Chapter 8

Foreign Currency Derivatives
Futures and Forwards, and options
Adapted from ESM book
[email protected]
Foreign exchange derivatives
“Well, it helps to look at derivatives like atoms.
Split them one way and you have heat and energy useful stuff. Split them another way and you have a
bomb. You have to understand the subtleties.”
Kate Jennings
Moral Hazard, 2002, p. 8
Introduction to Forward Contracts
• Both futures and forwards specify a trade between two
– The seller (or the short) makes a commitment to deliver
an asset, at a specified forward price.
– the buyer (or the long) makes a commitment to take
delivery of an asset, at a specified forward price.
– At delivery, cash is exchanged for the asset.
Futures and Forwards: A Comparison
Default Risk:
Borne by Clearinghouse
Borne by Counter-Parties
Agreed on at Time
of Trade Then,
Agreed on at Time
of Trade. Payment at
Contract Termination
Where to Trade:
When to Trade:
Clearinghouse Makes it
Easy to Exit Commitment
Cannot Exit as Easily:
Must Make an Entire
New Contract
How Much to Trade:
What Type to Trade:
Collateral is negotiable
Offset prior to delivery
Delivery takes place
What to Trade:
The Forward/Futures
Liquidity Risk:
Typical Holding Pd.
©David Dubofsky and
Thomas W. Miller, Jr.
Futures Contract - Example
Specification of the Australian Dollar futures contract
(International Money Market at CME)
Delivery Month
Min. Price Move
Settlement Date
Stop of Trading
AUD 100,000
March, June, September,
$0.0001 ($10.00)
Third Wednesday of delivery
Two business days prior to
settlement date
Futures - The Clearing House
 When A “sells” a futures contract to B, the Clearing
House takes over and the result is:
 A sells to the Clearing House
 Clearing House sells to B
 The Clearing House keeps track of all transactions that
take place and calculates the “net position” of all
Futures - Marking to Market
 Futures contracts are “marked to market” daily.
 Generates cash flows to (or from) holders of foreign
currency futures from (or to) the clearing house.
 Mechanics:
 Buy a futures contract this morning at the price of f0,T
 At the end of the day, the new price is f1,T
 The change in your futures account will be:
[f1,T - f0,T] x Contract Face Value = Cash Flow
Purpose of Marking to Market
 Daily marking to market means that profits and losses
are realized as they occur. Therefore, it minimizes the
risk of default.
 By defaulting, the investor merely avoids the latest
marking to market outflow. All previous losses have
already been settled in cash.
Marking to Market – Example
 Trader buys 1 AUD contract on 1 Feb for
 USD value = 100,000 x 0.5000 = USD 50,000.
Value of Contract
Margin A/c
1 Feb
2 Feb
3 Feb
4 Feb
- 200
+ 100
+ 300
- 100
Forward Contracts:
Payoff Profiles
Long forward
The long side gains if the spot price at
delivery, S(T), exceeds the original
forward price, F(0,T).
Short forward
The short side gains if the price at
delivery, S(T), is below the
original forward price, F(0,T).
Profits for Forward Contracts
If S(T) > F(0,T), the long side gains by S(T) - F(0,T) per unit, and the short side
loses this amount.
If S(T) < F(0,T), the short side profits by F(0,T) - S(T) per unit, and the long loses
this amount.
Example: You sell ¥20 million forward at a forward price of $0.0090/ ¥. At
expiration, the spot price is $0.0083/ ¥.
– Did you profit or did you lose?
– How much?
Default Risk for Forwards, I.
• If the forward price is “fair” at initiation:
– The contract is valueless.
– There is no immediate default risk.
• As time goes by, the forward price (for delivery on the
same date as the original contract subsequently) can
– Existing forward contracts acquire value: They become an asset
for one party and a liability for the other.
– Default risk appears.
– (Q: Which party faces default risk?)
Default Risk for Forwards (cont.)
• At any time, only one counter-party has the incentive to
• It is the counter-party for whom the forward contract has
become a liability.
• The amount exposed to default risk at time t is:
PV{ F(0,T) - F(t,T) }, 0 < t < T
Recall from Corporate finance the present value of a future
outlay = Discounted cash flow to the present time.
Example: Default Risk for Forwards
On April 4th, you buy 100,000 bbl of oil forward at a
forward price of $27/bbl. The delivery date is July 4th. On
May 4th, the forward price for delivery on July 4th is
– Who has the incentive to default?
– If the interest rate on May 4th for 2-month debt instruments is 5%, what is the
dollar amount exposed to default risk?
The expected loss amount is the loss that might materialize at the expiration day, 2
month from now, if the spot price stays at 24$, the total expected loss is
3$*100,000=300,000 $ discounted at 5% “2 month yield)
=1/(1+0.05)*300,000=5714.286$. The dollar amount that is exposed to default risk
is 5714.286$.
Forward Rate Agreements (FRAs)
• A FRA is a forward contract on an interest rate (not on a bond,
or a loan).
• The buyer of a FRA profits from an increase in interest rates.
The seller of a FRA profits from a decline in rates.
• The buyer effectively has agreed to borrow an amount of
money in the future at the stated forward (contract) rate. The
seller has effectively locked in a lending rate.
• FRA’s are cash settled.
Forward Rate Agreements (FRAs)
• Only the difference in interest rates is paid. The principal is
not exchanged.
• FRAs are cash settled.
origination date
Loan period
settlement date, or
delivery date
end of forward
Forward Rate Agreements (FRAs)
• If the spot rate at delivery (“settlement rate”, r(t1,t2)) exceeds
the forward rate agreed to in the FRA (“contract rate” =
fr(0,t1,t2), the FRA buyer profits.
• The amount paid (at time t1) is the present value of the
difference between the settlement rate and the contract rate
times the notional principal times the fraction of the year of the
forward period.
• A FRA’s value is initially zero, when the contract rate is the
theoretical forward rate. Subsequently, forward rates will change,
so the FRA will have positive value for one party (and equally
negative value for the other).
Part II Foreign Currency Derivatives
 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
Foreign Currency Derivatives
• Derivatives are used by firms to achieve one of more
of the following individual benefits:
– Permit firms to achieve payoffs that they would not be
able to achieve without derivatives, or could achieve only
at greater cost
– Hedge risks that otherwise would not be possible to hedge
– Make underlying markets more efficient (price discovery)
– Reduce volatility of stock returns (by writing call options
on stocks you own)
– Minimize earnings volatility (hedging against currency risk)
– Reduce tax liabilities (if capital gains tax is lower)
– Motivate management (agency theory effect)
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, interest-bearing
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 (CME).
Foreign Currency Futures
• Major features that are standardized are:
Contract size
Method of stating exchange rates
Maturity date
Last trading day
Collateral and maintenance margins
Use of a clearinghouse as a counterparty
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
– 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)
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
Foreign Currency Options
• The buyer of an option is termed the holder.
• the one who writes the option is referred to as the writer or
• 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 price, or value of the option itself
– The underlying spot exchange rate in the market
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 date.
• A European option can be exercised only on its
expiration date, not before. (you can always sell
the option at a higher price at the market
because of the time value)
• The premium, or option price, is the cost of the
Foreign Currency Options
• An option whose exercise price is the same as the
spot price of the underlying currency is said to be atthe-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, excluding the
cost of the premium, if exercised immediately is
referred to as out-of-the money (OTM)
Option Pricing & Valuation
max(ST - X, 0)
max(X - ST, 0)
in the money
ST – X > 0
X – ST > 0
at the money
ST – X = 0
X – ST = 0
out of the money
ST – X < 0
X – ST < 0
CT – Int. value
PT – Int. value
Intrinsic value
Time Value
An example: buy a call on Swiss Franc
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
What happens at the expiration day?
Note, the strike price is important, it is the price you choose
to buy the asset if exercised. Your profit is Spot rate in the
market-strike price at the expiration day.
Exhibit 8.4 Buying a Call Option on Swiss Francs
Exhibit 8.5 Writing a Call Option on Swiss Francs
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 – volatile market, buy or sale of put
and/or call
Option Market Speculation
• Writer of a call:
– 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 have to buy the currency at the spot at the
expiration day and take the loss to deliver 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
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 $0.585/SF when the market
price of that currency drops
– If the spot price drops to $0.575/SF, the buyer of the put will deliver
Swiss 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 $0.005/SF
– The buyer of a put (like the buyer of the call) can never lose more than
the premium paid up front
Exhibit 8.6 Buying a Put Option on Swiss Francs
Option Market Speculation
• Seller (writer) of a put:
– In this case, if the spot price of francs drops below
58.5 cents per Swiss franc, the option will be
– Below a price of 58.0 cents per Swiss franc, the
writer will lose more than the premium received
from 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
Exhibit 8.7 Selling a Put Option on Swiss
Option Pricing and Valuation
 The pricing of any currency option combines six
 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
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
– For a call option, intrinsic value is zero when the strike
price is above the spot price
– When the spot price rises above the strike price, the
intrinsic value become positive
On the date of maturity, an option will have a value equal to
its intrinsic value (zero time remaining means zero time
Currency Option Pricing Sensitivity
• The time value of an option exists because the
price of the underlying currency, the spot rate,
can potentially move into the money between
the present time and the option’s expiration date.
• 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.
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 arbitrage-pricing structure of
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 = Δ premium
Δ spot rate
– The higher the delta, the greater the probability of
the option expiring in-the-money
Currency Option Pricing Sensitivity
• Time to maturity – value and deterioration
– Option values increase with the length of time to
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
Option Pricing & Valuation
Exhibit 8.11 Theta: Option Premium
Time Value Deterioration
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
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, when the option premiums falls.
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.
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
Exhibit 8.13 Interest Differentials and
Call Option Premiums
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
• Consideration must be given to the tradeoff
between strike prices and premiums. See next
Exhibit 8.14 Option Premiums for
Alternative Strike Rates
Exhibit 8.15 Summary of Option
Premium Components
Mini-Case Questions: Warren Buffett’s Love-Hate
Relationship with Derivatives
• In his 2002 letter to shareholders, what does
Warren Buffett seem to fear most about
financial derivatives?
• In his 2007 letter to shareholders, what does
Warren Buffett admit that he and Charlie had
• Do you think there is an underlying
consistency in his viewpoint on the proper use
of derivatives?
Exhibit 8.1 Mexican Peso Futures,
US$/Peso (CME)
Exhibit 8.2 Currency Futures and
Forwards Compared
Exhibit 8.3 Swiss Franc Option
Quotations (U.S. cents/SF)
Exhibit 8.8
Analysis of Call
Option on British
Pounds with a
Strike Price =
Exhibit 8.9 The Intrinsic, Time, and Total Value Components of the
90-Day Call Option on British Pounds at Varying Spot Exchange
Exhibit 8.10 Decomposing Call Option
Premiums: Intrinsic Value and Time
Exhibit 8.12 Foreign Exchange Implied Volatility for Foreign Currency Options, January 30,

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