This document discusses various currency derivatives including futures, options, and swaps. It begins with an introduction to derivatives and their uses for speculation and hedging. It then covers the basics of currency futures and forwards contracts including how futures are traded and marked to market daily. The document also discusses currency options, including the basics of calls and puts as well as how options are priced and valued based on factors like the exchange rate and time to expiration. Finally, the document defines currency swaps and provides an example of an interest rate swap where two parties agree to exchange their interest rate payment obligations to jointly lower their borrowing costs.

1. Currency Futures, Options
& Swaps
Reading: Chapters 7 & 14 (474-485)

2. Lecture Outline
 Introduction to Derivatives
 Currency Forwards and Futures
 Currency Options
 Interest Rate Swaps
 Currency Swaps
 Unwinding Swaps
2

3. Introduction
 A derivative (or derivative security) is a financial
instrument whose value depends on the value of other,
more basic underlying variables/assets:
 Share options (based on share prices)
 Foreign currency futures (based on exchange rates)
 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.
3

4. Definition of Futures and Forwards
 Currency futures and forward contracts both represent
an obligation to buy or sell a certain amount of a
specified currency some time in the future at an
exchange rate determined now.
 But, futures and forward contracts have different
characteristics.
4

5. Futures versus Forwards
5

6. Futures Contract - Example
Specification of the Australian Dollar futures contract
(International Money Market at CME)
Size AUD 100,000
Quotation USD / AUD
Delivery Month March, June, September,
December
Min. Price Move $0.0001 ($10.00)
Settlement Date Third Wednesday of delivery
month
Stop of Trading Two business days prior to
settlement date
6

7. 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
members.
7

8. 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
8

9. 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.
9

10. Marking to Market – Example
 Trader buys 1 AUD contract on 1 Feb for USD0.5000/
AUD
 USD value = 100,000 x 0.5000 = USD 50,000.
Date Settlement Value of Contract Margin A/c
________________________________________________________________________________
1 Feb 0.4980 49,800 - 200
2 Feb 0.4990 49,900 + 100
3 Feb 0.5020 50,200 + 300
4 Feb 0.5010 50,100 - 100
10

11. Trouble with Forwards/Futures?
+ Seller (short) Buyer (long)
US$ US$
0 $ Spot
1.80 2.00
A$ 1.90/US$
Forward/Futures
Rate
-
11

12. Basics of Options
 Options give the option holder the right, but not the
obligation to buy or sell the specified amount of the
underlying asset (currency) at a pre-determined price
(exercise or strike price).
 The buyer of an option is termed the holder, while the
seller of the option is referred to as the writer or
grantor.
 Types of options:
 Call: gives the holder the right to buy
 Put: gives the holder the right to sell
12

13. 0
Basics of 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.
 The premium, or option price, is the cost of the
option.
13

14. Basics of Options
 The Philadelphia Exchange commenced trading
in currency options in 1982.
 Currencies traded on the Philadelphia exchange:
• Australian dollar, British pound, Canadian dollar,
Japanese yen, Swiss franc and the Euro.
 Expiration months:
• March, June, September, December plus two near-term
months.
14

15. Basics of Options
Spot rate, 88.15 ¢/€
Size of contract:
€62,500
Exercise price The indicated contract price is:
0.90 ¢/€
€62,500 × $0.0125/€ = $781.25
Maturity month
One call option gives the holder the right to purchase
€62,500 for $56,250 (= €62,500 × $0.90/€)
15

16. 0
Options Trading
 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 $0.005/SF.
– At all spot rates below the strike price of 58.5, the
purchase of the option would choose not to exercise
because it would be cheaper to purchase SF on the open
market.
– At all spot rates above the strike price, the option
purchaser would exercise the option, purchase SF at the
strike price and sell them into the market netting a
profit (less the option premium).
16

17. 17

18. 0
Options Trading
 Writer of a call:
– What the holder, or buyer of an option loses, the writer
gains.
– 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 now have to buy the currency
at the spot and take the loss delivering 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.
18

19. 19

20. 0
Options Trading
 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 when the market price of
that currency drops (not rises as in the case of the call option).
– If the spot price drops to $0.575/SF, the buyer of the put will
deliver 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
$0.05/SF premium.
– The buyer of a put (like the buyer of the call) can never lose more
than the premium paid up front.
20

21. 21

22. 0
Options Trading
 Seller (writer) of a put:
– In this case, if the spot price of francs drops below 58.5
cents per franc, the option will be exercised.
– Below a price of 58.5 cents per franc, the writer will
lose more than the premium received fro 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.
22

23. 23

24. 0
Option Pricing & Valuation
 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).
24

25. Option Pricing & Valuation
Call Put
Intrinsic value 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
Time Value CT – Int. value PT – Int. value
25

26. Option Pricing & Valuation
 current exchange rate (S) – as S ↑, Call ↑ and Put ↓
 strike price (X) – as X ↑, Call ↓ and Put ↑
 time to expiration (T) – as T ↑, both ↑
 volatility of the exchange rate (σ) – as σ ↑, both ↑
 domestic interest rate (id) – as id ↑, Call ↑ and Put ↓
 foreign interest rate (if) – as if ↑, Call ↓ and Put ↑
26

27. 0
Option Pricing & Valuation
27

28. Forwards versus Options
$0.90
.
$0.75
Value of Forward/Put Option at Expiration
$0.60
$0.45
$0.30
$0.15
$0.00
-$0.15
-$0.30
Value of Forward Sale at Expiration
-$0.45
Value of Put at Expiration
-$0.60
-$0.75
-$0.90
$0.10
$0.20
$0.30
$0.70
$0.80
$1.00
$1.10
$1.50
$1.60
$1.70
$0.00
$0.40
$0.50
$0.60
$0.90
$1.20
$1.30
$1.40
$1.80
Spot Rate at Expiration
28

29. What are Swaps?
Swaps are contractual agreements to exchange
or swap a series of cash flows.
These cash flows are most commonly the
interest payments associated with debt service.
– If the agreement is for one party to swap its fixed
interest rate payments for the floating interest rate
payments of another, it is termed an interest rate swap.
– If the agreement is to swap currencies of debt service
obligation, it is termed a currency swap.
– A single swap may combine elements of both interest
rate and currency swaps.
29

30. What are Swaps?
 The swap itself is not a source of capital, but
rather an alteration of the cash flows associated
with payment.
 What is often termed the plain vanilla swap is an
agreement between two parties to exchange fixed-
rate for floating-rate financial obligations.
 This type of swap forms the largest single
financial derivative market in the world.
30

31. What are Swaps?
 There are two main reasons for using swaps:
1. A corporate borrower has an existing debt service
obligation. Based on their interest rate predictions
they want to swap to another exposure (e.g. change
from paying fixed to paying floating).
2. Two borrowers can work together to get a lower
combined borrowing cost by utilizing their
comparative borrowing advantages in two different
markets.
31

32. What are Swaps?
 For example, a firm with fixed-rate debt that
expects interest rates to fall can change fixed-rate
debt to floating-rate debt.
 In this case, the firm would enter into a pay
floating/receive fixed interest rate swap.
32

33. Swap Bank
 A swap bank is a generic term used to describe a
financial institution that facilitates swaps between
counterparties.
 The swap bank serves as either a broker or a dealer.
 A broker matches counterparties but does not assume any of
the risk of the swap. The swap broker receives a
commission for this service.
 Today most swap banks serve as dealers or market makers.
As a market maker, the swap bank stands willing to accept
either side of a currency swap.
33

34. Example of an Interest Rate Swap
 Bank A is a AAA-rated international bank located
in the U.K. that wishes to raise $10,000,000 to
finance floating-rate Eurodollar loans.
 Bank A is considering issuing 5-year fixed-rate
Eurodollar bonds at 10 percent.
 It would make more sense for the bank to issue
floating-rate notes at LIBOR to finance the floating-rate
Eurodollar loans.
34

35. Example of an Interest Rate Swap
 Company B is a BBB-rated U.S. company. It needs
$10,000,000 to finance an investment with a five-
year economic life, and it would prefer to borrow at
a fixed rate.
 Firm B is considering issuing 5-year fixed-rate
Eurodollar bonds at 11.75 percent.
 Alternatively, Firm B can raise the money by issuing 5-
year floating rate notes at LIBOR + ½ percent.
 Firm B would prefer to borrow at a fixed rate.
35

36. Example of an Interest Rate Swap
The borrowing opportunities of the two firms are shown in
the following table.
COMPANY B BANK A DIFFERENTIAL
Fixed rate 11.75% 10% 1.75%
Floating rate LIBOR + 0.50% LIBOR 0.50%
36

37. Example of an Interest Rate Swap
 Bank A has an absolute advantage in borrowing
relative to Company B
 Nonetheless, Company B has a comparative
advantage in borrowing floating, while Bank A has a
comparative advantage in borrowing fixed.
 That is, the two together can borrow more cheaply if
Bank A borrows fixed, while Company B borrows
floating.
37

38. Example of an Interest Rate Swap
To see the potential advantages to a swap, imagine the two
entities trying to minimize their combined borrowing costs:
COMPANY B BANK A TOGETHER
Borrow preferred
11.75% LIBOR LIBOR + 11.75%
method
Borrow opposite
LIBOR + 0.50% 10% LIBOR + 10.50%
and swap
POTENTIAL SAVINGS: 1.25%
38

39. Example of an Interest Rate Swap
COMPANY B BANK A TOGETHER
Borrow preferred
11.75% LIBOR LIBOR + 11.75%
method
Borrow opposite
LIBOR + 0.50% 10% LIBOR + 10.50%
and swap
POTENTIAL SAVINGS: 1.25%
Now, we must determine how to split the swap savings!
If Swap Bank takes 0.25% that leaves 1% for Bank A &
Company B. If they share this equally then:
- Bank A pays LIBOR - 0.5% = LIBOR – 0.5%
- Company B pays 11.75% - 0.5% = 11.25%
39

40. Example of an Interest Rate Swap
Swap
Bank
10 3/8%
LIBOR – 1/8%
Bank The swap bank makes
A this offer to Bank A: You
pay LIBOR – 1/8 % per
year on $10 million for 5
years, and we will pay
you 10 3/8% on $10
million for 5 years.
40

41. Example of an Interest Rate Swap
Swap
Bank
10 3/8%
LIBOR – 1/8% Why is this swap
Bank desirable to Bank A?
A With the swap, Bank A
10% pays LIBOR-1/2%
COMPANY B BANK A DIFFERENTIAL
Fixed rate 11.75% 10% 1.75%
Floating rate LIBOR + 0.50% LIBOR 0.50%
41

42. Example of an Interest Rate Swap
Swap
Bank
10 ½%
The swap bank makes this LIBOR – ¼%
offer to Company B: You
pay us 10 ½ % per year on Company
$10 million for 5 years, B
and we will pay you
LIBOR – ¼ % per year on
$10 million for 5 years.
42

43. Example of an Interest Rate Swap
Swap
Bank
10 ½%
Why is this swap LIBOR – ¼%
desirable to Company B?
Company
With the swap, Company B
B pays 11¼% LIBOR + ½%
COMPANY B BANK A DIFFERENTIAL
Fixed rate 11.75% 10% 1.75%
Floating rate LIBOR + 0.50% LIBOR 0.50%
43

44. Example of an Interest Rate Swap
Will the swap bank
make money? Swap
10 3/8 % Bank 10 ½%
LIBOR – 1/8% LIBOR – ¼%
Bank Company
A B
44

45. Example of an Interest Rate Swap
The swap bank Swap
makes ¼ %
Bank
10 3/8 % 10 ½%
LIBOR – ¼%
LIBOR – 1/8%
Bank Company LIBOR
10%
Note that the total savings + ½%
A ½ + ½ + ¼ = 1.25 % = QSD B
A saves ½ % B saves ½ %
COMPANY B BANK A DIFFERENTIAL
Fixed rate 11.75% 10% 1.75%
Floating rate LIBOR + 0.50% LIBOR 0.50%
QSD = 1.25%
45

46. The QSD
 The Quality Spread Differential (QSD) represents the
potential gains from the swap that can be shared
between the counterparties and the swap bank.
 There is no reason to presume that the gains will be
shared equally.
 In the above example, Company B is less credit-worthy
than Bank A, so they probably would have gotten less
of the QSD, in order to compensate the swap bank for
the default risk.
46

47. Currency Swaps
 Since all swap rates are derived from the yield curve in
each major currency, the fixed-to-floating-rate interest rate
swap existing in each currency allows firms to swap across
currencies.
 The usual motivation for a currency swap is to replace
cash flows scheduled in an undesired currency with flows
in a desired currency.
 The desired currency is probably the currency in which the
firm’s future operating revenues (inflows) will be
generated.
 Firms often raise capital in currencies in which they do not
possess significant revenues or other natural cash flows (a
significant reason for this being cost).
47

48. Currency Swaps
 Example: Suppose a U.S. MNC, Company A,
wants to finance a £10,000,000 expansion of a
British plant.
 They could borrow dollars in the U.S. where they are well
known and exchange dollars for pounds. This results in
exchange rate risk, OR
 They could borrow pounds in the international bond market,
but pay a lot since they are not well known abroad.
48

49. Example continued..
 If Company A can find a British MNC with a
mirror-image financing need, both companies
may benefit from a swap.
 If the exchange rate is S0 = 1.60 $/£, Company
A needs to find a British firm wanting to finance
dollar borrowing in the amount of $16,000,000.
49

50. Example continued..
 Company A is the U.S.-based MNC and Company B is
a U.K.-based MNC.
 Both firms wish to finance a project of the same size in
each other’s country (worth £10,000,000 or
$16,000,000 as S = 1.60 $/£). Their borrowing
opportunities are given below.
$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
50

51. A’s Comparative Advantage
 A is the more credit-worthy of the two.
 A pays 2% less to borrow in dollars than B.
 A pays 0.4% less to borrow in pounds than B:
$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
51

52. B’s Comparative Advantage
 B has a comparative advantage in borrowing in £.
 B pays 2% more to borrow in dollars than A.
 B pays only 0.4% more to borrow in pounds than
A:
$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
52

53. Potential Savings
$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
Differential (B-A) 2.0% 0.4%
Potential Savings = 2.0% - 0.4% = 1.6%
If Swap Bank takes 0.4% and A&B split the rest:
Company A pays 11.6% - 0.6% = 11%
Company B pays 10% - 0.6% = 9.4%
53

54. Example of a Currency Swap
Swap
Bank
i$=8% i$=9.4%
i£=12%
i£=11%
i$=8% Company Company i£=12%
A B
$ £
Company A 8.0% 11.6%
Company B 10.0% 12.0%
Differential (B-A) 2.0% 0.4%
54

55. Example of a Currency Swap
Swap
Bank
i$=8% i$=9.4%
i£=12%
i£=11%
i$=8% Company Company i£=12%
A B
A’s net position is to borrow at i£=11%
$ £
A saves i£=0.6%
Company A 8.0% 11.6%
Company B 10.0% 12.0%
Differential (B-A) 2.0% 0.4%
55

56. Example of a Currency Swap
Swap
Bank
i$=8% i$=9.4%
i£=12%
i£=11%
i$=8% Company Company i£=12%
A B
$ £ B’s net position is to borrow at i$=9.4%
Company A 8.0% 11.6%
B saves i$=0.6%
Company B 10.0% 12.0%
56

57. Example of a Currency Swap
The swap bank makes 1.4% of $16 million
Swap financed with 1% of £10
money too:
Bank million per year for 5
years.
i$=8% i$=9.4%
i£=12%
i£=11%
i$=8% Company At S0 = 1.60 $/£, that is a Company i£=12%
A gain of $64,000 per year B
for 5 years.
$ £ The swap bank
Company A 8.0% 11.6% faces exchange rate
Company B 10.0% 12.0% risk, but maybe
they can lay it off
in another swap.
57

58. Unwinding a Swap
 Discount the remaining cash flows under the swap
agreement at current interest rates, and then (in the case
of a currency swap) convert the target currency back to
the home currency of the firm.
 Payment of the net settlement of the swap terminates
the swap.
58

59. Unwinding a Swap
 Suppose in the previous example, Company A wanted
to unwind its (5 year) currency swap with the Swap
Bank at the end of Year 3. Assume that at Year 3, the
applicable dollar interest rate is 7.75% per annum, the
applicable pound interest rate is 11.25% per annum,
and S=1.65 $/£.
 What will the net settlement amount be?
59

60. Unwinding a Swap
 There are two years of interest payments and repayment of face
values remaining.
 For Company A:
 Paying 11% p.a. on £10,000,000
 Receiving 8% p.a. on $16,000,000
 Must return £10,000,000 and receive $16,000,000 at end
 Net settlement for Company A is:
+ (16*0.08)/1.0775 + (16*0.08)/(1.0775)2 + 16/(1.0775)2
– [(10*0.11)/1.1125 + (10*0.11)/(1.1125)2 + 10/(1.1125)2]x1.65
= -0.358 million dollars (must pay this amount to unwind swap)
60