期貨與選擇權
Hedging & Options
1
Brief History of Futures
1848, CBOT (Chicago Board of Trade)
芝加哥交易所成立遠期契約，1860’s 期貨契約
grains → financial instruments, specious metals (金、銀、銅、石油)
商品期貨：農產品、金屬、能源、軟性 (咖啡、可可)
金融期貨：外匯、利率 (短期、長期)、股價指數、利率指數等
A futures contract is a legally binding commitment to make
or take delivery of a standardized quantity and quality of a
commodity at a price agreed upon in the trading pit or ring
of a commodity exchange at the time the contract is
executed.
2
Brief History of Futures（續）
“forward contracts” v.s. “futures contracts”
（遠期契約）
terms: amount, delibery
date, quality, price are
set in private by the buyers
& sellers
（期貨契約）
terms are standaredized with
the exception of price
( price is discovered through
public auction at an
established exchange)
Clearing Corporation
– it assumes the
*1.標準化—交易標的物之定義 opposite side of each
trade.
交易標的數量
契約到期日
交割方式
2.消除違約風險（結算所背書保證）
3.逐日結算
3
Hedging 避險期貨交易
“Hedge” means “protection”.
Hedge：The buying and selling of offsetting positions in the futures
（期貨） market in order to provide protection against an adverse
change in price.
Hedging → ↓price risk
（If expect P↓→ sell futures contracts；
expect P↑→ purchase futures contract ）
The initiation of a futures position that is intended as a temporary
substitute for the sale or purchase of the actual commodity.
Usually, actual commodity does not change hands in the futures
markets : The sale of futures contracts can be offset by the purchase of
an equal number of futures contract's at a later date before the contract's
delivery date.
4
 The Market Participants：
1.
hedgers (避險交易者), include: farmers, country elevator
operators, processors, livestock feeders, exporters,
importers.
To lock in a price and obtain protection against
P↑ (buying futures)—“long” position（多頭）
(bullish)
P↓ (selling futures)—“short” position（空頭）
(bearish)
風險轉移的原理： They seek protection against adverse
price changes by initiating a position in the futures market
as a temporary substitute for the sale or purchase of the
actual commodity.
5
2. ”speculators”（投機者）- people who assume risk in
antipation of profiting from a change in prices
Speculation 有 助 於 價 格 穩 定 . Speculators facilitate
hedging by providing liquidity
- the ability to enter and exit the market quickly & easily.
To profit from P↑(buying futures); P↓(selling futures).
They can realize a highly leveraged profit if they prove to
be correct in anticipating the direction and timing of price
changes.
3. Arbitrager （套利交易人）：
同時買賣現貨、期貨，以賺取無風險價差
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保證金
“margin” – money that buyers and sellers of futures contracts must
deposit
with their brokers and that brokers in turn must deposit with the
Clearing Corporation.
– money deposit in case 
of losses happen
“margin call” --- loss ↓, gain ↑ minimum amount
Deposit more money to maintain
↑
until the
minimum margin requirement
open position is closed
Clearing Corporation （結算所）assumes the opposite side of each
open position and thereby assures the financial integrity of every futures
contract traded at the CBOT. Hedge: the buying & selling of offsetting7
positions in order to provide protection against an adverse change in price.
reasons for buying
future contracts
reasons for selling
future contracts
Hedgers
(farmers, exporters,
processors, elevator
operators, livestock
feeders)
to lack in price and
obtain protection
against rising prices
to lack in prices and
obtain protection
against declining prices
Public speculators
Floor traders
to profit from rising
prices
to profit from decline
prices
8
對沖交易
Hedge
避險期貨交易
Selling (short) hedge - 空頭避險
Buying (long) hedge – 多頭避險
避險功能
投機功能
價格發現功能
(price discovery)
bearish 看跌→short； bullish 看漲（多）→long
有opening transaction,
一定要在到期日之前進行closing transaction = liquidation （平倉）
9
“basis” = cash price - futures price
基差
現貨價格
期貨價格
影響Basis之因素：transportation costs, storage costs, interests, S
& D (local & overall market)
產地：cash price<future price "normal market"
Gulf Coast：cash>future price "inverted market”
+
stronger ↑
0
-
+ ↓weakening, ↑strengthening
0
weaker ↓
- ↑strengthening, ↓weakening
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Hedging
long hedge
short hedge
basis gain
basis loss
basis loss
basis gain
if basis weaken
(cash falls more or rises less)
if basis strengthens
(cash falls less or rises more)
11
price $
futures price
transportation cost
convergence
carrying charges
local cash price
time
present
future
12
Hedging利用期貨之價差來彌補現貨之價差。不避險時，面對
現貨市場價格波動，避險時面對兩市場間之基差波動（basis
risk）。因為期貨與現貨價格具高度相關性，互沖效果使基差
之波動小於現貨市場價格之波動，故hedging即以basis risk取代
price risk。
Usually, cash price and futures price move in the same
direction.Basis fluctuations are usually smaller than cash price
fluctuations.
$
futures p.
cash p.
time
13
eg1: short, futures gain, no basis change ( perfect hedge )
selling (short) hedges: a corn farmer wants to lock in corn price of $2.20/bu.
cash
Sep.
Price for new-crop corn
$2.20/bu
Nov.
futures
(5,000 bu each)
$0.25/bu.
sells 2 Dec. Corn
Dec.
$2.04/bu
$0.25 under Dec.
contracts at $2.29/bu
to offset initial short futures posit ion
$0.16/bu gain
results:
Under
contracts at $2.45/bu
buys 2 Dec Corn
Sells 10,000 bu corn at
Basis
cash sale price $2.04/bu
+ futures gain 0.16
net selling price $2.20/bu
no change
cash forward bid $2.20/bu
no basis change 0
net selling price $2.20/bu
14
eg2: short, futures loss, no basis change ( perfect hedge )
cash
$2.20
selling $2.50
results:
cash sale price 2.50
futures loss - 0.30
net selling price 2.20

futures
basis
sells $2.45
$0.25
under
buys $2.75
$0.25
under
$0.30 loss no basis change
price objective $2.20
no basis gain/loss
0
net selling price $2.20
“perfect hedges ” : basis does not change between the time a
hedge was placed and lifted
15
eg.3 : short, basis weaken ( loss )
cash
Sep
price for new-crop corn
$2.20/bu
Nov.
sells 10,000 bu corn at
$2.00/bu
futures
sells 2 Dec. corn contracts
$2.45/bu
basis
$0.25 under Dec.
buys 2 Dec. corn contracts
at $2.30/bu to offset
initial short futures position
$0.30 under Dec.
0.15/bu gain
$0.05 basis loss
results: cash sale price $2.00/bu
price objective $2.20/bu
+ futures gain 0.15
- basis loss $0.05/bu
net selling price $2.15/bu = net selling price $2.15/bu
16
eg4: short, basis strengthen ( gain )
Cash
Sep $2.20
sell Nov $2.18
futures
sell $2.45
buy $2.38
$0.07/bu gain
basis
$0.25
$0.20
basis gain $0.05
under
under
results:
cash sale price $2.18/bu
+ futures gain 0.07
net selling price 2.25/bu
price objective $2.20
+ basis gain $0.05
$2.25/bu
17
eg.5: short, basis weaken ( loss )
A processor hedges to protect his soybean oil inventory against price ↓
cash
futures
May
cash forward bid for
soybean oil ￠18.5/lb
basis
(60,000 lbs each)
sells 3 Sep. soybean oil
contracts at ￠17.5/lb
￠1.00/lb over Sep.
Aug
sells 180,000 lbs
buys 3 Sep. soybean oil
soybean oil at ￠16.25/lb contracts at ￠15.5/lb
to offset intial short
futures position
￠2.0/lb gain
￠0.75/lb over Sep.
￠0.25/lb basis loss
results:
cash sale 16.25
+ futures gain 2.00
net selling price 18.25 cents/lb
cash forward bid 18.50
- basis loss 0.25
net selling price 18.25
18
Buying (Long) Hedges: used to protect against ↑ in cash price.
eg1.
Cash
poultry
producer
Oct.
cash price for soybean
meal $148/ton
Dec.
buys soybean meal at
$156/ton
Futures
(100 tons each)
buys 1 Jan soybean meal
contract at $153/ton
sells 1 Jan soybean meal
contract at $161/ton
to offset initial long
futures position
$8/ton gain
basis
$5 under Jan
$5under Jan
no change
results:
cash purchase price $156/ton price objective $148/ton
- futures gain $ 8/ton
no basis change
0
net purchase price $148/ton net purchase price $148/ton
19
eg3. long, basis weaken ( gain )
cash
futures
basis
Oct.
cash price for soybean buys u Jan soybean meal $5 under Jan.
meal $148/ton
contract at $153/ton
Dec.
buys soybean meal at sells 1 Jan soybean meal $9 under Jan.
$151/ton
contract at $160/ton to
offset initial long futures
position
$7/ton gain
$4 basis gain
results:
cash purchase price $151/ton
price objective $148/ton
- futures gain $ 7/ton
basis gain
$4/ton
net purchase price $144/ton
net purchase price $144/ton
20
eg4: long, basis strengthen ( loss )
cash
Oct.
cash price for soybean
meals $148/ton
Dec.
buys soybean meal at
$156/ton
futures
basis
buys 1 Jan soybean meal
contract at $153/ton
$5 under Jan.
sells 1 Jan soybean meal
contract at $158/ton to
offset initial long futures
position
$5/ton gain
$2 under Jan.
$3 basis loss
results:
cash purchase price $156/ton
futures gain $ 5/ton
net purchase price $151/ton
price objective $148/ton
+ basis loss $ 3/ton
net purchase price $151/ton
21
eg5. long, basis weaken ( gain )
grain exporter
cash
futures
basis
July
make commitment to sell buys 100 Dec. wheat $0.10 over Dec.
1 million bu wheat at
contract at $2.62/bu
$2.72/bu
Nov.
buys 1 million bu wheat sells 200 Dec. wheat
$0.04 over Dec.
at $2.78/bu
contract at $2.74/bu to
offset initial long futures
position
$0.12/bu gain
$0.06 basis gain
results:
cash purchase price $2.78/bu
price objective $2.72/bu
futures gain 0.12/bu
- basis gain $0.06/bu
net purchase price $2.66/bu
net purchase price $2.66/bu
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Options ( 選擇權 )
Options: the right, but not the obligation, to buy or sell a
futures contract at some predetermined price at anytime
within a specific time period
strike price
Oct. 31, 1984 － soybeans
Feb. 27, 1985 － corn
+ wheat, soybean oil, soybean meal etc.
An option is a legally binding contract that gives the option
buyer the right, but not the obligation, to buy or sell
something under specific conditions in exchange for the
payment of a premium.
( the price of an option )
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( It is the buyer's (holder) decision whether to exercise that right;
only the seller (writer) of the option is obligated to perform.)
options
“calls” – the right to buy 買權
“puts” – the right to sell 賣權
(not opposite side of the same transaction)
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eg: Buy Nov. $8.00 soybean put option before Nov. harvest.
If at harvest, market price of soybean futures is $7.00,you would certainly exercise
your right to sell at $8.00, or you would sell the option rights to someone else.
If Nov. soybean futures at harvest are trading at $8.50/bu, you would not
exercise the right to sell at only $8.00. You would simply let the option expire (and
lose the premium) or sell it to someone else.
And option buyer ( holders ) has several choices:
1.liquidate his option position by selling an identical option anytime prior to
expiration
2.let the option expire
3.exercise his option
Choices of writers:
1.before been noticed for exercise – buy an offsetting option
2.after been noticed – selling an offsetting futures contract
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Options on Futures Contract
The buyer of a call obtains protection against rising prices -similar to the protection of a long hedge with futures -- but without
giving up the chance to benefit from rising prices.
The buyer of a put obtains protection against declining prices -similar to the protection of a short hedge with futures of forward
contracting -- but without giving up the chance to benefit from
declining prices.
履約價格
Strike price -- the price at which the holder of a call (or put) may
choose to exercise his right to purchase (or sell) the underlying
futures contract.
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內含價值
Intrinsic value : the difference between strike price & current
market price
call option: current futures price > strike price
put option: current futures price < strike price
An option is not worth exercising if it has no intrinsic value.
In-the-money (worth exercising) -- an option that has intrinsic value
Out-of-the-money -- an option that has no intrinsic value
call option: current futures price < strike price
put option: current futures price > strike price
An option that is out-of-the-money at expiration will have
no value, and the holder will allow it to expire worthless.
At-the-money -- strike price = underlying futures price
( i.e. intrinsic value = 0 )
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Time value -- the amount that buyers are currently willing to pay for a
given option over and above any intrinsic value, in anticipation that, over
time, a change in the underlying futures price will cause the option to
increase in value.
time value
權利金
Option premiums -- time value + intrinsic value
time
value
expiration
the price of an option (the option buyer pays the option writer)
Options are traded the same way futures contracts are traded, with the
exception of margin requirements.
Most option buyers and sellers elect to liquidate their option positions by
an offsetting sale or purchase at or prior to expiration.
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履約
Exercise: only an option buyer (holder) has the right to
exercise an option when a call (put) is exercised, the holder
will acquire a long (short) futures position at the strike price.
factors influencing premiums:
1. The length of time remaining until expiration
2. The volatility of the underlying futures price
3. The relationship of strike price and market price
4. Short-term risk-free interest rates
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option
futures
strike
Settlement price (premium)
July 85
price
2773/4
price
260
270
280
290
300
Calls
177/8
9
3
7/8
1/4
puts
1/4
13/8
47/8
121/2
22
Strategies for buying and selling options
• Buying put options: to establish a minimum price for sales
A farmer might wish to purchase a put during the spring or
summer in order to establish a minimum price for the sale of his
crop at harvest.
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eg1: In May a soybean producer pays a premium of $0.25 for a Nov.
$7.50 put.
(This gives him the right to go short in the futures market at a
price of $7.50. The right continues for as long as he holds the
option -- until he sells it, or exercise it, or until it expires in October)
By harvest time, the Nov. futures price has declined to $6.50
the put with a strike price of $7.50 have an intrinsic value of $1.00
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Cash
May.
price for new-crop
soybeans is $7.25/bu
Nov.
sells 5,000 bu
soybeans at $6.50/bu
Option
buy Nov. $7.50 put at a premium of $0.25/bu
sells Nov. $7.50 put to receive premium of $1.00/bu
and offset initial long option position
+ $0.75 ($1.00 - $0.25) .... option gain
result : cash sale price
+ option gain
$6.50/bu
$0.75/bu
net selling price $7.25/bu
32
eg2:
cash
May.
price for new-crop
soybeans is $7.25
Nov.
sells 5,000 bu
soybeans at $8.00/bu
options
buys Nov. $7.50 put
at a premium of $0.25/bu
let option expire
result:
cash sale price $8.00/bu
- cost of option premium 0.25/bu
net selling price $7.75/bu
33
• Buying call options: to sell the crops now (at harvest) and avoid storage costs
(and P ↓), and also profit from P↑in winter or spring
futures
options
Oct.
May soybean futures
buys May. $8.00 call
are $8.00/bu
at a premium of $0.15/bu
Apr.
May soybean futures
sells May $8.00 call at a
are $8.50/bu
premium of $0.50/bu and offsets initial
long option position
result:
gain from option position $0.50/bu
- cost of premium
0.15/bu
net gain
$0.35/bu
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• Selling call options
- to earn the option premium
- when do not expect a substantial price increase
"covered call" - write a call option against a commodity
you own.
- own commodity, cash market value
of your commodity move with the same
direction as the futures price
"uncovered" or "naked" option - options not covered by
having a cash or futures
market position in the
commodity
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• Selling put options
- to earn the option premium
- puts are written by individuals who do not expect a substantial
decrease in price
1. Buying put options for protection against lower prices.
2. Buying put options for "price insurance" when you store your crop.
3. Writing call options to achieve a higher effective selling price for a crop
you are storing.
4. Buying call options at harvest to profit form a winter/spring price
increase.
5. Buying call options for short-term protection against rising prices.
36
If futures
price at
expiration is:
(basis
maintains
at –0.20)
$6.50
$7.00
$7.50
$8.00
$8.50
Your net return if you
Write call with strike price of
0.43
0.30
0.20
0.13
Hedg
e or
contra
ct
at
$7.50
$6.73
$7.23
$7.48
$7.48
$7.48
6.60
7.10
7.60
7.60
7.60
6.50
7.00
7.50
7.75
7.75
6.43
6.93
7.43
7.93
7.93
7.30
7.30
7.30
7.30
7.30
$7.25
$7.50
$7.75
$8.00
premiums
Buy put with
$7.50 strike
price
at a premium
of
$0.30
Do
noth
ing
7.00
7.00
7.00
7.50
8.00
6.30
6.80
7.30
7.80
8.30
8.50-0.20+(7.25-8.50)+0.43
6.50-0.20+(7.50-6.50)-0.30
Futures price when you sell your crop – Local basis at the
time you sell – Premium paid for option + Intrinsic value of
option (if any) = Net return
37
net return $
do nothing
buy put
hedge or contract
7.30
7.00
7.50
future price
38