trading costs,chooses to buy the S&P 500 futures
contracts as a substitute for actual stock holdings,If the index is
now at 1,350,the one- month delivery futures price is 1,363.50,
and the T-bill rate is 1% per month,it would buy 400 contracts,
(Each contract controls $250－＞ 1,350－＞ $337,500 worth of
stock,and $135million/$337,500＝ 400.) The institution thus has
a long position on 100,000 times the S&P 500 index (400
contracts times the contract multiplier of 250),To cover
payment of the futures price,it must invest 100,000 times the
present value of the futures price in T- bills,This equals
100,000Ｘ１,363.50/1.01)＝ $135 million market value of bills,
Notice that the $135 million outlay in bills is precisely equal to
the amount that would have been needed to buy the stock
directly,(The face value of the bills will be 100,000Ｘ 1,363.50＝
$136.35 million.)
23-17
使用股指期货建立综合头寸
Using Stock Index Contracts to Create Synthetic Positions
This is an artificial,or synthetic,stock position,What is the
value of this portfolio at the maturity date? Call ST the
value of the stock index on the maturity date T,and as
usual,let F0 be the original futures price:
The total payoff on the contract maturity date is exactly proportional to the
value of the stock index,In other words,adopting this portfolio strategy is
equivalent to holding the stock index itself,aside from the issue of interim dividend
distributions and tax treatment,
23-18
股指期货定价
Pricing on Stock Index Contracts
现货与期货价格之间的平价关系是 ;
The spot-futures price parity that was developed in
Chapter 22 is given as;
F0＝ S0(1＋ r f – d ) T
实证研究已经证实期货价格与现货价格密切相关,
Empirical investigations have shown that the actual
pricing relationship on index contracts follows the
spot-futures relationship.
d:为年红利率 dividend rate,
23-19
寻找股票和股指间的价格差
Exploiting mispricing between underlying stocks
and the futures index contract.
期货价太高 -卖空股指期货买股指股票
Futures Price too high - short the future and buy
the underlying stocks.
期货价太低 -买股指期货卖空股指股票 Futures
price too low - long the future and short sell the
underlying stocks.
指数套利
Index Arbitrage
23-20
实际上指数套利很难进行
This is difficult to implement in practice.
Transactions costs are often too large.
Trades cannot be done simultaneously.
程序交易的发展
Development of Program Trading
Used by arbitrageurs to perform index arbitrage.
Permits acquisition of securities quickly.
三重魔力日
Triple-witching hour
Evidence that index arbitrage impacts volatility.
指数套利和程序交易
Index Arbitrage and Program Trading
23-21
对冲系统风险
Hedging Systematic Risk
为保护股票市场价格的下降,买空相应数量的股指期货,
To protect against a decline in level stock prices,
short the appropriate number of futures index
contracts.
用股指期货可低成本和更快速
Less costly and quicker to use the index
contracts.
使用资产组合 β来决定对冲率
Use the beta for the portfolio to determine the
hedge ratio.
23-22
对冲系统风险,举例
Hedging Systematic Risk,Text Example
Portfolio Beta =,8 S&P 500 = 1,000
Decrease = 2.5% S&P falls to 975
投资组合价值 Portfolio Value = $30 million
Project loss if market declines by 2.5% = (.8) (2.5) = 2%
2% of $30 million = $600,000
Each S&P500 index contract will change $6,250 for a 2.5%
change in the index
23-23
对冲率,举例
Hedge Ratio,Text Example
H =
=
投资组合的变化 Change in the portfolio value
一个期货合约的利润 Profit on one futures contract
$600,000
$6,250
= 96 合约 (空头 ) contracts short
23-24
利率期货
Interest Rate Futures
本国利率合约
Domestic interest rate contracts
– 国库券,票据和债券 T-bills,notes and bonds
– 市政债券 municipal bonds
国际合约 International contracts
– 欧洲美元 Eurodollar
对冲 Hedging
– 承销商 Underwriters
– 公司发行债务 Firms issuing debt
23-25
利率套期保值的运用
Uses of Interest Rate Hedges
拥有固定收益资产组合的投资者保护利率的上升
Owners of fixed-income portfolios protecting
against a rise in rates.
计划发行债券的公司保护利率上升 Corporations
planning to issue debt securities protecting
against a rise in rates.
投资者锁定计划未来投资的收益率（对冲利率的下降）
Investor hedging against a decline in rates for a
planned future investment.
23-26
对冲利率风险
Hedging Interest Rate Risk,Text Example
组合价值 Portfolio value = $10 million
定义的久期 Modified duration = 9 years
如果利率上升 10个基点 If rates rise by 10 basis points (.1%)
价值变化 Change in value = ( 9 ) (,1%) =,9% or $90,000
基点现值 Present value of a basis point (PVBP) = $90,000 / 10
= $9,000
23-27
对冲率,举例
Hedge Ratio,Text Example
H =
=
投资组合的 PVBP for the portfolio
对冲工具的 PVBP for the hedge vehicle
$9,000
$90
= 100 contracts
23-28
商品期货定价
Commodity Futures Pricing
股票定价原理也可运用到商品期货定价
General principles that apply to stock apply to commodities.
商品有持有成本 Carrying costs are more for commodities.
CrPF f )1(00
Where; F0 = futures price P0 = cash price of the asset
C = Carrying cost c = C/P0
)1(00 crPF f
23-29
商品期货定价
Commodity Futures Pricing
因为市场价格不允许存在套利机会，所以这种净投资为零的无风险策略的最终现金流应该为零。如果现金流为正，按照这种方法不需任何投资就可获得可靠的收益。如果现金流为负
，采取相反的步骤仍可获利。实际上，反向操作需要卖空商品
，这是不常见的,不过只要卖空合理地考虑了存储成本就仍是可行的 。
23-30
商品期货定价
Commodity Futures Pricing
Because market prices should not allow for arbitrage opportunities,the terminal
cash flow of this zero net investment,risk-free strategy should be zero,If the
cash flow were positive,this strategy would yield guaranteed profits for no in-
vestment,If the cash flow were negative,the reverse of this strategy also would
yield prof- its,In practice,the reverse strategy would involve a short sale of the
commodity,This is unusual but may be done as long as the short sale contract
appropriately accounts for storage costs
23-31
利率互换 Interest rate swap
汇率互换 Foreign exchange swap
信用风险互换 Credit risk on swaps
互换的其它类型 Swap Variations
– 利率上限合约 Interest rate cap
– 利率下限合约 Interest rate floor
– 利率双限合约 Collars
– 互换期权 Swaptions
互换
Swaps
23-32
互换是一系列的期货合约
Swaps are essentially a series of forward contracts.
互换和期货合约的不同是：互换在每个周期内有相同的收支而与此同时期货合约在不同的周期有不同的收支．
One difference is that the swap is usually structured
with the same payment each period while the forward
rate would be different each period.
互换定价
Pricing on Swap Contracts
23-33
用汇率互换作为例子,互换定价将被由下式定义
Using a foreign exchange swap as an example,the swap pricing
would be described by the following formula.
其中 y1与 y2分别是用来对一年期与二年期美元现金流进行贴现的收益率，该收益 率可以从收益曲线上得到。
where y1 and y2 are the appropriate yields from the yield
curve for discounting dollar cash flows of one- and two-year
maturities,respectively,
2
2
*
1
*
2
2
2
1
1
)1()1()1()1( y
F
y
F
y
F
y
F
互换定价
Pricing on Swap Contracts
23-34
各种股票市场指数的期货合约都采用现金结算。把这些合约与国库券结合可以构造综合股票头寸，对市场时机决定者来说，
这是一种非常有价值的工具。同样，股票指数期货合约也可以被套利者用来从市场的非平价关系中套利。
Futures contracts calling for cash settlement are traded on
various stock market indexes,The contracts may be mixed
with Treasury bills to construct artificial equity positions,
which makes them potentially valuable tools for market
timers,Market index contracts are used also by arbitrageurs
who attempt to profit from violations of the parity relationship.
Summary
23-35
外汇期货合约有好多品种，其中还包括欧洲货币指数。外汇期货的利率平价关系为：
Foreign exchange futures trade on several foreign currencies,as
well as on a European currency index,The interest rate parity
relationship for foreign exchange futures is
Summary
其中汇率是用每单位外币的美元数标价的。如果期货价格偏离了这个价值就意味 着存在套利机会。不过，实证研究表明，通常平价关系都是满足的。
with exchange rates quoted as dollars per foreign currency,Deviations of
the futures price from this value imply arbitrage opportunity,Empirical
evidence,however,suggests that generally the parity relationship is
satisfied.
23-36
对冲要求投资者购买那种能抵消其投资组合特殊来源风险的敏感性资产．一个对冲头寸要求对冲工具能带来与要保护的头寸相反方向的收入。
Hedging requires investors to purchase assets that
will offset the sensitivity of their portfolios to
particular sources of risk,A hedged position requires
that the hedging vehicle provide profits that vary
inversely with the value of the position to be
protected.
Summary
23-37
由于存在着标的商品的储存成本，所以商品期货的定价比较复杂。当投资者愿意储存商品时，用储存成本扣除便利收益，可以得到如下期货定价方程：
F0＝ P0(1＋ rf＋ c)
非利息的净储存成本 c，就相当于一种“负红利”。
Commodity futures pricing is complicated by costs for storage
of the underlying commodity,When the asset is willingly stored
by investors,then the storage costs net of convenience yield
enter the futures pricing equation as follows:
F0＝ P0(1＋ r f＋ c)
The non–interest net carrying costs,c,play the role of a
“negative dividend” in this context.
Summary
23-38
当商品不是出于投资目的而储存起来时，正确的期货价格应该根据一般的风险补偿原则确定，即
When commodities are not stored for investment purposes,
the correct futures price must be determined using general
risk–return principles,In this event,
Summary
合理的期货均衡价格与无套利预期是彼此一致的。
The equilibrium (risk–return) and the no-arbitrage
predictions of the proper futures price are consistent with
one another for stored commodities.
23-39
可以把一系列现金流进行交换的互换看作是远期合约的资产组合 。 每次交换都可以看作是一个单独的远期协议 。 不过,
与把每次交换都单独定价不同的是,互换把一个,远期价格
” 用于所有的交换 。 因此,互换的价格应该是每次交换都单独定价得到的远期价格的平均值 。
Summary
Swaps,which call for the exchange of a series of cash
flows,may be viewed as portfolios of forward contracts,
Each transaction may be viewed as a separate forward
agreement,However,instead of pricing each exchange
independently,the swap sets one,forward price” that
applies to all of the transactions,Therefore,the swap price
will be an average of the forward prices that would prevail
if each exchange were priced separately.
