INTERNATIONAL
FINANCIAL
MANAGEMENT
Fifth Edition
EUN / RESNICK
McGraw-Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
Futures and Options
on Foreign Exchange
7
Chapter Seven
Chapter Objective:
This chapter discusses exchange-traded currency
futures contracts, options contracts, and options on
currency futures.
7-1
Futures Contracts: Preliminaries

A futures contract is like a forward contract:


A futures contract is different from a forward
contract:

7-2
It specifies that a certain currency will be
exchanged for another at a specified time in the
future at prices specified today.
Futures are standardized contracts trading on
organized exchanges with daily resettlement
through a clearinghouse.
Futures Contracts: Preliminaries

Standardizing Features:



7-3
Contract Size
Delivery Month
Daily resettlement
Daily Resettlement: An Example





Consider a long position in the CME Euro/U.S.
Dollar contract.
It is written on €125,000 and quoted in $ per €.
The strike price is $1.30 the maturity is 3
months.
At initiation of the contract, the long posts an
initial performance bond of $6,500.
The maintenance performance bond is $4,000.
7-4
Daily Resettlement: An Example




Recall that an investor with a long position gains
from increases in the price of the underlying asset.
Our investor has agreed to BUY €125,000 at
$1.30 per euro in three months time.
With a forward contract, at the end of three
months, if the euro was worth $1.24, he would
lose $7,500 = ($1.24 – $1.30) × 125,000.
If instead at maturity the euro was worth $1.35,
the counterparty to his forward contract would
pay him $6,250 = ($1.35 – $1.30) × 125,000.
7-5
Daily Resettlement: An Example


With futures, we have daily resettlement of
gains an losses rather than one big settlement at
maturity.
Every trading day:



if the price goes down, the long pays the short
if the price goes up, the short pays the long
After the daily resettlement, each party has a
new contract at the new price with one-dayshorter maturity.
7-6
Performance Bond Money




Each day’s losses are subtracted from the
investor’s account.
Each day’s gains are added to the account.
In this example, at initiation the long posts an
initial performance bond of $6,500.
The maintenance level is $4,000.

7-7
If this investor loses more than $2,500 he has a
decision to make: he can maintain his long position
only by adding more funds—if he fails to do so, his
position will be closed out with an offsetting short
position.
Daily Resettlement: An Example

Over the first 3 days, the euro strengthens then
depreciates in dollar terms:
Settle
$1.31
$1.30
$1.27
Gain/Loss
Account Balance
$1,250 = ($1.31$7,750
– $1.30)×125,000
= $6,500 + $1,250
–$1,250
$6,500
–$3,750
$2,750 + $3,750 = $6,500
On third day suppose our investor keeps his long
position open by posting an additional $3,750.
7-8
Currency Futures Markets


The Chicago Mercantile Exchange (CME) is by
far the largest.
Others include:




7-9
The Philadelphia Board of Trade (PBOT)
The MidAmerica Commodities Exchange
The Tokyo International Financial Futures Exchange
The London International Financial Futures Exchange
Reading Currency Futures Quotes
OPEN
HIGH
LOW
SETTLE
CHG
OPEN
INT
.0028
.0025
172,396
2,266
Euro/US Dollar (CME)—€125,000; $ per €
Mar
Jun
1.4748
1.4737
1.4830
1.4818
1.4700
1.4693
1.4777
1.4763
Closing price
Expiry
month
Daily Change
Opening price
Lowest price that day
Number of open contracts
Highest price that day
7-10
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.
7-11
Reading Currency Futures Quotes
OPEN
HIGH
LOW
SETTLE
CHG
OPEN
INT
.0028
.0025
172,396
2,266
Euro/US Dollar (CME)—€125,000; $ per €
Mar
Jun
1.4748
1.4737
1.4830
1.4818
1.4700
1.4693
1.4777
1.4763
Notice that open interest is greatest in the nearby contract,
in this case March, 2008.
In general, open interest typically decreases with term to
maturity of most futures contracts.
7-12
Basic Currency Futures Relationships
OPEN
HIGH
LOW
SETTLE
CHG
OPEN
INT
.0028
.0025
172,396
2,266
Euro/US Dollar (CME)—€125,000; $ per €
Mar
Jun
1.4748
1.4737
1.4830
1.4818
1.4700
1.4693
1.4777
1.4763
The holder of a long position is committing himself to pay
$1.4777 per euro for €125,000—a $184,712.50 position.
As there are 172,396 such contracts outstanding, this
represents a notational principal of over $31.8 billion!
7-13
Reading Currency Futures Quotes
OPEN
HIGH
LOW
SETTLE
CHG
OPEN
INT
.0028
.0025
172,396
2,266
Euro/US Dollar (CME)—€125,000; $ per €
Mar
Jun
1.4748
1.4737
1.4830
1.4818
1.4700
1.4693
1.4777
1.4763
Recall from chapter 6, our interest rate parity condition:
1 + i$
F($/€)
=
1 + i€
S($/€)
7-14
Reading Currency Futures Quotes
OPEN
HIGH
LOW
SETTLE
CHG
OPEN
INT
.0028
.0025
172,396
2,266
Euro/US Dollar (CME)—€125,000; $ per €
Mar
Jun
1.4748
1.4737
1.4830
1.4818
1.4700
1.4693
1.4777
1.4763
From March to June 2008 we should expect lower interest
rates in dollar denominated accounts: if we find a higher rate in
a euro denominated account, we may have found an arbitrage.
7-15
Trading irregularities

Futures Markets are also a great place to launder
money

7-16
The zero sum nature of futures is the key to
laundering the money.
Money Laundering: Hillary
Clinton’s Cattle Futures
James B. Blair
outside counsel to
Tyson Foods Inc.,
Arkansas' largest
employer, gets
Hillary’s
discretionary
order.
7-17
winners
losers
Submits
identical long
and short trades
Robert L. "Red" Bone,
(Refco broker), allocates
trades ex post facto.
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


7-18
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.
Options Contracts: Preliminaries

European vs. American options



7-19
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.
Options Contracts: Preliminaries

In-the-money


At-the-money


The exercise price is less than the spot price of the
underlying asset.
The exercise price is equal to the spot price of the
underlying asset.
Out-of-the-money

7-20
The exercise price is more than the spot price of the
underlying asset.
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
7-21
=
Intrinsic
Value
+
Speculative
Value
PHLX Currency Option
Specifications
Currency
Australian dollar
British pound
Canadian dollar
Euro
Japanese yen
Swiss franc
Contract Size
AD10,000
£10,000
CAD10,000
€10,000
¥1,000,000
SF10,000
http://www.phlx.com/products/xdc_specs.htm
7-22
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]
7-23
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]
7-24
Basic Option Profit Profiles
Profit
Owner of the call
If the call is in-themoney, it is worth
ST – E.
Long 1 call
If the call is out-ofthe-money, it is
worthless and the
–c0
buyer of the call
loses his entire
investment of c0.
loss
7-25
ST
E + c0
E
Out-of-the-money
In-the-money
Basic Option Profit Profiles
Profit
Seller of the call
If the call is in-themoney, the writer
loses ST – E.
If the call is out-ofc0
the-money, the writer
keeps the option
premium.
ST
E + c0
E
loss
7-26
Out-of-the-money
In-the-money
short 1
call
Basic Option Profit Profiles
Profit
If the put is inthe-money, it is E – p
0
worth E – ST.
The maximum
gain is E – p0
If the put is outof-the-money, it
is worthless and – p0
the buyer of the
put loses his
entire investment
of p0.
loss
7-27
Owner of the put
ST
E – p0
long 1 put
E
In-the-money
Out-of-the-money
Basic Option Profit Profiles
If the put is inthe-money, it is
worth E –ST. The
maximum loss is
– E + p0
Profit
p0
If the put is outof-the-money, it
is worthless and
the seller of the
put keeps the
option premium
– E + p0
of p0.
loss
7-28
Seller of the put
ST
E – p0
E
short 1 put
Example



Profit
Consider a call
option on €31,250.
Long 1 call
on 1 pound
The option premium
is $0.25 per €
The exercise price is
$1.50 per €.
–$0.25
ST
$1.75
$1.50
loss
7-29
Example



Profit
Consider a call
option on €31,250.
Long 1 call
on €31,250
The option premium
is $0.25 per €
The exercise price is
$1.50 per €.
–$7,812.50
ST
$1.75
$1.50
loss
7-30
Example
Profit What is the maximum gain on this put option?
$42,187.50 = €31,250×($1.50 – $0.15)/€
$42,187.50


Consider a put
option on €31,250.
The option premium
is $0.15 per €
At what exchange rate do you break even?
ST
–$4,687.50
$1.35

The exercise price is
$1.50 per euro.
loss
7-31
$1.50
Long 1 put
on €31,250
$4,687.50 = €31,250×($0.15)/€
American Option Pricing
Relationships

With an American option, you can do
everything that you can do with a European
option AND you can exercise prior to expiry—
this option to exercise early has value, thus:
CaT > CeT = Max[ST - E, 0]
PaT > PeT = Max[E - ST, 0]
7-32
Market Value, Time Value and Intrinsic
Value for an American Call
Profit
The red line shows the
payoff at maturity, not
profit, of a call option.
Long 1 call
Note that even an outof-the-money option
has value—time value.
Intrinsic value
Time value
Out-of-the-money
loss
7-33
In-the-money
E
ST
European Option Pricing
Relationships
Consider two investments
1
Buy a European call option on the British pound
futures contract. The cash flow today is –Ce
2
Replicate the upside payoff of the call by
Borrowing the present value of the dollar exercise
price of the call in the U.S. at i$
1
E
The cash flow today is
(1 + i$)
2
Lending the present value of ST at i£
The cash flow today is
7-34
–
ST
(1 + i£)
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 than the borrowing and lending
strategy.
Thus:
ST
E
Ce > Max (1 + i ) – (1 + i ) , 0
£
$
7-35
European Option Pricing
Relationships
Using a similar portfolio to replicate the upside
potential of a put, we can show that:
Pe > Max
7-36
E
ST
–
,0
(1 + i$) (1 + i£)
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.
7-37
The Hedge Ratio

In the example just previous, we replicated the
payoffs of the call option with a levered
position in the underlying asset. (In this case,
borrowing dollars to buy euro at the spot.)
The hedge ratio of a option is the ratio of change in
the price of the option to the change in the price of
the underlying asset:
C up– C down
H = up
S1 – S1down
This ratio gives the number of units of the underlying
asset we should hold for each call option we sell in
order to create a riskless hedge.
7-38
Hedge Ratio


This practice of the construction of a riskless
hedge is called delta hedging.
The delta of a call option is positive.
Recall from the example:
$0.375
5
$0.375 – $0
C up– C down
=
=
H = up
down =
9
S1 – S1
$1.875 – $1.20 $0.675

The delta of a put option is negative.
Deltas change through time.
7-39
Take-Away Lessons
Convert future values from one currency to another
using forward exchange rates.
Convert present values using spot exchange rates.
Discount future values to present values using the
correct interest rate, e.g. i$ discounts dollar amounts
and i€ discounts amounts in euro.
To find the risk-neutral probability, set the forward
price derived from IRP equal to the expected value of
the payoffs.
To find the option value discount the expected value
of the option payoffs calculated using the risk neutral
probabilities at the correct risk free rate.
7-40
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.
7-41
Currency Futures Options





Why a derivative on a derivative?
Transactions costs and liquidity.
For some assets, the futures contract can have
lower transactions costs and greater liquidity
than the underlying asset.
Tax consequences matter as well, and for some
users an option contract on a future is more tax
efficient.
The proof is in the fact that they exist.
7-42
Option Pricing
1.03
– .80
1.02
p=
1.25 – 0.80
Find the value of an at-the-money call
and a put on €1 with
Strike Price = $1.50
i$ = 3%
$1.50
i€ = 2%
u = 1.25
C0 = $.169744
d = .8
.5338 × $0.30
.4662× $0.375
7-43
1.03
$1.875 = 1.25 × $1.50
$0.375 = Call payoff
$0 = Put payoff
$1.20 = 0.8 × $1.50
$0 =Call payoff
$0.30 = Put payoff
P0 = $0.15555
C0 =
= .4662
= $.169744
P0 =
1.03
= $0.15555
Hedging a Call Using the Spot Market
We want to sell call options. How many units of the
underlying asset should we hold to form a riskless portfolio?
H=
$0.375 – $0
$1.875 – $1.20
= 5/9
$1.875 = 1.25 × $1.50
$0.375 = Call payoff
$1.50
Sell 1 call option; buy 5/9 of the
underlying asset to form a riskless
portfolio.
If the underlying is indivisible, buy 5
units of the underlying and sell 9 calls.
7-44
$1.20 = 0.8 × $1.50
$0 = Call payoff
Hedging a Call Using the Spot Market
T=0
Cash Flows
T=1
S1($|€) = $1.875
C1= $.375
= 5/9
H=
Call finishes in-the-money,
$1.875 – $1.20
so we must buy an additional €4 at $1.875.
Cost = 4 × $1.875 = $7.50
S0($|€) = $1.50/€
Cash inflow call exercise = 9 × $1.50 = $13.50
Portfolio cash flow = $6.00
Go long PV of €5.
S1($|€) = $1.20
€5 $1.50
C1= $0
×
= $7.3529
Cost today =
1.02 €1.00
Call finishes out-of-the-money, so we
Write 9 calls:
can sell our now-surplus €5 at $1.20.
Cash inflow = 9 × $0.169744 = $1.5277
Cash inflow = 5 × $1.20 = $6.00
Portfolio cash flow today = –$5.8252
$0.375 – $0
Handy thing to notice: $5.8252 × 1.03 = $6.00
7-45
Hedging a Put Using the Spot Market
We want to sell put options. How many units of the
underlying asset should we hold to form a riskless portfolio?
H=
$0 – $0.30
$1.875 – $1.20
= – 4/9
S1($|€) = $1.875
Put payoff = $0.0
S0($|€) = $1.50/€
S1($|€) = $1.20
Put payoff = $0.30
Sell 1 put option; short sell 4/9 of the underlying asset to form a
riskless portfolio. If the underlying is indivisible, short 4 units of
the underlying and sell 9 puts.
7-46
Hedging a Put Using the Spot Market
T=0
H=
$0 – $0.30
$1.875 – $1.20
Cash Flows
= – 4/9
S0($|€) = $1.50/€
Borrow the PV of €4 at i€ = 2%.
€4 $1.50
Inflow =
×
= $5.8824
1.02 €1.00
Write 9 puts:
Cash inflow = 9 × $0.15555 = $1.3992
Portfolio Inflow today = $7.2816
T=1
S1($|€) = $1.875
Put finishes out-of-the-money.
To repay loan buy €4 at $1.875.
Cost = 4 × $1.875 = $7.50
Option cash inflow = 0
Portfolio cash flow = $7.50
S1($|€) = $1.20
put finishes in-the-money, so we
must buy 9 units of underlying at
$1.50 each = 9×1.50 = $13.50
use 4 units to cover short sale, sell
remaining 5 units at $1.20 = $6.00
Handy thing to notice: $7.2816 × 1.03 = $7.50
Portfolio cash flow = $7.50
7-47
Hedging a Call Using Futures
S1($|€) =
$1.875
Futures contracts matures: buy 5 units at
forward price. Cost = 5× $1.5147 = $7.5735
S0($|€) =
Call finishes in-the-money, we must buy 4 additional units of
$1.50/€
underlying at S1($/€) = $1.875. Cost = 4 × $1.875 = $7.50
Option cash inflow = 9 × $1.50 = $13.50
Portfolio cash flow = –$1.5735
S1($|€) =
Go long 5 futures contracts. $1.20 Futures contracts matures: buy 5 units at
forward price. Cost = 5× $1.5147 = $7.5735
Cost today = 0
$1.50 1.03
×
= $1.5147Call finishes out-of-the-money, so we
Forward Price =
€1.00 1.02
Write 9 calls:
sell our 5 units of underlying at $1.20.
Cash inflow = 9 × $0.169744 = $1.5277
Cash inflow = 5 × $1.20 = $6.00
Portfolio cash flow today = $1.5277
Portfolio cash flow = –$1.5735
7-48
Handy thing to notice: $1.5277 × 1.03 = $1.5735
Hedging a Put Using Futures
S1($|€) =
$1.875
S0($|€) =
$1.50/€
Futures contracts matures: sell €5 at forward price.
Loss = 4× [$1.875 – $1.5147] = $1.4412
Put finishes out-of-the-money. Option cash flow = 0
Portfolio cash flow = –$1.4412
S1($|€) =
Go short 4 futures contracts. $1.20
Put finishes in-the-money, we must
Cost today = 0
buy €9 at $1.50/€ = 9×1.50 = $13.50
$1.50 1.03
×
= $1.5147 Futures contracts matures: sell €4 at
Forward Price =
€1.00 1.02
forward price $1.5147/€
Write 9 puts:
4× $1.5147 = $6.0588
Cash inflow = 9 × $0.15555 = $1.3992
sell remaining €5 at $1.20 = $6.00
Portfolio Inflow today = $1.3992
Portfolio cash flow = –$1.4412
7-49
Handy thing to notice: $1.3992 × 1.03 = $1.4412