2.1
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Futures Markets and
the Use of Futures
for Hedging
Chapter 2
2.2
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Futures Contracts
Available on a wide range of underlyings
Exchange traded
Specifications(规定 ) need to be defined:
– What can be delivered,
– Where it can be delivered,&
– When it can be delivered
Settled(结算 ) daily
2.3
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Margins(保证金 )
A margin is cash or marketable
securities deposited by an investor with
his or her broker
The balance(余额 ) in the margin
account（保证金帐户） is adjusted to
reflect daily settlement
Margins minimize the possibility of a
loss through a default(违约 ) on a
contract
2.4
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Example of a Futures Trade
An investor takes a long position in
2 December gold futures contracts
on June 3
– contract size is 100 oz.
– futures price is US$400 per oz.
– Initial margin(初始保证金 ) requirement is
US$2,000/contract (US$4,000 in total)
– maintenance margin(维持保证金 ) is
US$1,500/contract (US$3,000 in total)
2.5
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
A Possible Outcome
Table 2.1,Page 25
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
400.00 4,000
3-Jun 397.00 (600) (600) 3,400 0.,,,,,
.,,,,,.,,,,,
11-Jun 393.30 (420) (1,340) 2,660 1,340.,,,,,
.,,,,.,,,,,
17-Jun 387.00 (1,140) (2,600) 2,740 1,260.,,,,,
.,,,,,.,,,,,
24-Jun 392.30 260 (1,540) 5,060 0
+
= 4,000
3,000
+
= 4,000
<
保证金催付
2.6
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Other Key Points About
Futures
They are settled daily
Closing out(平仓 ) a futures
position involves entering into
an offsetting(反向 ) trade
Most contracts are closed out
before maturity
2.7
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Delivery
If a contract is not closed out before maturity,
it usually settled by delivering the assets
underlying the contract,When there are
alternatives about what is delivered,where it
is delivered,and when it is delivered,the
party with the short position chooses.
A few contracts (for example,those on stock
indices and Eurodollars) are settled in cash.
2.8
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Some Terminologies
Open interest(未平仓合约数 ),the total
number of contracts outstanding
– equal to number of long positions or
number of short positions
Settlement price(结算价格 ),the price just
before the final bell each day
– used for the daily settlement process
Volume of trading(交易量 ),the number of
trades in 1 day
2.9
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Convergence of Futures to
Spot (Figure 2.1,page 32)
Time Time
(a) (b)
Futures
Price
Futures
PriceSpot Price
Spot Price
2.10
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Questions
When a new trade is completed
what are the possible effects on
the open interest?
Can the volume of trading in a day
be greater than the open interest?
2.11
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Regulation of Futures
Regulation is designed to
protect the public interest
Regulators try to prevent
questionable trading practices
by either individuals on the floor
of the exchange or outside
groups
2.12
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Accounting & Tax
If a contract is used for
– Hedging,it is logical to recognize
profits (losses) at the same time as on
the item being hedged
– Speculation,it is logical to recognize
profits (losses) on a mark to market
basis
Roughly speaking,this is what the
treatment of futures in the U.S.and many
other countries attempts to achieve
2.13
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Long & Short Hedges
A long futures hedge(多头期货套期保值 ) is appropriate when you know you
will purchase an asset in the future &
want to lock in the price
A short futures hedge(空头期货套期保值 ) is appropriate when you know you
will sell an asset in the future & want
to lock in the price
2.14
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Basis Risk
Basis(基差 ) is the difference
between spot price of asset
to be hedged & futures price
of contract used
Basis risk (基差风险 ) arises
because of the uncertainty
about the basis when the
hedge is closed out
2.15
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Long Hedge
Suppose that
F1,Initial Futures Price
F2,Final Futures Price
S2,Final Asset Price
You hedge the future purchase of an
asset by entering into a long futures
contract
Cost of Asset=S2 +F1-F2 = F1 + Basis2
2.16
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Short Hedge
Suppose that
F1,Initial Futures Price
F2,Final Futures Price
S2,Final Asset Price
You hedge the future sale of an asset
by entering into a short futures contract
Price Realized=S2 +F1-F2 = F1 + Basis2
2.17
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Choice of Contract
Choose a delivery month that is as
close as possible to,but later than,the
end of the life of the hedge
When there is no futures contract on the
asset being hedged,choose the
contract whose futures price is most
highly correlated with the asset price,
There are then 2 components to basis
2.18
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Optimal Hedge Ratio
The hedge ratio h(套期比例 ) is the ratio
of the size of the position taken in futures
contracts to the size of the exposure.
Proportion of the exposure that should
optimally be hedged is
where
h S
F
2.19
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
S,spot price,
F,futures price,
S,standard deviation of DS,change
in spot price during the life of the
hedge
F,standard deviation of DF,change
in the futures price,
,coefficient of correlation between
DS & DF
Proof,page 39.
2.20
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Rolling The Hedge Forward
We can use a series of futures
contracts to increase the life of a
hedge
Each time we switch from 1 futures
contract to another we incur a type of
basis risk
2.21
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Forward Contracts vs Futures
Contracts (Table 2.3,page 44)
Private contract between 2 parties Exchange traded
Non-standard contract Standard contract
Usually 1 specified delivery date Range of delivery dates
Settled at maturity Settled daily
Delivery or final cash
settlement usually occurs
Contract usually closed out
prior to maturity
FORWARDS FUTURES
2.22
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Assignments
(page 46-49,4th edition)
2.6,2.10,2.12,2.14,2.19
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Futures Markets and
the Use of Futures
for Hedging
Chapter 2
2.2
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Futures Contracts
Available on a wide range of underlyings
Exchange traded
Specifications(规定 ) need to be defined:
– What can be delivered,
– Where it can be delivered,&
– When it can be delivered
Settled(结算 ) daily
2.3
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Margins(保证金 )
A margin is cash or marketable
securities deposited by an investor with
his or her broker
The balance(余额 ) in the margin
account（保证金帐户） is adjusted to
reflect daily settlement
Margins minimize the possibility of a
loss through a default(违约 ) on a
contract
2.4
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Example of a Futures Trade
An investor takes a long position in
2 December gold futures contracts
on June 3
– contract size is 100 oz.
– futures price is US$400 per oz.
– Initial margin(初始保证金 ) requirement is
US$2,000/contract (US$4,000 in total)
– maintenance margin(维持保证金 ) is
US$1,500/contract (US$3,000 in total)
2.5
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
A Possible Outcome
Table 2.1,Page 25
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
400.00 4,000
3-Jun 397.00 (600) (600) 3,400 0.,,,,,
.,,,,,.,,,,,
11-Jun 393.30 (420) (1,340) 2,660 1,340.,,,,,
.,,,,.,,,,,
17-Jun 387.00 (1,140) (2,600) 2,740 1,260.,,,,,
.,,,,,.,,,,,
24-Jun 392.30 260 (1,540) 5,060 0
+
= 4,000
3,000
+
= 4,000
<
保证金催付
2.6
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Other Key Points About
Futures
They are settled daily
Closing out(平仓 ) a futures
position involves entering into
an offsetting(反向 ) trade
Most contracts are closed out
before maturity
2.7
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Delivery
If a contract is not closed out before maturity,
it usually settled by delivering the assets
underlying the contract,When there are
alternatives about what is delivered,where it
is delivered,and when it is delivered,the
party with the short position chooses.
A few contracts (for example,those on stock
indices and Eurodollars) are settled in cash.
2.8
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Some Terminologies
Open interest(未平仓合约数 ),the total
number of contracts outstanding
– equal to number of long positions or
number of short positions
Settlement price(结算价格 ),the price just
before the final bell each day
– used for the daily settlement process
Volume of trading(交易量 ),the number of
trades in 1 day
2.9
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Convergence of Futures to
Spot (Figure 2.1,page 32)
Time Time
(a) (b)
Futures
Price
Futures
PriceSpot Price
Spot Price
2.10
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Questions
When a new trade is completed
what are the possible effects on
the open interest?
Can the volume of trading in a day
be greater than the open interest?
2.11
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Regulation of Futures
Regulation is designed to
protect the public interest
Regulators try to prevent
questionable trading practices
by either individuals on the floor
of the exchange or outside
groups
2.12
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Accounting & Tax
If a contract is used for
– Hedging,it is logical to recognize
profits (losses) at the same time as on
the item being hedged
– Speculation,it is logical to recognize
profits (losses) on a mark to market
basis
Roughly speaking,this is what the
treatment of futures in the U.S.and many
other countries attempts to achieve
2.13
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Long & Short Hedges
A long futures hedge(多头期货套期保值 ) is appropriate when you know you
will purchase an asset in the future &
want to lock in the price
A short futures hedge(空头期货套期保值 ) is appropriate when you know you
will sell an asset in the future & want
to lock in the price
2.14
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Basis Risk
Basis(基差 ) is the difference
between spot price of asset
to be hedged & futures price
of contract used
Basis risk (基差风险 ) arises
because of the uncertainty
about the basis when the
hedge is closed out
2.15
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Long Hedge
Suppose that
F1,Initial Futures Price
F2,Final Futures Price
S2,Final Asset Price
You hedge the future purchase of an
asset by entering into a long futures
contract
Cost of Asset=S2 +F1-F2 = F1 + Basis2
2.16
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Short Hedge
Suppose that
F1,Initial Futures Price
F2,Final Futures Price
S2,Final Asset Price
You hedge the future sale of an asset
by entering into a short futures contract
Price Realized=S2 +F1-F2 = F1 + Basis2
2.17
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Choice of Contract
Choose a delivery month that is as
close as possible to,but later than,the
end of the life of the hedge
When there is no futures contract on the
asset being hedged,choose the
contract whose futures price is most
highly correlated with the asset price,
There are then 2 components to basis
2.18
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Optimal Hedge Ratio
The hedge ratio h(套期比例 ) is the ratio
of the size of the position taken in futures
contracts to the size of the exposure.
Proportion of the exposure that should
optimally be hedged is
where
h S
F
2.19
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
S,spot price,
F,futures price,
S,standard deviation of DS,change
in spot price during the life of the
hedge
F,standard deviation of DF,change
in the futures price,
,coefficient of correlation between
DS & DF
Proof,page 39.
2.20
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Rolling The Hedge Forward
We can use a series of futures
contracts to increase the life of a
hedge
Each time we switch from 1 futures
contract to another we incur a type of
basis risk
2.21
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Forward Contracts vs Futures
Contracts (Table 2.3,page 44)
Private contract between 2 parties Exchange traded
Non-standard contract Standard contract
Usually 1 specified delivery date Range of delivery dates
Settled at maturity Settled daily
Delivery or final cash
settlement usually occurs
Contract usually closed out
prior to maturity
FORWARDS FUTURES
2.22
Options,Futures,and Other Derivatives,4th edition? 2000 by John C,Hull
Tang Yincai,? 2005
Assignments
(page 46-49,4th edition)
2.6,2.10,2.12,2.14,2.19
