1. 5
Chapter
Currency Derivatives
International Finance

2. 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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3. Foreign Currency Derivatives
In this chapter, we will look at the following important instruments
Forwards
Futures
Swaps
Currency options
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4. Forward Market
A forward contract is an agreement between a firm and an intermediary to exchange a specified amount of a currency at a specified exchange rate (called the forward rate) on a specified date in the future.
Let us assume that a UK company has a 6 month dollar receivable it wants to hedge. This raises the question of the price at which the intermediary should agree to buy the dollars and sell the customer sterling. The answer is based on the intermediary’s ability to hedge its exposure, a theory of forward pricing often referred to as the cost of carry model
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5. Forward Market
Let us assume at the $/£ spot rate is 1.5 and that the 6 m interest rate (per annum) for £ and $ is 10 % and 6 % resp.
In order to eliminate its risk, the intermediary will need to undertake the following:
borrow US dollars today;
exchange these into sterling at the current spot rate;
deposit these for six months in sterling
At the maturity of the forward contract the customer will pay the bank US dollars, which can be used to repay the initial dollar loan and the maturing sterling deposit is used to pay the customer the contracted sterling amount
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6. Forward Market Assume the contract is for $ 1 000 000
The bank will borrow /(1 + 0,06/2) = This amounts to /1,5 = £
Future value of £ deposit * (1+ 0,10/2) =
Forward exchange rate / = $1.4714/£
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7. Forward Market
We saw that the forward rate is different from the spot rate, and this is normally the case. The % by which the forward rate (F ) differs from the spot rate (S ) is labelled p and is called the forward premium if p > 0 or discount if p < 0 and is normally expressed on an annual basis
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8. Forward Market http://markets.ft.com/ft/markets/reports/FTReport.asp?dockey=DSP-150808
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9. 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, the weather etc.
Futures more or less eliminate credit risk as a clearing house is the contract party
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10. 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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11. CME Norwegian Krone
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12. Currency Futures August 15 – 2008 http://markets. ft
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13. Currency Futures Market
Speculators often sell currency futures when they expect the underlying currency to depreciate, and vice versa.
1. Contract to sell 500,000 pesos @ £.056/peso (£28,000) on June 17.
April 4
2. Buy 500,000 pesos @ £.050/peso (£25,000) from the spot market.
June 17
3. Sell the pesos to fulfill contract.
Gain £3,000.
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14. Currency Futures Market
Companies may purchase currency futures to hedge their foreign currency payables, or sell currency futures to hedge their receivables.
1. Expect to receive 500,000 pesos. Contract to sell 500,000 pesos @ £.056/peso on June 17.
April 4
2. Receive 500,000 pesos as expected.
June 17
3. Sell the pesos at the locked-in rate.
International Finance

15. 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.
International Finance

16. Daily Resettlement: An Example
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.
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17. 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-day-shorter maturity.
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18. 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.
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.
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19. Daily Resettlement: An Example
Over the first 3 days, the euro strengthens then depreciates in dollar terms:
Settle
Gain/Loss
Account Balance
$1.31
$1,250
= ($1.31 – $1.30)×125,000
$7,750
= $6,500 + $1,250
$1.30
–$1,250
$6,500
$1.27
–$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.
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20. Daily Resettlement: An Example
Over the next 2 days, the long keeps losing money and closes out his position at the end of day five.
Settle
Gain/Loss
Account Balance
$1.31
$1,250
$7,750
$1.30
–$1,250
$6,500
$1.27
–$3,750
$2,750 + $3,750 = $6,500
$1.26
–$1,250
$5,250
= $6,500 – $1,250
$1.24
–$2,500
$2,750
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21. Toting Up
At the end of his adventures, our investor has three ways of computing his gains and losses:
Sum of daily gains and losses
– $7,500 = $1,250 – $1,250 – $3,750 – $1,250 – $2,500
Contract size times the difference between initial contract price and last settlement price.
– $7,500 = ($1.24/€ – $1.30/€) × €125,000
Ending balance on account minus beginning balance on account, adjusted for deposits or withdrawals.
– $7,500 = $2,750 – ($6,500 + $3,750)
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22. Daily Resettlement: An Example
Gain/Loss
Account Balance
$1.30
–$–
$6,500
$1.31
$1,250
$7,750
$1.30
–$1,250
$6,500
$1.27
–$3,750
$2,750 + $3,750
$1.26
–$1,250
$5,250
$1.24
–$2,500
$2,750
Total loss = – $7,500
= ($1.24 – $1.30) × 125,000
= $2,750 – ($6,500 + $3,750)
International Finance

23. Currency swaps
Swaps came to public knowledge in the early 1980s and is the newest member of the derivative product set
Widely used swaps are interest rate swaps and currency swaps
A currency swap involves the exchange of principal and interest in one currency for the same in another currency
International Finance

24. The first swap
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25. Interest rates and comparative advantage
AAACorp wants a floating interest rate
BBBCorp wanta a fixed interest rate
Fixed
Floating
AAACorp
4.0%
6-month LIBOR %
BBBCorp
5.2%
6-month LIBOR + 1.0%

26. Comparative advantage
AAA can borrow at better terms in both markets since it is more creditworthy
1.2 % lower in the market for fixed interest rates
0.7 % lower in the market for floating interest rates
AAAs advantage is the highest in the market for fixed interest rates, hence AAA should borrow there according to comparative advantage
BBBs disadvantage is lowest in the market for floating interest rates, and it borrows floating
Both can gain by exploiting comparative advantage

27. A good deal for both
AAA borrows fixed at 4 %, BBB floating at LIBOR + 1 %, men this is not the kind of finance the companies prefer
AAA agrees to pay BBB LIBOR
BBB agrees to pay AAA 3.95 % fixed
Interest rate for AAA is 4 % % + LIBOR = LIBOR % (0.25 % lower than what they could have obtained on their own)
Interest rate fo BBB now is LIBOR + 1 % - LIBOR % = 4.95 % (0.25 % lower)

28. Currency swap - example
DuPont, the US chemicals company, needs to raise sterling for its UK operations. At the same time ICI, the British chemicals company, needs US dollars for its North American operations. They agree to swap (that is, exchange) sterling for dollars for, say, five years. The terms are that ICI pays the five year US$ rate of 5 per cent on the US dollar amount of US$15 million and DuPont the five year sterling rate at 6 per cent on £10 million. Payments are usually made on a net basis (that is, the differences). The effective exchange rate is therefore US$1.50 = £1. At the end of the transaction, the principal amounts are reexchanged by both parties (at the contracted rate).
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29. Du Pont – ICI swap
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30. Cash flow from ICI`s perspective
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31. Currency swaps
At initiation, the present value of the swap is 0 for both parties
Once the swap is active it may move away from the original valuation conditions. This means the swap will have a value to one party and be a liability to the other
Assume that after 2 years, the USD interest rate fall to 4.5% and the GBP interest rate increase to 7 %. Moreover, the spot rate changes to $1.45/£.
Is the swap an asset or a liability for ICI?
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32. Conditions change
ICI may now have incentive to walk away from the deal. Credit risk increase over time.
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33. 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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34. 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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35. 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.
Options are traded on exchanges as well as OTC
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36. 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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37. Currency Call Options A call option is
in the money if exchange rate > strike price,
at the money if exchange rate = strike price,
out of the money if exchange rate < strike price.
A put option is
in the money if exchange rate < strike price,
out of the money if exchange rate > strike price.
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38. 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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39. Currency options http://equivalentsrdc.cme.com:443/index_XB.html

40. Example – page 164
Jim is a speculator who buys a € call option from Linda with a strike price of £0.700 and a December settlement date. The current spot rate is about £0.682 and Jim pays a premium of £.005 per unit for the call option. Just before expiration, the spot rate reaches £0.724
What is the profit? One contract equals €
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41. Profit and loss
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42. 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, where ST is the spot rate at time T and X the exercise rate.
If the call is out-of-the-money, it is worthless.
CaT = CeT = Max[ST - X, 0]
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43. 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]
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44. Basic Option Profit Profiles
If the call is in-the-money, it is worth ST – X.
If the call is out-of-the-money, it is worthless and the buyer of the call loses his entire investment of c0 (premium)
Long 1 call ST
–c0
X + c0 X
Out-of-the-money
In-the-money
loss
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45. Basic Option Profit Profiles
If the call is in-the-money, the writer loses ST – X.
If the call is out-of-the-money, the writer keeps the option premium. c0 X
X + c0 ST
short 1 call
Out-of-the-money
In-the-money
loss
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46. Basic Option Profit Profiles
If the put is in-the-money, it is worth X – ST. The maximum gain is X – p0
If the put is out-of-the-money, it is worthless and the buyer of the put loses his entire investment of p0.
X – p0
X – p0 X ST
– p0
long 1 put
In-the-money
Out-of-the-money
loss
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47. Basic Option Profit Profiles
If the put is in-the-money, it is worth X – ST. The maximum loss is – X + p0
If the put is out-of-the-money, it is worthless and the seller of the put keeps the option premium of p0. p0 X
X – p0 ST
short 1 put
– X + p0
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loss

48. 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
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49. 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
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50. 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
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51. 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 - X, 0]
PaT > PeT = Max[X - ST, 0]
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52. Option Pricing and Valuation
The pricing of any currency option combines six elements:
Present spot rate
Exercise price
Time to maturity
Home currency interest rate
Foreign currency interest rate
Volatility (standard deviation of daily spot price movements)
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53. How can volatility be measured?
There are three ways of determining a value for volatility: the historical approach, the implied volatility approach and the forecast volatility method.
The historical way involves calculating the volatility based on a series of historical price data
The implied volatility is obtained by backing out of the pricing formula. The other variables can be observed – the only unknown is the volatility – so it can be implied from the values of the other variables.
Forecast volatility is derived by means of an estimating technique, typically a time series method, that aims to predict what volatility will be over the option period.
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54. 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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55. 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 + =
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56. 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.
Note that even an out-of-the-money option has value—time value.
Long 1 call
Market Value
Intrinsic value ST
Time value
Out-of-the-money
In-the-money
loss X
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57. 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.
We only need to know the signs – calculating the values (option greeks) is not covered in this course
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58. Option Value Determinants
Call Put
1. Exchange rate – 2. Exercise price – Interest rate home currency + – 4. Interest rate in other country – Variability in exchange rate Expiration date
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59. 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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60. 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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61. Garman - Kohlhagen
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62. 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 r* = 3,7 %
Time to expiration: 365 days (T = 1)
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63. Garman - Kohlhagen
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64. 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
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65. Long straddle What is the most you can lose? When do you make money?
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66. Short straddle What is the most you can lose? When do you make money?
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67. Long currency strangle
Call option premium on $ = £ 0.015
Put option premium on $ = £ 0.025
Call option strike price = £ 0.625/$
Put option strike price = £ 0,575/$
One option contract = A$
What is the profit or loss?
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68. Long currency strangle
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69. 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
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70. Currency bull spread
Two call options on A$ are available. One has a strike of £0,41 and a premium of £0,01. The next has a strike of £0,42 and premium of £0,005. One contract is A$
What is the profit or loss if the A$ is either £0,40 or £0,44 at expiry, and you have bought the 0,41 call and sold (written) the 0,42 call?
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71. Currency bull spread
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