I have prepared this slide to use in my class for my International Finance students at Universiti Utara Malaysia.

1. Currency Derivatives

2. What are Derivatives
• Derivatives are financial contracts whose cash flows and
value derives from some underlying financial asset or
commodity or indicator. For example, stock options
provided to managers.
• Underlying assets may be financial assets, commodities,
currencies, etc.
• Counterparties are typically known as buyer (long) and
seller (short).
• Forwards and Options are the most contract type
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3. Currency Forwards
• The exchange of one currency for another at a future
date using a pre-determined exchange rate
• At inception, the two parties—long and short—simply agree
on the forward price.
• At maturity, the short delivers the contracted units of the
base currency and in return the long makes payment
using the terms currency.
• Certain currency forwards do not entail actual delivery of
the foreign currency and are known as non-deliverable
forwards (NDF).
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4. Currency Forwards
• Example 3.2… page 54 – 55
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5. Currency Forwards
Terms to remember
• Underlying asset
– Units of base currency
• Maturity
– Delivery date for the currency
• Forward price
– Units of the terms/payment currency per unit of base currency
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6. Currency Forwards
Market structure
• Currency forwards are traded in the interbank markets
• Outright forwards are different from foreign exchange
swaps (to discuss later)
• Forward markets are private and normally parties of
transactions are known to each other
• Banks are the key players in such market, MNCs
participate through banks
• Most transactions are large, exceeding USD 10 million.
• Often, online systems are used to help speedier and
synchronized trades
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7. Currency Forwards
Forward price
• Notations
– Price of the base currency in the spot market, 𝑆
– Forward price of the base currency, 𝐹
– Domestic interest rate, 𝑟
– Foreign interest rate, 𝑟∗
– Maturity of the forward contract, 𝑡
• Suppose you want to obtain one unit of base currency
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8. Currency Forwards
Forward price
• Suppose you want to obtain one unit of base currency at
time 𝑡.
• You have two alternatives:
• Alternative A: buy the currency using forward contract
– Pay the forward price, 𝐹, at time 𝑡.
• Alternative B: borrow money to buy the currency today,
deposit in bank until time 𝑡.
– Borrow 𝑆 at interest rate 𝑟, use it to buy the base currency
– Deposit the base currency and earn at 𝑟∗ until time 𝑡.
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9. Currency Forwards
Forward price
• In equilibrium, alternative A and B should cost the same
and following relationship must be satisfied:
𝐹 = 𝑆 ×
1 + 𝑟
1 + 𝑟∗
𝑡
• Rearranging the equation:
𝐹
𝑆
=
1 + 𝑟
1 + 𝑟∗
𝑡
• If 𝑟∗
> 𝑟, then
𝐹
𝑆
< 1, and 𝐹 < 𝑆; in this case, forward
premium, 𝐹𝑃 =
𝐹
𝑆
− 1 =
1+𝑟
1+𝑟∗
𝑡
− 1
• Thus, if 𝑟∗
> 𝑟, forward premium is negative (forward
discount) and if 𝑟 > 𝑟∗
, forward premium is positive.
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10. Currency Forwards
Forward price
• Example 3.3… page 56 – 57.
• Problem 5… page 77.
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11. Currency Forwards
Counterparty risk in forward contracts
• Nonperformance by any of the two parties in the forward
contract results in the presence of counterparty risk or
default risk.
• MNCs conduct due diligence on their counterparties
prior to engaging in forward contracts.
• Despite the presence of such risk, forward contracts are
attractive because of its advantage of customization in
terms of currency, size, and maturity.
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12. Currency Forwards
Counterparty risk in forward contracts
• Example 3.4… page 57
• Problem 2… page 77
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13. Currency Futures
• Participants of forward market is limited to large institutions
and MNCs due to the problem of counterparty risk
associated with forward contracts.
• Futures markets satisfy the demand for similar derivative
contracts of the parties left outside the forward market.
• A futures contract
– is an exchange traded version of the forward contract
– is standardized with specific maturity and size
– allows wider range of players for its relatively small size compared
to forward contracts
– offers anonymity
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14. Currency Futures
Market structure
• Chicago Mercantile Exchange (CME) is the market
leader in currency futures.
• These exchanges provide
– infrastructure
– clearing functions
• Trading may occur
– on the trading floor of the exchange
– electronically or virtually around the clock
• Settlement procedure may vary
– actual delivery
– cash settlement
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15. Currency Futures
Daily settlement
• Futures are traded anonymously
• Hence, some sort of collateral, or third party guarantee is
necessary for trading to take place
• Consequently, both the long and the short in the futures
transaction must set up margin accounts (also called
performance bonds) at their brokerages
• Margin accounts are cash accounts to protect concerned
parties against default.
• These margin accounts serve as collateral
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16. Currency Futures
Daily settlement
• The margin account balances must be more than sufficient
to cover any changes in contract value
• It is difficult to cover against default arising out of a
large change in the price of underlying currency over a
longer period
• However, price changes in any given day would be
significantly less compared to that over the contract life
• This is why futures exchanges require accounts to be
settled every day.
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17. Currency Futures
Daily settlement
• Initial deposit in the margin account is called initial margin
• At the end of each trading day, change in value of the
futures contract is calculated by
(current day’s close – previous day’s close)
• If the contract value increases
– fund is transferred from short’s account to long’s account
• If the contract value decreases
– fund is transferred from long’s account to short’s account
• The clearing house of the exchange facilitates these transfers
• An alternative term used to denote such daily settlement
– mark to market
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18. Currency Futures
Daily settlement
• If the margin accounts are allowed to contain too low balance,
it may fail to provide protection when price declines sharply
• A minimum balance of the account is required to maintain
– maintenance margin
• Maintenance margin is lower than the initial margin
• If the balance of a margin account falls below the
maintenance margin, it triggers additional funds are
requested to deposit
– margin call
• If the margin call is ignored, the remaining funds are used
to close out the futures position
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19. Currency Futures
Daily settlement
• Futures are similar to forward contracts
• Cash flows in futures are also quite similar to forward
contracts with only one difference
– cash flows of futures are settled every day, whereas that of
forward contract is settled only once at maturity
• The sum total of daily settlements in futures should be
equal to the final settlement of an equivalent forward
contract
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20. Currency Futures
Daily settlement
• Example 3.5…page 60
• An MNC enters into futures contract to buy CAD @
USD 0.90
• Initial margin is USD 0.60
• Maintenance margin is USD 0.03
• Days remaining before contract maturity, 4 days
• Calculate cash flows per unit of foreign currency.
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21. Currency Futures
Daily settlement
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Day Price
Long Short
RemarksChange Balance CF Change Balance CF
0 0.90 0.06 -0.06 0.06 -0.06 Initial margin
1 0.92 +0.02 0.08 -0.02 0.04
2 0.94 +0.02 0.10 -0.02 0.02 Margin call
0.06 -0.04 Call met
3 0.91 -0.03 0.07 +0.03 0.09
4 0.89 -0.02 0.05 +0.05 +0.02 0.11 +0.11 Close
-0.89 +0.89 Delivery
-0.90 +0.90 Total

22. Currency Futures
Daily settlement
• Problem 4… page 77 (assignment)
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23. Currency Futures
Daily settlement
• Actual futures prices are widely disseminated
• Futures contracts are essentially similar to forward
contracts
• We can use currency forward pricing formula to calculate
futures price, using annual compounding convention
𝐹 = 𝑆 ×
1 + 𝑟
1 + 𝑟∗
𝑡
or using LIBOR convention
𝐹 = 𝑆 ×
1 + 𝑟𝑡
1 + 𝑟∗ 𝑡
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24. Currency Futures
Daily settlement
• Example 3.6… page 61
• Problem 6… page 77
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25. Futures vs. Forward Prices
in the Currency Markets
• Currency markets offer simultaneous trading of forward and
futures
• Forwards are traded in interbank market
• Futures are traded in exchanges like CME
• Difference of forward and futures price of the same
currency often brings the opportunity to exploit such price
discrepancy
• Electronic trading systems such as BARX and Globex as
well as computerized program trading help many institutions
to make profit in this way
• However, in equilibrium, futures price should be equal to
forward price
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26. Currency Options
• An instrument that provides the long the right to purchase or
sell the underlying/base currency
– at a prespecified strike price denominated in the terms currency
– at a future date
• only at maturity (European style options)
• at or prior to maturity (American style options)
• Right to purchase is provided by call options
• Right to sell is provided by put options
• Unlike forward/futures, options are more flexible because
– future purchase/sale of the underlying asset is optional
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27. Currency Options
Options parameters and terminology
• Options give the holder the flexibility of taking one of two
actions as appropriate
• Financial options: the underlying asset is any financial
asset like a foreign currency
• Real options: business situations that provide flexibility
that brings the ability of increasing cash flows by making
proper choice
• Underlying asset: commodity, instrument, index, or
currency that is bought or sold using the option
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28. Currency Options
Options parameters and terminology
• Strike price/exercise price: contractual price at which the
underlying asset is bought or sold using the option
• Maturity is finite, majority expiring in 6 months
– option’s value diminishes with each passing day
– this is why options are often called ‘wasting assets’
– ‘American options’ can be exercised at any point in time prior
to maturity
– ‘European options’ can be exercised only at maturity
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29. Currency Options
Options parameters and terminology
• Option premium: at the time of making the contract, option
holder pays a premium to the option seller.
• A rational option holder will exercise the option only if it
is profitable
• Hence, option holder cannot lose money from the option
• However, the counterparty or the option seller loses money
whenever the option is exercised
• The option premium is the compensation for such loss of
the option seller
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30. Currency Options
Market structure
• The Philadelphia Stock Exchange (PHLX) pioneered
trading in foreign currency options
• At present, PHLX and CME are the main
exchanges
• Popularity of exchange traded currency options is less
than that of currency futures
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31. Currency Options
Option exercise and cash flows
• Payoff equals cash flow at maturity, also called gross
profit, or maturity cash flow
• Profit equals payoff net of premium, also called net profit
or net cash flow.
• Steps:
– Determine the cash flow at inception, based on premium
– Estimate the payoff, which is the difference between spot price
and exercise price
– Calculate the profit, by deducting premium from the payoff
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32. Currency Options
Option exercise and cash flows: call option
• A purchases a European style currency call option from
B by paying a premium of USD0.06. The underlying
asset is EUR 1. The option expires in 3 months, and has
a strike price of USD1.25.
• Calculate the payoff and profit to the long, if the currency
value at maturity is USD 1.34.
• Answer:
– payoff is 0.09 to the long
– profit is 0.03 to the long
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33. Currency Options
Option exercise and cash flows: call option
• Calculate payoff and profit to the long for different values of the currency at
maturity.
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Call Option: Payoff & Profit to Long (Buyer)
Call Parameters: C = 0.06, X =1.25
All Values in USD
At Contract
Inception Cash Flows At Maturity
Overall
Result
Currency
Value at
Maturity Premium Paid Exercise Price Paid Value Received Payoff Profit
1.16 0.06 No Exercise No Exercise 0 -0.06
1.19 0.06 No Exercise No Exercise 0 -0.06
1.22 0.06 No Exercise No Exercise 0 -0.06
1.25 0.06 No Exercise No Exercise 0 -0.06
1.28 0.06 1.25 1.28 0.03 -0.03
1.31 0.06 1.25 1.31 0.06 0.00
1.34 0.06 1.25 1.34 0.09 0.03
1.37 0.06 1.25 1.37 0.12 0.06
Note: Payoff & Profit to Short (Seller) is the exact opposite (that is, positive values are
negative and negative values are positive)

34. Currency Options
Option exercise and cash flows: call option
• Graphically show the payoff and profit to the long for different values of the currency at maturity.
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35. Currency Options
Option exercise and cash flows: put option
• P purchases a European style currency put option from
Q by paying a premium of USD0.03. The underlying
asset is EUR 1. The option expires in 3 months, and has
a strike price of USD1.25.
• Calculate the payoff and profit to the long, if the currency
value at maturity is USD 1.16.
• Answer:
– payoff is 0.09 to the long
– profit is 0.06 to the long
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36. Currency Options
Option exercise and cash flows: put option
• Calculate payoff and profit to the long for different values of the currency at maturity.
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Put Option: Payoff & Profit to Long (Buyer)
Call Parameters: P = 0.03, X =1.25
All Values in USD
At Contract
Inception Cash Flows At Maturity
Overall
Result
Currency
Value at
Maturity Premium Paid
Exercise Price
Received Value Given Up Payoff Profit
1.16 0.03 1.25 1.16 0.09 0.06
1.19 0.03 1.25 1.19 0.06 0.03
1.22 0.03 1.25 1.22 0.03 0.00
1.25 0.03 No Exercise No Exercise 0 -0.03
1.28 0.03 No Exercise No Exercise 0 -0.03
1.31 0.03 No Exercise No Exercise 0 -0.03
1.34 0.03 No Exercise No Exercise 0 -0.03
1.37 0.03 No Exercise No Exercise 0 -0.03
Note: Payoff & Profit to Short (Seller) is the exact opposite (that is, positive values
are negative and negative values are positive)

37. Currency Options
Option exercise and cash flows: put option
• Graphically show the payoff and profit to the long for different values of the currency at maturity.
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38. Currency Options
Option exercise and cash flows: call vs. put option
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39. Currency Options
Summary of option payoffs and profits
• Notations:
𝑆𝑡 = price of underlying asset at maturity
𝑋 = option strike or exercise price
𝐶 = call premium
𝑃 = put premium
• Call options are exercised when
𝑆𝑡 > 𝑋
• Put options are exercised when
𝑆𝑡 < 𝑋
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40. Currency Options
Summary of option payoffs and profits
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41. Currency Options
Summary of option payoffs and profits
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42. Currency Options
Summary of option payoffs and profits
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43. Currency Options
Summary of option payoffs and profits
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44. Currency Options
Summary of option payoffs and profits
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45. Currency Options
Summary of option payoffs and profits
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46. Currency Options
Summary of option payoffs and profits
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47. Currency Options
Summary of option payoffs and profits
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48. Currency Options
Summary of option payoffs and profits
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49. Currency Options
Summary of option payoffs and profits
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50. Currency Options
Factors affecting call option prices
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• Value of underlying asset, (𝑺)
• Strike price (𝑿)
• Maturity (𝒕)
– Time value
– both for call and put
• Volatility (𝝈)
– Both for call and put
• Domestic currency interest rate (𝒓)
• Foreign currency interest rate (𝒓∗
)

51. Currency Options
Pricing call and put options
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• Value of underlying asset, (𝑆)
• Strike price (𝑋)
• Maturity (𝑡)
• Volatility (𝜎)
• Domestic currency interest rate (𝑟)
• Foreign currency interest rate (𝑟∗
)
• 𝑒 = 2.7182818283
• 𝑁(. ) is the cumulative distribution
function of the standard normal
distribution
.
,
2
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,
),()(
12
2
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21
*
tdd
and
T
trr
X
S
d
where
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







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

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