Currency Derivatives

1
Currency Derivatives
5
Chapter
See c5.xls for spreadsheets to accompany this
chapter.
2
Chapter Objectives

• To explain how forward contracts are used to
  hedge based on anticipated exchange rate
  movements
• To explain how currency futures contracts are
  used to speculate or hedge based on anticipated
  exchange rate movements and
• To explain how currency options contracts are
  used to speculate or hedge based on anticipated
  exchange rate movements.

3
Forward Market

• A forward contract is an agreement between a
  corporation and a commercial bank to exchange a
  specified amount of a currency at a specified
  exchange rate (called the forward rate) on a
  specified date in the future.
• When MNCs anticipate future need or future
  receipt of a foreign currency, they can set up
  forward contracts to lock in the exchange rate.
• Forward contracts are not normally used by
  consumers or small firms.

4
Forward Market

• If the forward rate exceeds the existing spot
  rate, it contains a premium. If it is less than
  the existing spot rate, it contains a discount.
• Suppose spot rate 1.681, and
• 90-day forward rate 1.677.
• forward 1.677 - 1.681 x 360 0.95
• discount 1.681 90
• The premium (or discount) reflects the difference
  between the home interest rate and the foreign
  interest rate, so as to prevent arbitrage.

5
Euro spot and forward august 15 2005
6
Forward Market

• Non-deliverable forward contracts (NDFs) are
  forward contracts whereby the currencies are not
  actually exchanged. Instead, a net payment is
  made by one party to the other based on the
  contracted rate and the market exchange rate on
  the day of settlement.
• While the NDF does not involve delivery, it can
  effectively hedge future foreign currency cash
  flows that are anticipated by the MNC.

7
Currency Futures Market

• Currency futures contracts are contracts
  specifying a standard volume of a particular
  currency to be exchanged on a specific settlement
  date, typically the third Wednesdays in March,
  June, September, and December.
• The contracts can be traded by firms or
  individuals on the trading floor of an exchange,
  on automated trading systems, or over the counter.

8
Currency Futures Market

• The contracts are guaranteed by the exchange
  clearinghouse, and margin requirements are
  imposed to cover fluctuations in value.
• Corporations that have open positions in foreign
  currencies can use futures contracts to offset
  such positions.
• Speculators also use them to capitalize on their
  expectation of a currencys future movement.
• Brokers who fulfill orders to buy or sell futures
  contracts earn a transaction fee in the form of a
  bid/ask spread.

9
Currency Futures Markets

• The Chicago Mercantile Exchange (CME) is by far
  the largest.
• Others include
• The Philadelphia Board of Trade (PBOT)
• The New York Board of Trade (NYBOT)
• The Tokyo International Financial Futures
  Exchange
• The London International Financial Futures
  Exchange

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Currency Futureswww. nybot.com and www.cme.com
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Norwegian Krone futures
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Norwegian Krone futures
13
Norwegian Krone futures
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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.

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Futures Contracts Preliminaries

• A major difference between a forward contract and
  a futures contract is the way the underlying
  asset is priced for future purchase or sale
• A forward contract states a price for the future
  transaction
• By contrast, a futures contract is settled-up or
  marked-to-market, daily at the settlement price
• The settlement price is a price representative of
  futures transaction prices at the close of daily
  trading on the exchange.

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Futures Contracts Preliminaries

• A buyer of a futures contract (one who holds a
  long position) in which the settlement price is
  higher (lower) than the previous day's settlement
  price has a positive (negative) settlement for
  the day.
• Since a long position entitles the owner to
  purchase the underlying asset, a higher (lower)
  settlement price means the futures price of the
  underlying asset has increased (decreased).
  Consequently, a long position in the contract is
  worth more (less).

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Futures Contracts Preliminaries

• The change in settlement prices from one day to
  the next determines the settlement amount
• Settlement amount is equal to the change in
  settlement prices per unit of the underlying
  asset, multiplied by the size of the contract,
  and equals the size of the daily settlement to be
  added or subtracted from the margin account
• Futures trading between the long and the short is
  a zero-sum game

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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
1150.
19
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

20
Daily Resettlement An Example

• If tomorrow, the futures rate closes at 1
  149, then your positions 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

You have lost 559.28 overnight.
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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.

• 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.

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Options and forward contracts

• In the case of forward contracts, we convert a
  future uncertain outcome to a fixed,
  predetermined rate
• Sometimes this is beneficial, but if subsequently
  the exchange rate moves in our favor, there is an
  opportunity loss
• What we really want is a situation where we can
  have forward cover and the opportunity to gain if
  the outcome is to our advantage we want the
  cake and eat it too
• Solution - options

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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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Currency options FT (from CME)
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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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Currency Call Options

• A currency call option grants the right to buy a
  specific currency at a specific price (called the
  exercise or strike price) within a specific
  period of time.
• A call option is in the money when the present
  exchange rate exceeds the strike price, at the
  money when the rates are equal, and out of the
  money otherwise.
• Option owners will at most lose the premiums they
  paid for their options.

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Currency Call Options

• Premiums of call options vary due to
• the level of existing spot price relative to
  strike price,
• the length of time before the expiration date,
  and
• the potential variability of the currency.
• Corporations can use currency call options to
  cover their foreign currency positions.
• Unlike a futures or forward contract, if the
  anticipated need does not arise, the firm can
  choose to let the options contract expire. The
  firm can also sell or exercise the option.

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Currency Call Options

• Individuals may also speculate in the currency
  options market based on their expectations of the
  future movements in a particular currency.
• When brokerage fees are ignored, the currency
  call buyers gain will be the sellers loss if
  both parties begin and close out their positions
  at the same time.
• The purchaser of a call option will break even
  when the spot rate at which the currency is sold
  is equal to the strike price plus the option
  premium.

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Currency Put Options

• A currency put option grants the right to sell a
  specific currency at a specific price (the strike
  price) within a specific period of time.
• A put option is in the money when the present
  exchange rate is less than the strike price, at
  the money when the rates are equal, and out of
  the money otherwise.
• Since option owners are not obligated to exercise
  their options, they will at most lose the
  premiums they paid.

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Currency Put Options

• Premiums of put options vary due to
• the level of existing spot price relative to
  strike price,
• the length of time before the expiration date,
  and
• the potential variability of the currency.
• Corporations can use currency put options to
  cover their foreign currency positions.
• Individuals may also speculate with currency put
  options based on their expectations of the future
  movements in a particular currency.

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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 7.
Dividends
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Example page 144

• Jim is a speculator who buys a British Pound call
  option from Linda with a strike price of 1.40
  and a December settlement date. The current spot
  rate is about 1.39 and Jim pays a premium of
  .012 per unit for the call option. Just before
  expiration, the spot rate reaches 1.41
• What is the profit? One contract equals 31 250

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Profit and loss
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PHLX Currency Option Specifications
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Options Contracts Preliminaries

• Intrinsic Value
• The difference between the exercise price of the
  option and the spot price of the underlying
  asset.
• Time Value
• The difference between the option premium and the
  intrinsic value of the option.

Option Premium
Intrinsic Value
Time Value


36
Intrinsic Value, Time Value, and Total Value of
a Call Option on British Pounds with a Strike
Price of 1.70
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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 X.
• If the call is out-of-the-money, it is worthless.
• CaT CeT MaxST - X, 0

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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 X - ST.
• If the put is out-of-the-money, it is worthless.
• PaT PeT MaxX - ST, 0

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Contingency Graphs for Currency Options
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Contingency Graphs for Currency Options
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Example
Profit

• Consider a call option on 31,250.
• The option premium is 0.25 per pound
• The exercise price is 1.50 per pound.

Long 1 call on 1 pound
ST
0.25
1.50
loss
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Example
Profit

• Consider a call option on 31,250.
• The option premium is 0.25 per pound
• The exercise price is 1.50 per pound.

Long 1 call on 31,250
ST
7,812.50
1.50
loss
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Example
Profit
What is the maximum gain on this put option? At
what exchange rate do you break even?
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 pound
• The exercise price is 1.50 per pound.

ST
Long 1 put on 31,250
1.50
4,687.50 31,250(0.15)/
loss
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Option pricing

• The Black-Scholes option-pricing model applied to
  currencies often goes by the name of the Garman
  -Kohlhagen model as these authors were the first
  to publish a closed form model
• This model alleviates the restrictive assumption
  used in the Black Scholes model that borrowing
  and lending is performed at the same risk free
  rate.
• In the foreign exchange market there is no reason
  that the risk free rate should be identical in
  each country
• The risk free foreign interest rate in this case
  can be thought of as a continuous dividend yield
  being paid on the foreign currency

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Garman - Kohlhagen

• Model assumptions include
• the option can only be exercised on the expiry
  date (European style)
• there are no taxes, margins or transaction costs
• the risk free interest rates (domestic and
  foreign) are constant
• the price volatility of the underlying instrument
  is constant and
• the price movements of the underlying instrument
  follow a lognormal distribution.

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Garman - Kohlhagen
47
Garman - Kohlhagen

• Suppose we have
• Spot exchange rate S 0,92/
• Exercise rate X 0,9/
• Standard deviation s 10
• Dollar interest rate r 6
• Euro denominated interest rate rc 3,2
• Time to expiration 365 days

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Garman - Kohlhagen
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Impact of Currency Derivatives on an MNCs Value
E (CFj,t ) expected cash flows in currency j
to be received by the U.S.
parent at the end of period t E (ERj,t )
expected exchange rate at which currency j can
be converted to dollars at the end
of period t k the weighted average cost of
capital of the U.S. parent