Chapter 5
Foreign Currency
Derivatives
Foreign Currency Derivatives
• Financial management of the MNE in the 21st century
involves financial derivatives.
• These derivatives, so named because their values are
derived from underlying assets, are a powerful tool
used in business today.
• These instruments can be used for two very distinct
management objectives:
– Speculation – use of derivative instruments to take a position
in the expectation of a profit
– Hedging – use of derivative instruments to reduce the risks
associated with the everyday management of corporate cash
flow
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5-2
Foreign Currency Futures
• A foreign currency futures contract is an
alternative to a forward contract that calls for
future delivery of a standard amount of foreign
exchange at a fixed time, place and price.
• It is similar to futures contracts that exist for
commodities such as cattle, lumber, interestbearing deposits, gold, etc.
• In the US, the most important market for
foreign currency futures is the International
Monetary Market (IMM), a division of the
Chicago Mercantile Exchange.
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5-3
Foreign Currency Futures
• Contract specifications are established by the exchange
on which futures are traded.
• Major features that are standardized are:
– Contract size
– Method of stating exchange rates
– Maturity date
– Last trading day
– Collateral and maintenance margins
– Settlement
– Commissions
– Use of a clearinghouse as a counterparty
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5-4
Foreign Currency Futures
• Foreign currency futures contracts differ from forward
contracts in a number of important ways:
– Futures are standardized in terms of size while forwards
can be customized
– Futures have fixed maturities while forwards can have
any maturity (both typically have maturities of one year
or less)
– Trading on futures occurs on organized exchanges while
forwards are traded between individuals and banks
– Futures have an initial margin that is market to market
on a daily basis while only a bank relationship is needed
for a forward
– Futures are rarely delivered upon (settled) while
forwards are normally delivered upon (settled)
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5-5
Foreign Currency Options
• A foreign currency option is a contract giving
the option purchaser (the buyer) the right, but
not the obligation, to buy or sell a given
amount of foreign exchange at a fixed price per
unit for a specified time period (until the
maturity date).
• There are two basic types of options, puts and
calls.
– A call is an option to buy foreign currency
– A put is an option to sell foreign currency
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5-6
Foreign Currency Options
• The buyer of an option is termed the holder,
while the seller of the option is referred to as
the writer or grantor.
• Every option has three different price elements:
– The exercise or strike price – the exchange rate at
which the foreign currency can be purchased (call)
or sold (put)
– The premium – the cost, price, or value of the
option itself
– The underlying or actual spot exchange rate in the
market
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5-7
Foreign Currency Options
• An American option gives the buyer the
right to exercise the option at any time
between the date of writing and the
expiration or maturity date.
• A European option can be exercised only
on its expiration date, not before.
• The premium, or option price, is the cost
of the option.
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5-8
Foreign Currency Options
• An option whose exercise price is the same as
the spot price of the underlying currency is said
to be at-the-money (ATM).
• An option the would be profitable, excluding
the cost of the premium, if exercised
immediately is said to be in-the-money (ITM).
• An option that would not be profitable, again
excluding the cost of the premium, if exercised
immediately is referred to as out-of-the money
(OTM)
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5-9
Foreign Currency Options
• In the past three decades, the use of foreign
currency options as a hedging tool and for
speculative purposes has blossomed into a
major foreign exchange activity.
• Options on the over-the-counter (OTC) market
can be tailored to the specific needs of the firm
but can expose the firm to counterparty risk.
• Options on organized exchanges are
standardized, but counterparty risk is
substantially reduced.
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5-10
Foreign Currency Speculation
• Speculation is an attempt to profit by trading
on expectations about prices in the future.
• Speculators can attempt to profit in the:
– Spot market – when the speculator believes the
foreign currency will appreciate in value
– Forward market – when the speculator believes the
spot price at some future date will differ from
today’s forward price for the same date
– Options markets – extensive differences in risk
patters produced depending on purchase or sale of
put and/or call
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5-11
Option Market Speculation
• Buyer of a call:
– Assume purchase of August call option on Swiss
francs with strike price of 58½ ($0.5850/SF), and a
premium of $0.005/SF
– At all spot rates below the strike price of 58.5, the
purchase of the option would choose not to exercise
because it would be cheaper to purchase SF on the
open market
– At all spot rates above the strike price, the option
purchaser would exercise the option, purchase SF at
the strike price and sell them into the market netting
a profit (less the option premium)
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5-12
Exhibit 5.4 Profit and Loss for the Buyer
of a Call Option on Swiss francs
“At the money”
Strike price
Profit
(US cents/SF)
“Out of the money”
“In the money”
+ 1.00
+ 0.50
0
- 0.50
Unlimited profit
57.5
58.0
58.5
59.0
59.5
Spot price
(US cents/SF)
Limited loss
Break-even price
- 1.00
Loss
The buyer of a call option on SF, with a strike price of 58.5 cents/SF, has a limited loss of
0.50 cents/SF at spot rates less than 58.5 (“out of the money”), and an unlimited profit
potential at spot rates above 58.5 cents/SF (“in the money”).
5-13
Option Market Speculation
• Writer of a call:
– What the holder, or buyer of an option loses, the writer
gains
– The maximum profit that the writer of the call option
can make is limited to the premium
– If the writer wrote the option naked, that is without
owning the currency, the writer would now have to buy
the currency at the spot and take the loss delivering at
the strike price
– The amount of such a loss is unlimited and increases as
the underlying currency rises
– Even if the writer already owns the currency, the writer
will experience an opportunity loss
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5-14
Exhibit 5.5 Profit and Loss for the Writer of a Call
Option on Swiss francs
“At the money”
Strike price
Profit
(US cents/SF)
+ 1.00
+ 0.50
0
- 0.50
Break-even price
Limited profit
57.5
58.0
58.5
59.0
59.5
Spot price
(US cents/SF)
Unlimited loss
- 1.00
Loss
The writer of a call option on SF, with a strike price of 58.5 cents/SF, has a limited profit of
0.50 cents/SF at spot rates less than 58.5, and an unlimited loss potential at spot rates
above (to the right of) 59.0 cents/SF.
5-15
Option Market Speculation
• Buyer of a Put:
– The basic terms of this example are similar to those just
illustrated with the call
– The buyer of a put option, however, wants to be able to sell
the underlying currency at the exercise price when the market
price of that currency drops (not rises as in the case of the call
option)
– If the spot price drops to $0.575/SF, the buyer of the put will
deliver francs to the writer and receive $0.585/SF
– At any exchange rate above the strike price of 58.5, the buyer
of the put would not exercise the option, and would lose only
the $0.05/SF premium
– The buyer of a put (like the buyer of the call) can never lose
more than the premium paid up front
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5-16
Exhibit 5.6 Profit and Loss for the Buyer of a Put
Option on Swiss francs
“At the money”
Strike price
Profit
(US cents/SF)
“In the money”
“Out of the money”
+ 1.00
+ 0.50
0
Profit up
to 58.0
57.5
58.5
59.0
59.5
Spot price
(US cents/SF)
Limited loss
- 0.50
- 1.00
58.0
Break-even
price
Loss
The buyer of a put option on SF, with a strike price of 58.5 cents/SF, has a limited loss of
0.50 cents/SF at spot rates greater than 58.5 (“out of the money”), and an unlimited profit
potential at spot rates less than 58.5 cents/SF (“in the money”) up to 58.0 cents.
5-17
Option Market Speculation
• Seller (writer) of a put:
– In this case, if the spot price of francs drops below
58.5 cents per franc, the option will be exercised
– Below a price of 58.5 cents per franc, the writer will
lose more than the premium received fro writing the
option (falling below break-even)
– If the spot price is above $0.585/SF, the option will
not be exercised and the option writer will pocket
the entire premium
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5-18
Exhibit 5.7 Profit and Loss for the Writer of a Put
Option on Swiss francs
“At the money”
Profit
(US cents/SF)
Strike price
+ 1.00
+ 0.50
Break-even
price
Limited profit
0
- 0.50
57.5
58.0
58.5
59.0
59.5
Spot price
(US cents/SF)
Unlimited loss
up to 58.0
- 1.00
Loss
The writer of a put option on SF, with a strike price of 58.5 cents/SF, has a limited profit of
0.50 cents/SF at spot rates greater than 58.5, and an unlimited loss potential at spot rates
less than 58.5 cents/SF up to 58.0 cents.
5-19
Option Pricing and Valuation
• The pricing of any currency option combines
six elements:
– Present spot rate
– Time to maturity
– Forward rate for matching maturity
– US dollar interest rate
– Foreign currency interest rate
– Volatility (standard deviation of daily spot price
movements)
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5-20
Option Pricing and Valuation
• The total value (premium) of an option is equal to the intrinsic
value plus time value.
• Intrinsic value is the financial gain if the option is exercised
immediately.
– For a call option, intrinsic value is zero when the strike price is
above the market price
– When the spot price rises above the strike price, the intrinsic
value become positive
– Put options behave in the opposite manner
– On the date of maturity, an option will have a value equal to
its intrinsic value (zero time remaining means zero time value)
• The time value of an option exists because the price of the
underlying currency, the spot rate, can potentially move further
and further into the money between the present time and the
option’s expiration date.
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5-21
Exhibit 5.8 Intrinsic Value, Time Value & Total Value for a
Call Option on British Pounds with a Strike Price of $1.70/£
Option Premium
(US cents/£)
-- Valuation on first day of 90-day maturity --
6.0
5.67
Total value
5.0
4.00
4.0
3.30
3.0
2.0
1.67
Time value
Intrinsic
value
1.0
0.0
1.66
1.67
1.68
1.69
1.70
1.71
1.72
1.73
1.74
Spot rate ($/£)
5-22
Currency Option Pricing Sensitivity
• If currency options are to be used
effectively, either for the purposes of
speculation or risk management, the
individual trader needs to know how
option values – premiums – react to their
various components.
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5-23
Currency Option Pricing Sensitivity
• Forward rate sensitivity:
– Standard foreign currency options are priced around
the forward rate because the current spot rate and
both the domestic and foreign interest rates are
included in the option premium calculation
– The option-pricing formula calculates a subjective
probability distribution centered on the forward rate
– This approach does not mean that the market
expects the forward rate to be equal to the future
spot rate, it is simply a result of the arbitragepricing structure of options
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5-24
Currency Option Pricing Sensitivity
• Spot rate sensitivity (delta):
– The sensitivity of the option premium to a
small change in the spot exchange rate is
called the delta
delta = Δ premium
Δ spot rate
– The higher the delta, the greater the
probability of the option expiring in-themoney
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5-25
Currency Option Pricing Sensitivity
• Time to maturity – value and
deterioration (theta):
– Option values increase with the length of
time to maturity
theta = Δ premium
Δ time
– A trader will normally find longer-maturity
option better values, giving the trader the
ability to alter an option position without
suffering significant time value deterioration
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5-26
Exhibit 5.11 Theta: Option Premium Time Value Deterioration
Option Premium
(US cents/£)
A Call Option on British Pounds: Spot Rate = $1.70/£
7.0
In-the-money (ITM)
call ($1.65 strike price)
6.0
5.0
4.0
At-the-money (ATM)
call ($1.70 strike price)
3.0
2.0
Out-of-the-money (OTM)
call ($1.75 strike price)
1.0
0.0
90
80
70
60
50
40
Days remaining to maturity
30
20
10
0
5-27
Currency Option Pricing Sensitivity
• Sensitivity to volatility (lambda):
– Option volatility is defined as the standard deviation
of daily percentage changes in the underlying
exchange rate
– Volatility is important to option value because of an
exchange rate’s perceived likelihood to move either
into or out of the range in which the option will be
exercised
lambda = Δ premium
Δ volatility
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5-28
Currency Option Pricing Sensitivity
• Volatility is viewed in three ways:
– Historic
– Forward-looking
– Implied
• Because volatilities are the only judgmental component that the
option writer contributes, they play a critical role in the pricing of
options.
• All currency pairs have historical series that contribute to the
formation of the expectations of option writers.
• In the end, the truly talented option writers are those with the
intuition and insight to price the future effectively.
• Traders who believe that volatilities will fall significantly in the
near-term will sell (write) options now, hoping to buy them back for
a profit immediately volatilities fall, causing option premiums to fall.
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5-29
Currency Option Pricing Sensitivity
• Sensitivity to changing interest rate differentials (rho and phi):
– Currency option prices and values are focused on the
forward rate
– The forward rate is in turn based on the theory of Interest
Rate Parity
– Interest rate changes in either currency will alter the
forward rate, which in turn will alter the option’s premium
or value
• A trader who is purchasing a call option on foreign currency
should do so before the domestic interest rate rises. This
timing will allow the trader to purchase the option before its
price increases.
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5-30
Currency Option Pricing Sensitivity
• The expected change in the option premium
from a small change in the domestic interest
rate (home currency) is the term rho.
rho = Δ premium
Δ US $ interest rate
• The expected change in the option premium
from a small change in the foreign interest rate
(foreign currency) is termed phi.
phi = Δ premium
Δ foreign interest rate
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5-31
Exhibit 5.13 Interest Differentials and Call Option Premiums
Option Premium (US cents/£)
8.0
A Call Option on British Pounds: Spot Rate = $1.70/£
7.0
ITM call ($1.65 strike price)
6.0
5.0
4.0
ATM call ($1.70 strike price)
3.0
2.0
OTM call ($1.75 strike price)
1.0
0.0
-4.0
-3.0
-2.0
-1.0
0
1.0
2.0
Interest differential: iUS$ - i £ (percentage)
3.0
4.0
5.0
5-32
Currency Option Pricing Sensitivity
• The sixth and final element that is important to
option valuation is the selection of the actual
strike price.
• A firm must make a choice as per the strike
price it wishes to use in constructing an option
(OTC market).
• Consideration must be given to the tradeoff
between strike prices and premiums.
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5-33
Exhibit 5.14 Option Premiums for Alternative Strike Rates
Option Premium
(US cents/£)
Current spot rate = $1.70/£
7.0
6.0
5.0
OTM Strike rates
4.0
ITM Strike rates
3.0
2.0
1.0
0.0
1.66
1.67
1.68
1.69
1.70
1.71
1.72
Call strike price (U.S. dollars/£)
1.73
1.74
5-34
1.75