1. 5 Currency Derivatives 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 = $ $1.681 x 360 = – 0.95%
discount $
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 currency’s 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

10. Currency Futures www. nybot.com and www.cme.com

11. Norwegian Krone futures

12. Norwegian Krone futures

13. Norwegian Krone futures

14. 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.

15. 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.

16. 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).

17. 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

18. 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.

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 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
You have lost $ overnight.

21. Daily Resettlement: An Example
The $ comes out of your $3, margin account, leaving $2,774.05
This is short of the $3, 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.

22. 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

23. 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.

24. Currency options – FT (from CME)

25. 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.

26. 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.

27. 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.

28. 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 buyer’s gain will be the seller’s 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.

29. 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.

30. 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.

31. Option Value Determinants
Call Put
1. Exchange rate – 2. Exercise price – Interest rate in U.S – 4. Interest rate in other country Variability in exchange rate Expiration date
7. Dividends – +

32. 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 £

33. Profit and loss

34. PHLX Currency Option Specifications
Contract Size
Australian dollar
AD50,000
British pound
£31,250
Canadian dollar
CD50,000
Euro
€62,500
Japanese yen
¥6,250,000
Swiss franc
SF62,500

35. 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

37. 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 = Max[ST - X, 0]

38. 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 = Max[X - ST, 0]

39. Contingency Graphs for Currency Options
+$.02
+$.04
- $.02
- $.04
$1.46
$1.50
$1.54
Net Profit per Unit
Future Spot Rate
For Buyer of £ Call Option
Strike price = $1.50
Premium = $ .02
+$.02
+$.04
- $.02
- $.04
$1.46
$1.50
$1.54
Net Profit per Unit
Future Spot Rate
For Seller of £ Call Option
Strike price = $1.50
Premium = $ .02

40. Contingency Graphs for Currency Options
+$.02
+$.04
- $.02
- $.04
$1.46
$1.50
$1.54
Net Profit per Unit
Future Spot Rate
For Buyer of £ Put Option
Strike price = $1.50
Premium = $ .03
+$.02
+$.04
- $.02
- $.04
$1.46
$1.50
$1.54
Net Profit per Unit
Future Spot Rate
For Seller of £ Put Option
Strike price = $1.50
Premium = $ .03

41. Example Long 1 call on 1 pound ST $1.50 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
$1.75 ST
–$0.25
$1.50
loss

42. Example Long 1 call on £31,250 ST $1.50 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
$1.75 ST
–$7,812.50
$1.50
loss

43. Example Long 1 put on £31,250 ST $1.50 Profit
What is the maximum gain on this put option?
At what exchange rate do you break even?
$42, = £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.
$1.35 ST
–$4,687.50
Long 1 put on £31,250
$1.50
$4, = £31,250×($0.15)/£
loss

44. 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

45. 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.

46. Garman - Kohlhagen

47. Garman - Kohlhagen Suppose we have Spot exchange rate S = $1,49/€
Exercise rate X = $1,45/€
Standard deviation σ = 20 %
Dollar interest rate r = 5 %
Euro denominated interest rate rc = 3,7 %
Time to expiration: 365 days (T = 1)

48. Garman - Kohlhagen

49. Currency option combinations
For various reasons, hedgers or speculators may own combinations of options
Two of the most popular combinations are:
Straddles (long stradde involves buying both call and put, and short straddle involves selling both call and put), exercise prices are identical in both cases
Strangles are almost identical to straddles, but exercise prices are different

50. Long straddle
When do you make money?
What is the most you can lose?

51. Long straddle Call option premium on £ = $ 0,035
Put option premium on £ = $ 0,025
Strike price = $ 1,50/£
One option contract = £
Spot at expiration = $ 1,40/£
What is the profit or loss?

52. Long currency strangle

53. Long currency strangle
Call option premium on £ = $ 0,030
Put option premium on £ = $ 0,025
Call option strike price = $ 1,60/£
Put option strike price = $ 1,50/£
One option contract = £
Spot at expiration = $ 1,52/£
What is the profit or loss?

54. Currency spreads
A spread involves buying and writing options for the same underlying currency
Bull spread involves buying a call and at the same time selling a call with a higher exercise price. There will be a gain if the underlying currency appreciates somewhat
A bull spread can also be constructed using puts
A bear spread takes the opposite position, and there will be a gain if the underlying currency depreciates somewhat

55. Currency bull spread
Two call options on A$ are available. One has a strike of $0,64 and a premium of $0,019. The next has a strike of $0,65 and premium of $0,015. One contract is A$
What is the profit or loss if the A$ is either $0,645 or $0,70 at expiry, and you have bought the 0,64 call and sold (written) the 0,65 call?

56. Impact of Currency Derivatives
on an MNC’s Value
Currency futures
Currency options
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