Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
INTERNATIONAL
FINANCIAL
MANAGEMENT
EUN / RESNICK
Second Edition
9Chapter NineFutures and Options on Foreign Exchange
Chapter Objective:
This chapter discusses exchange-traded currency
futures contracts,options contracts,and options on
currency futures,
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Chapter Outline
? Futures Contracts,Preliminaries
? Currency Futures Markets
? Basic Currency Futures Relationships
? Eurodollar Interest Rate Futures Contracts
? Options Contracts,Preliminaries
? Currency Options Markets
? Currency Futures Options
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Chapter Outline (continued)
? Basic Option Pricing Relationships at Expiry
? American Option Pricing Relationships
? European Option Pricing Relationships
? Binomial Option Pricing Model
? European Option Pricing Model
? Empirical Tests of Currency Option Models
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Futures Contracts,Preliminaries
? A futures contract is like a forward contract:
? It specifies that a certain currency will be
exchanged for another at a specified time in the
future at prices specified today.
? A futures contract is different from a forward
contract:
? Futures are standardized contracts trading on
organized exchanges with daily resettlement
through a clearinghouse.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Futures Contracts,Preliminaries
? Standardizing Features:
? Contract Size
? Delivery Month
? Daily resettlement
? Initial Margin (about 4% of contract value,cash or
T-bills held in a street name at your brokers).
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Daily Resettlement,An Example
? Suppose you want to speculate on a rise in the $/￥
exchange rate (specifically you think that the
dollar will appreciate),
Currently $1 = ￥140,The 3-month forward price is $1=￥150.
C u r r e n c y p e r
U,S, $ e q u iv a le n t U,S, $
W e d Tue W e d Tue
J a pa n ( y e n) 0, 0 0 7 1 4 2 8 5 7 0, 0 0 7 1 9 4 2 4 5 140 139
1 - m o n t h f o r w a r d 0, 0 0 6 9 9 3 0 0 7 0, 0 0 7 0 4 2 2 5 4 143 142
3 - m o n t h s f o r w a r d 0, 0 0 6 6 6 6 6 6 7 0, 0 0 6 7 1 1 4 0 9 150 149
6 - m o n t h s f o r w a r d 0, 0 0 6 2 5 0, 0 0 6 2 8 9 3 0 8 160 159
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Daily Resettlement,An Example
? Currently $1 = ￥140 and it appears that the dollar
is strengthening,
? If you enter into a 3-month futures contract to sell
￥ at the rate of $1 = ￥150 you will make money if
the yen depreciates,The contract size is
￥12,500,000
? Your initial margin is 4% of the contract value:
5 0
$10? 2,5 0 0,0 0,0 4 $ 3,3 3 3, 3 3 ???
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Daily Resettlement,An Example
If tomorrow,the futures rate closes at $1 = ￥149,
then your position’s value drops.
Your original agreement was to sell ￥12,500,000
and receive $83,333.33
But now ￥12,500,000 is worth $83,892.62
4 9
$10? 2,5 0 0,0 062.892,83$ ??
You have lost $559.28 overnight.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Daily Resettlement,An Example
? The $559.28 comes out of your $3,333.33 margin
account,leaving $2,774.05
? This is short of the $3,355.70 required for a new
position.
4 9
$10? 2,5 0 0,0 0,0 4 $ 3,3 5 5, 7 0 ???
?Your broker will let you slide until you run
through your maintenance margin,Then you must
post additional funds or your position will be closed
out,This is usually done with a reversing trade.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Currency Futures Markets
? The Chicago Mercantile Exchange (CME) is by
far the largest,
? Others include:
? The Philadelphia Board of Trade (PBOT)
? The MidAmerica commodities Exchange
? The Tokyo International Financial Futures Exchange
? The London International Financial Futures Exchange
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
The Chicago Mercantile Exchange
? Expiry cycle,March,June,September,December.
? Delivery date 3rd Wednesday of delivery month.
? Last trading day is the second business day
preceding the delivery day.
? CME hours 7:20 a.m,to 2:00 p.m,CST.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
CME After Hours
? Extended-hours trading on GLOBEX runs from
2:30 p.m,to 4:00 p.m dinner break and then back
at it from 6:00 p.m,to 6:00 a.m,CST.
? Singapore International Monetary Exchange
(SIMEX) offer interchangeable contracts.
? There’s other markets,but none are close to CME
and SIMEX trading volume.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Basic Currency
Futures Relationships
? Open Interest refers to the number of contracts
outstanding for a particular delivery month.
? Open interest is a good proxy for demand for a
contract.
? Some refer to open interest as the depth of the
market,The breadth of the market would be how
many different contracts (expiry month,currency)
are outstanding.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Reading a Futures Quote
O pen Hi Lo Set t l e Chang e Li f et i m e
H i g h
Li f et i m e
Low
O pen
I nt er es t
Sept,9282,9325,9276,9309 +,0027 1.2085,8636 74,639
Expiry month
Opening price
Highest price that day
Lowest price that day
Closing price
Daily Change
Highest and lowest
prices over the
lifetime of the
contract.
Number of open contracts
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reserved,
Eurodollar Interest Rate
Futures Contracts
? Widely used futures contract for hedging short-
term U.S,dollar interest rate risk.
? The underlying asset is a hypothetical $1,000,000
90-day Eurodollar deposit—the contract is cash
settled.
? Traded on the CME and the Singapore
International Monetary Exchange.
? The contract trades in the March,June,September
and December cycle.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Reading Eurodollar Futures Quotes
EURODOLLAR (CME)— $1 million; pts of 100%
Open High Low Settle Chg Yield
Settle Change
Open
Interest
July 94.69 94.69 94.68 94.68 -.01 5.32 +.01 47,417
Eurodollar futures prices are stated as an index number of three-month
LIBOR calculated as F = 100-LIBOR.
The closing price for the July contract is 94.68 thus the implied yield is
5.32 percent = 100 – 98.68
The change was,01 percent of $1 million representing $100 on an
annual basis,Since it is a 3-month contract one basis point corresponds
to a $25 price change.
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reserved,
Options Contracts,Preliminaries
? An option gives the holder the right,but not the
obligation,to buy or sell a given quantity of an
asset in the future,at prices agreed upon today.
? Calls vs,Puts
? Call options gives the holder the right,but not the
obligation,to buy a given quantity of some asset at
some time in the future,at prices agreed upon today.
? Put options gives the holder the right,but not the
obligation,to sell a given quantity of some asset at
some time in the future,at prices agreed upon today.
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reserved,
Options Contracts,Preliminaries
? European vs,American options
? European options can only be exercised on the
expiration date.
? American options can be exercised at any time up to
and including the expiration date.
? Since this option to exercise early generally has value,
American options are usually worth more than
European options,other things equal.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Options Contracts,Preliminaries
? In-the-money
? The exercise price is less than the spot price of the
underlying asset.
? At-the-money
? The exercise price is equal to the spot price of the
underlying asset.
? Out-of-the-money
? The exercise price is more than the spot price of the
underlying asset.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Options Contracts,Preliminaries
? Intrinsic Value
? The difference between the exercise price of the option
and the spot price of the underlying asset.
? Speculative Value
? The difference between the option premium and the
intrinsic value of the option.
Option
Premium =
Intrinsic
Value
Speculative
Value+
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Currency Options Markets
? PHLX
? HKFE
? 20-hour trading day.
? OTC volume is much bigger than exchange
volume.
? Trading is in seven major currencies plus the euro
against the U.S,dollar.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
PHLX Currency Option Specifications
Curre ncy Cont rac t Size
Aus tr alian doll ar AD50,000
Brit ish pound ￡ 31,250
Ca nadian doll ar CD 50,000
Deuts ch e m ark DM 62,500
Fr enc h f r anc FF 250,000
J apa ne s e y e n ￥ 6,250,000
Swiss f r anc SF 62,500
E ur o
62,500
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reserved,
Currency Futures Options
? Are an option on a currency futures contract.
? Exercise of a currency futures option results in a
long futures position for the holder of a call or the
writer of a put.
? Exercise of a currency futures option results in a
short futures position for the seller of a call or the
buyer of a put.
? If the futures position is not offset prior to its
expiration,foreign currency will change hands.
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reserved,
Basic Option Pricing
Relationships at Expiry
? At expiry,an American call option is worth the
same as a European option with the same
characteristics.
? If the call is in-the-money,it is worth ST – E.
? If the call is out-of-the-money,it is worthless.
CaT = CeT = Max[ST - E,0]
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reserved,
Basic Option Pricing
Relationships at Expiry
? At expiry,an American put option is worth the
same as a European option with the same
characteristics.
? If the put is in-the-money,it is worth E - ST.
? If the put is out-of-the-money,it is worthless.
PaT = PeT = Max[E - ST,0]
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reserved,
Basic Option Profit Profiles
CaT = CeT = Max[ST - E,0]
profit
loss
E E+C
ST
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reserved,
Basic Option Profit Profiles
CaT = CeT = Max[ST - E,0]
profit
loss
E E+C ST
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reserved,
Basic Option Profit Profiles
PaT = PeT = Max[E - ST,0]
profit
loss
E
E - p
ST
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reserved,
Basic Option Profit Profiles
CaT = CeT = Max[ST - E,0]
profit
loss
E
ST
E - p
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reserved,
American Option Pricing
Relationships
? With an American option,you can do everything
that you can do with a European option—this
option to exercise early has value.
CaT > CeT = Max[ST - E,0]
PaT > PeT = Max[E - ST,0]
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reserved,
Market Value,Time Value and
Intrinsic Value for an American Call
CaT > Max[ST - E,0]
Profit
loss
E ST
Market Value
Intrinsic value
Time value
Out-of-the-money In-the-money
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reserved,
European Option Pricing Relationships
Consider two investments
1 Buy a call option on the British pound futures
contract,The cash flow today is -Ce
2 Replicate the upside payoff of the call by
1 Borrowing the present value of the exercise price of
the call in the U.S,at i$ The cash flow today is
E /(1 + i$)
2 Lending the present value of ST at i￡ The cash flow is
- ST /(1 + i￡)
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reserved,
European Option Pricing Relationships
When the option is in-the-money both strategies
have the same payoff.
When the option is out-of-the-money it has a
higher payoff the borrowing and lending
strategy,
Thus:
0,
)1()1(
m a x
$￡
?
?
?
?
?
?
?
?
?
?
i
E
i
S
C Te
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
European Option Pricing Relationships
Using a similar portfolio to replicate the upside
potential of a put,we can show that:
0,
)1()1(
m a x
￡$
?
?
?
?
?
?
?
?
?
?
i
S
i
E
P Te
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Binomial Option Pricing Model
? Imagine a simple world where the dollar-euro
exchange rate is S0($/ ) = $1 today and in the
next year,S1($/ ) is either $1.1 or $.90.
$1
$.90
$1.10
S0($/ ) S1($/ )
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reserved,
Binomial Option Pricing Model
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )
? A call option on the euro with exercise price
S0($/ ) = $1 will have the following payoffs.
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reserved,
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )
Binomial Option Pricing Model
? We can replicate the payoffs of the call option,
With a levered position in the euro.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )
Binomial Option Pricing Model
debt
-$.90
-$.90
portfolio
$.20
$.00
Borrow the present value of $.90 today and buy 1,
Your net payoff in one period is either $.2 or $0.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Binomial Option Pricing Model
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )debt
-$.90
-$.90
portfolio
$.20
$.00
? The portfolio has twice the option’s payoff so the
portfolio is worth twice the call option value.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )debt
-$.90
-$.90
portfolio
$.20
$.00
Binomial Option Pricing Model
The portfolio value today is today’s
value of one euro less the present value
of a $.90 debt,)1(
90$.1$
$i?
?
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Binomial Option Pricing Model
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )debt
-$.90
-$.90
portfolio
$.20
$.00
We can value the option as half
of the value of the portfolio:
???
?
???
?
??? )1(
90$.1$
2
1
$
0 iC
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Binomial Option Pricing Model
? The most important lesson from the binomial
option pricing model is:
the replicating portfolio intuition.
? Many derivative securities can be valued by
valuing portfolios of primitive securities when
those portfolios have the same payoffs as the
derivative securities.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
European Option Pricing Formula
? We can use the replicating portfolio intuition
developed in the binomial option pricing formula
to generate a faster-to-use model that addresses a
much more realistic world,
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reserved,
European Option Pricing Formula
The model is TredNEdNFC
$)]()([ 210 ?????
Where
C0 = the value of a European option at time t = 0
Trrt eSF )( ￡$ ??
r$ = the interest rate available in the U.S.
r￡ = the interest rate available in the foreign country—in
this case the U.K.
,5.)/l n (
2
1 T
TEFd
?
??? Tdd ??? 12
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
European Option Pricing Formula
Find the value of a six-month call option on the
British pound with an exercise price of $1.50 = ￡1
The current value of a pound is $1.60
The interest rate available in the U.S,is r$ = 5%.
The interest rate in the U.K,is r￡ = 7%.
The option maturity is 6 months (half of a year).
The volatility of the $/￡ exchange rate is 30% p.a.
Before we start,note that the intrinsic value of the
option is $.10—our answer must be at least that.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
European Option Pricing Formula
Let’s try our hand at using the model,If you have a
calculator handy,follow along.
Then,calculate d1 and d2
1 0 6 0 6 6.05.4,5.)4.0(5.)50.1/4 8 5 0 7 5.1l n (5.)/l n (
22
1 ?
????
T
TEFd
?
?
First calculate
485075.150.1 50.0)07.05(.)( ￡$ ??? ?? eeSF Trrt
1 7 6 8 7 8.05.4.1 0 6 0 6 6.012 ?????? Tdd ?
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
European Option Pricing Formula
N(d1) = N(0.106066) =,5422
N(d2) = N(-0.1768) = 0.4298
TredNEdNFC $)]()([ 210 ?????
157.0$]4 2 9 8.50.15 4 2 2.4 8 5 0 7 5.1[ 5.*05.0 ????? ?eC
4 8 5 0 7 5.1?F
1 0 6 0 6 6.01 ?d
1 7 6 8 7 8.02 ??d
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reserved,
Option Value Determinants
Call Put
1,Exchange rate + –
2,Exercise price – +
3,Interest rate in U.S,+ –
4,Interest rate in other country + –
5,Variability in exchange rate + +
6,Expiration date + +
The value of a call option C0 must fall within
max (S0 – E,0) < C0 < S0.
The precise position will depend on the above factors.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Empirical Tests
The European option pricing model works fairly
well in pricing American currency options.
It works best for out-of-the-money and at-the-money
options.
When options are in-the-money,the European
option pricing model tends to underprice
American options.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
End Chapter Nine
reserved,
INTERNATIONAL
FINANCIAL
MANAGEMENT
EUN / RESNICK
Second Edition
9Chapter NineFutures and Options on Foreign Exchange
Chapter Objective:
This chapter discusses exchange-traded currency
futures contracts,options contracts,and options on
currency futures,
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Chapter Outline
? Futures Contracts,Preliminaries
? Currency Futures Markets
? Basic Currency Futures Relationships
? Eurodollar Interest Rate Futures Contracts
? Options Contracts,Preliminaries
? Currency Options Markets
? Currency Futures Options
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Chapter Outline (continued)
? Basic Option Pricing Relationships at Expiry
? American Option Pricing Relationships
? European Option Pricing Relationships
? Binomial Option Pricing Model
? European Option Pricing Model
? Empirical Tests of Currency Option Models
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Futures Contracts,Preliminaries
? A futures contract is like a forward contract:
? It specifies that a certain currency will be
exchanged for another at a specified time in the
future at prices specified today.
? A futures contract is different from a forward
contract:
? Futures are standardized contracts trading on
organized exchanges with daily resettlement
through a clearinghouse.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Futures Contracts,Preliminaries
? Standardizing Features:
? Contract Size
? Delivery Month
? Daily resettlement
? Initial Margin (about 4% of contract value,cash or
T-bills held in a street name at your brokers).
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Daily Resettlement,An Example
? Suppose you want to speculate on a rise in the $/￥
exchange rate (specifically you think that the
dollar will appreciate),
Currently $1 = ￥140,The 3-month forward price is $1=￥150.
C u r r e n c y p e r
U,S, $ e q u iv a le n t U,S, $
W e d Tue W e d Tue
J a pa n ( y e n) 0, 0 0 7 1 4 2 8 5 7 0, 0 0 7 1 9 4 2 4 5 140 139
1 - m o n t h f o r w a r d 0, 0 0 6 9 9 3 0 0 7 0, 0 0 7 0 4 2 2 5 4 143 142
3 - m o n t h s f o r w a r d 0, 0 0 6 6 6 6 6 6 7 0, 0 0 6 7 1 1 4 0 9 150 149
6 - m o n t h s f o r w a r d 0, 0 0 6 2 5 0, 0 0 6 2 8 9 3 0 8 160 159
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Daily Resettlement,An Example
? Currently $1 = ￥140 and it appears that the dollar
is strengthening,
? If you enter into a 3-month futures contract to sell
￥ at the rate of $1 = ￥150 you will make money if
the yen depreciates,The contract size is
￥12,500,000
? Your initial margin is 4% of the contract value:
5 0
$10? 2,5 0 0,0 0,0 4 $ 3,3 3 3, 3 3 ???
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Daily Resettlement,An Example
If tomorrow,the futures rate closes at $1 = ￥149,
then your position’s value drops.
Your original agreement was to sell ￥12,500,000
and receive $83,333.33
But now ￥12,500,000 is worth $83,892.62
4 9
$10? 2,5 0 0,0 062.892,83$ ??
You have lost $559.28 overnight.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Daily Resettlement,An Example
? The $559.28 comes out of your $3,333.33 margin
account,leaving $2,774.05
? This is short of the $3,355.70 required for a new
position.
4 9
$10? 2,5 0 0,0 0,0 4 $ 3,3 5 5, 7 0 ???
?Your broker will let you slide until you run
through your maintenance margin,Then you must
post additional funds or your position will be closed
out,This is usually done with a reversing trade.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Currency Futures Markets
? The Chicago Mercantile Exchange (CME) is by
far the largest,
? Others include:
? The Philadelphia Board of Trade (PBOT)
? The MidAmerica commodities Exchange
? The Tokyo International Financial Futures Exchange
? The London International Financial Futures Exchange
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
The Chicago Mercantile Exchange
? Expiry cycle,March,June,September,December.
? Delivery date 3rd Wednesday of delivery month.
? Last trading day is the second business day
preceding the delivery day.
? CME hours 7:20 a.m,to 2:00 p.m,CST.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
CME After Hours
? Extended-hours trading on GLOBEX runs from
2:30 p.m,to 4:00 p.m dinner break and then back
at it from 6:00 p.m,to 6:00 a.m,CST.
? Singapore International Monetary Exchange
(SIMEX) offer interchangeable contracts.
? There’s other markets,but none are close to CME
and SIMEX trading volume.
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Basic Currency
Futures Relationships
? Open Interest refers to the number of contracts
outstanding for a particular delivery month.
? Open interest is a good proxy for demand for a
contract.
? Some refer to open interest as the depth of the
market,The breadth of the market would be how
many different contracts (expiry month,currency)
are outstanding.
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Reading a Futures Quote
O pen Hi Lo Set t l e Chang e Li f et i m e
H i g h
Li f et i m e
Low
O pen
I nt er es t
Sept,9282,9325,9276,9309 +,0027 1.2085,8636 74,639
Expiry month
Opening price
Highest price that day
Lowest price that day
Closing price
Daily Change
Highest and lowest
prices over the
lifetime of the
contract.
Number of open contracts
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reserved,
Eurodollar Interest Rate
Futures Contracts
? Widely used futures contract for hedging short-
term U.S,dollar interest rate risk.
? The underlying asset is a hypothetical $1,000,000
90-day Eurodollar deposit—the contract is cash
settled.
? Traded on the CME and the Singapore
International Monetary Exchange.
? The contract trades in the March,June,September
and December cycle.
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reserved,
Reading Eurodollar Futures Quotes
EURODOLLAR (CME)— $1 million; pts of 100%
Open High Low Settle Chg Yield
Settle Change
Open
Interest
July 94.69 94.69 94.68 94.68 -.01 5.32 +.01 47,417
Eurodollar futures prices are stated as an index number of three-month
LIBOR calculated as F = 100-LIBOR.
The closing price for the July contract is 94.68 thus the implied yield is
5.32 percent = 100 – 98.68
The change was,01 percent of $1 million representing $100 on an
annual basis,Since it is a 3-month contract one basis point corresponds
to a $25 price change.
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reserved,
Options Contracts,Preliminaries
? An option gives the holder the right,but not the
obligation,to buy or sell a given quantity of an
asset in the future,at prices agreed upon today.
? Calls vs,Puts
? Call options gives the holder the right,but not the
obligation,to buy a given quantity of some asset at
some time in the future,at prices agreed upon today.
? Put options gives the holder the right,but not the
obligation,to sell a given quantity of some asset at
some time in the future,at prices agreed upon today.
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reserved,
Options Contracts,Preliminaries
? European vs,American options
? European options can only be exercised on the
expiration date.
? American options can be exercised at any time up to
and including the expiration date.
? Since this option to exercise early generally has value,
American options are usually worth more than
European options,other things equal.
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reserved,
Options Contracts,Preliminaries
? In-the-money
? The exercise price is less than the spot price of the
underlying asset.
? At-the-money
? The exercise price is equal to the spot price of the
underlying asset.
? Out-of-the-money
? The exercise price is more than the spot price of the
underlying asset.
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reserved,
Options Contracts,Preliminaries
? Intrinsic Value
? The difference between the exercise price of the option
and the spot price of the underlying asset.
? Speculative Value
? The difference between the option premium and the
intrinsic value of the option.
Option
Premium =
Intrinsic
Value
Speculative
Value+
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Currency Options Markets
? PHLX
? HKFE
? 20-hour trading day.
? OTC volume is much bigger than exchange
volume.
? Trading is in seven major currencies plus the euro
against the U.S,dollar.
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reserved,
PHLX Currency Option Specifications
Curre ncy Cont rac t Size
Aus tr alian doll ar AD50,000
Brit ish pound ￡ 31,250
Ca nadian doll ar CD 50,000
Deuts ch e m ark DM 62,500
Fr enc h f r anc FF 250,000
J apa ne s e y e n ￥ 6,250,000
Swiss f r anc SF 62,500
E ur o
62,500
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reserved,
Currency Futures Options
? Are an option on a currency futures contract.
? Exercise of a currency futures option results in a
long futures position for the holder of a call or the
writer of a put.
? Exercise of a currency futures option results in a
short futures position for the seller of a call or the
buyer of a put.
? If the futures position is not offset prior to its
expiration,foreign currency will change hands.
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reserved,
Basic Option Pricing
Relationships at Expiry
? At expiry,an American call option is worth the
same as a European option with the same
characteristics.
? If the call is in-the-money,it is worth ST – E.
? If the call is out-of-the-money,it is worthless.
CaT = CeT = Max[ST - E,0]
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
Basic Option Pricing
Relationships at Expiry
? At expiry,an American put option is worth the
same as a European option with the same
characteristics.
? If the put is in-the-money,it is worth E - ST.
? If the put is out-of-the-money,it is worthless.
PaT = PeT = Max[E - ST,0]
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reserved,
Basic Option Profit Profiles
CaT = CeT = Max[ST - E,0]
profit
loss
E E+C
ST
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reserved,
Basic Option Profit Profiles
CaT = CeT = Max[ST - E,0]
profit
loss
E E+C ST
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reserved,
Basic Option Profit Profiles
PaT = PeT = Max[E - ST,0]
profit
loss
E
E - p
ST
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reserved,
Basic Option Profit Profiles
CaT = CeT = Max[ST - E,0]
profit
loss
E
ST
E - p
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reserved,
American Option Pricing
Relationships
? With an American option,you can do everything
that you can do with a European option—this
option to exercise early has value.
CaT > CeT = Max[ST - E,0]
PaT > PeT = Max[E - ST,0]
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reserved,
Market Value,Time Value and
Intrinsic Value for an American Call
CaT > Max[ST - E,0]
Profit
loss
E ST
Market Value
Intrinsic value
Time value
Out-of-the-money In-the-money
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reserved,
European Option Pricing Relationships
Consider two investments
1 Buy a call option on the British pound futures
contract,The cash flow today is -Ce
2 Replicate the upside payoff of the call by
1 Borrowing the present value of the exercise price of
the call in the U.S,at i$ The cash flow today is
E /(1 + i$)
2 Lending the present value of ST at i￡ The cash flow is
- ST /(1 + i￡)
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reserved,
European Option Pricing Relationships
When the option is in-the-money both strategies
have the same payoff.
When the option is out-of-the-money it has a
higher payoff the borrowing and lending
strategy,
Thus:
0,
)1()1(
m a x
$￡
?
?
?
?
?
?
?
?
?
?
i
E
i
S
C Te
Irwin/McGraw-Hill Copyright ? 2001 by The McGraw-Hill Companies,Inc,All rights
reserved,
European Option Pricing Relationships
Using a similar portfolio to replicate the upside
potential of a put,we can show that:
0,
)1()1(
m a x
￡$
?
?
?
?
?
?
?
?
?
?
i
S
i
E
P Te
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reserved,
Binomial Option Pricing Model
? Imagine a simple world where the dollar-euro
exchange rate is S0($/ ) = $1 today and in the
next year,S1($/ ) is either $1.1 or $.90.
$1
$.90
$1.10
S0($/ ) S1($/ )
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reserved,
Binomial Option Pricing Model
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )
? A call option on the euro with exercise price
S0($/ ) = $1 will have the following payoffs.
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reserved,
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )
Binomial Option Pricing Model
? We can replicate the payoffs of the call option,
With a levered position in the euro.
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reserved,
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )
Binomial Option Pricing Model
debt
-$.90
-$.90
portfolio
$.20
$.00
Borrow the present value of $.90 today and buy 1,
Your net payoff in one period is either $.2 or $0.
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reserved,
Binomial Option Pricing Model
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )debt
-$.90
-$.90
portfolio
$.20
$.00
? The portfolio has twice the option’s payoff so the
portfolio is worth twice the call option value.
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reserved,
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )debt
-$.90
-$.90
portfolio
$.20
$.00
Binomial Option Pricing Model
The portfolio value today is today’s
value of one euro less the present value
of a $.90 debt,)1(
90$.1$
$i?
?
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reserved,
Binomial Option Pricing Model
$1
$.90
$1.10
S0($/ ) S1($/ )
$.10
$0
C1($/ )debt
-$.90
-$.90
portfolio
$.20
$.00
We can value the option as half
of the value of the portfolio:
???
?
???
?
??? )1(
90$.1$
2
1
$
0 iC
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reserved,
Binomial Option Pricing Model
? The most important lesson from the binomial
option pricing model is:
the replicating portfolio intuition.
? Many derivative securities can be valued by
valuing portfolios of primitive securities when
those portfolios have the same payoffs as the
derivative securities.
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reserved,
European Option Pricing Formula
? We can use the replicating portfolio intuition
developed in the binomial option pricing formula
to generate a faster-to-use model that addresses a
much more realistic world,
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reserved,
European Option Pricing Formula
The model is TredNEdNFC
$)]()([ 210 ?????
Where
C0 = the value of a European option at time t = 0
Trrt eSF )( ￡$ ??
r$ = the interest rate available in the U.S.
r￡ = the interest rate available in the foreign country—in
this case the U.K.
,5.)/l n (
2
1 T
TEFd
?
??? Tdd ??? 12
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reserved,
European Option Pricing Formula
Find the value of a six-month call option on the
British pound with an exercise price of $1.50 = ￡1
The current value of a pound is $1.60
The interest rate available in the U.S,is r$ = 5%.
The interest rate in the U.K,is r￡ = 7%.
The option maturity is 6 months (half of a year).
The volatility of the $/￡ exchange rate is 30% p.a.
Before we start,note that the intrinsic value of the
option is $.10—our answer must be at least that.
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reserved,
European Option Pricing Formula
Let’s try our hand at using the model,If you have a
calculator handy,follow along.
Then,calculate d1 and d2
1 0 6 0 6 6.05.4,5.)4.0(5.)50.1/4 8 5 0 7 5.1l n (5.)/l n (
22
1 ?
????
T
TEFd
?
?
First calculate
485075.150.1 50.0)07.05(.)( ￡$ ??? ?? eeSF Trrt
1 7 6 8 7 8.05.4.1 0 6 0 6 6.012 ?????? Tdd ?
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European Option Pricing Formula
N(d1) = N(0.106066) =,5422
N(d2) = N(-0.1768) = 0.4298
TredNEdNFC $)]()([ 210 ?????
157.0$]4 2 9 8.50.15 4 2 2.4 8 5 0 7 5.1[ 5.*05.0 ????? ?eC
4 8 5 0 7 5.1?F
1 0 6 0 6 6.01 ?d
1 7 6 8 7 8.02 ??d
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reserved,
Option Value Determinants
Call Put
1,Exchange rate + –
2,Exercise price – +
3,Interest rate in U.S,+ –
4,Interest rate in other country + –
5,Variability in exchange rate + +
6,Expiration date + +
The value of a call option C0 must fall within
max (S0 – E,0) < C0 < S0.
The precise position will depend on the above factors.
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reserved,
Empirical Tests
The European option pricing model works fairly
well in pricing American currency options.
It works best for out-of-the-money and at-the-money
options.
When options are in-the-money,the European
option pricing model tends to underprice
American options.
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reserved,
End Chapter Nine
