Chapter 5
Currency Derivatives
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Foreign Currency Derivatives
• In this chapter, we will look at the following
important instruments
– Forwards
– Futures
– Swaps
– Currency options
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Forward Market (1)
• A forward contract is an agreement
between a firm 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.
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Forward Market
• Assume the contract is for $ 1 000 000
– The bank will borrow 1 000 000/(1 + 0,06/2) =
970 874. This amounts to 970 874/1,5 = £ 647 249
– Future value of £ deposit 647 249 * (1+ 0,10/2) = 679 612
– Forward exchange rate 1 000 000/679 612 =
$1.4714/£
(1  home interest) t
Ft  S0 
(1  foreign interest) t
1  0, 06 / 2
Ft  1.5 
 1.4714
1  0,10 / 2
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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
F  S 360

S
n
1.4714  1.500 360
p

 0.0381 or  0.0191 non annualised
1.500
180
F  S  (1  p) i.e. F  1.5000  (1  0.0191)  1.4714
p
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Forward Market Janury 14 2013
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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, interestbearing deposits, gold, the weather etc.
• Futures more or less eliminate credit risk as a
clearing house is the contract party
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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)
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Currency futures 14 January 2013
http://markets.ft.com/RESEARCH/markets/DataArchiveFetchReport?Category=CU&Type=CFUT&Date=01/14/2013
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Currency Futures Market
• Speculators often sell currency futures
when they expect the underlying
currency to depreciate, and vice versa.
April 4
June 17
1. Contract to sell
500,000 pesos
@ £.056/peso
(£28,000) on
June 17.
2. Buy 500,000 pesos @
£.050/peso (£25,000)
from the spot market.
3. Sell the pesos to fulfill
contract.
Gain £3,000.
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
Currency Futures Market
• MNCs may purchase currency futures
to hedge their foreign currency
payables, or sell currency futures to
hedge their receivables.
April 4
June 17
1. Expect to receive
500,000 pesos.
Contract to sell
500,000 pesos @
£.056/peso on
June 17.
2. Receive 500,000 pesos
as expected.
3. Sell the pesos at the
locked-in rate.
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
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.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Daily Resettlement: An Example
• Over the first 3 days, the euro strengthens
then depreciates in dollar terms:
Settle
Gain/Loss
Account Balance
$7,750 = ($1.31 – $1.30)×125,000
= $6,500 + $1,250
$1.31
$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.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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
$1.27
–$3,750
$1.26
–$1,250
$5,250
$1.24
–$2,500
$2,750
$6,500
$2,750 + $3,750 = $6,500
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
= $6,500 – $1,250
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)
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Daily Resettlement: An Example
Settle
$1.30
Gain/Loss
–$–
Account Balance
$6,500
$1.31
$1,250
$7,750
$1.30
–$1,250
$6,500
$1.27
–$3,750
$1.26
–$1,250
$5,250
$1.24
–$2,500
$2,750
Total loss = – $7,500
$2,750 + $3,750
= ($1.24 – $1.30) × 125,000
= $2,750 – ($6,500 + $3,750)
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
The first swap
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Interest rates and comparative
advantage
• AAACorp wants a floating interest rate
• BBBCorp wants a fixed interest rate
Fixed
Floating
AAACorp
4.0%
6-month LIBOR + 0.30%
BBBCorp
5.2%
6-month LIBOR + 1.0%
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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 % - 3.95 % + LIBOR = LIBOR
+ 0.05 % (0.25 % lower than what they could have
obtained on their own)
– Interest rate fo BBB now is LIBOR + 1 % - LIBOR +
3.95 % = 4.95 % (0.25 % lower)
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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).
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Du Pont – ICI swap
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Cash flow from ICI`s perspective
Amount USD
Amount GBP
Exchange rate
Interest USD
Interest GBP
Time
0
1
2
3
4
5
15 000 000
10 000 000
1,5
5%
6%
USD
15 000 000
-750 000
-750 000
-750 000
-750 000
-15 750 000
GBP
-10 000 000
600 000
600 000
600 000
600 000
10 600 000
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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?
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Conditions change
Remaining cash flows
Time
0
1
2
3
4
5
USD
15 000 000
-750 000
-750 000
-750 000
-750 000
-15 750 000
GBP
-10 000 000
600 000
600 000
600 000
-750 000
600 000
-750 000
10 600 000 -15 750 000
600 000
600 000
10 600 000
Present value
-717 703
-686 797
-13 801 672
-15 206 172
at 1,45
560 748
524 063
8 652 757
9 737 568
-10 487 015
-749 447
ICI may now have incentive to walk away from the deal. Credit risk
increases over time.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Currency Options Market
• Currency options provide the right to
purchase or sell currencies at specified
prices. They are classified as calls or puts.
• Standardized options are traded on
exchanges through brokers.
• Customized options offered by brokerage
firms and commercial banks are traded in
the over-the-counter market.
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Currency Call Options
• A currency call option grants the holder 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
if exchange rate > strike price
– at the money
if exchange rate = strike price
– out of the money
if exchange rate < strike price.
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
Currency Call Options
• Speculators may purchase call options on a
currency that they expect to appreciate.
– Profit = selling (spot) price – option premium
– buying (strike) price
– At breakeven, profit = 0
• They may also sell (write) call options on a
currency that they expect to depreciate.
– Profit = option premium – buying (spot) price
+ selling (strike) price
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
Currency Put Options
• A currency put option grants the holder 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
if exchange rate < strike price
– at the money
if exchange rate = strike price
– out of the money
if exchange rate > strike price.
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
Currency Put Options
• Speculators may purchase put options on a
currency that they expect to depreciate.
– Profit = selling (strike) price – buying price
– option premium
• They may also sell (write) put options on a
currency that they expect to appreciate.
– Profit = option premium + selling price
– buying (strike) price
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
Currency Put Options
• One possible speculative strategy for
volatile currencies is to purchase both a
put option and a call option at the same
exercise price. This is called a straddle.
• By purchasing both options, the
speculator may gain if the currency
moves substantially in either direction, or
if it moves in one direction followed by
the other.
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
Efficiency of
Currency Futures and Options
• If foreign exchange markets are
efficient, speculation in the currency
futures and options markets should
not consistently generate abnormally
large profits.
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
Contingency Graphs for Currency Options
For Buyer of £ Call
Option
Strike price
= £1.50
Premium
For Seller of £ Call Option
Strike price
Premium
= £ .02
Net Profit
per Unit
Net
Profit
per Unit
+$.04
+£.04
+$.02
+£.02
0
0
$1.46 $1.50 $1.54
–
$.02
–
$.04
= £1.50
= £ .02
Futur
e
Spot
Rate
Future
Spot
Rate
£1.46
–
£.02
–
£.04
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
£1.50
£1.54
Contingency Graphs for Currency Options
For Buyer of $ Put Option
Strike price
Premium
For Seller of $ Put Option
= £1.50
= £ .03
Strike price
Premium
Net
Profit per
Unit
Net Profit
per Unit
+£.04
+£.04
+£.02
Future
Spot
Rate
= £1.50
= £ .03
+£.02
0
0
£0.58 £0.60 £0.62
£0.58
–
£.02
–
£.02
–
£.04
–
£.04
Cost and Management
International
Accounting:
FinancialAn
Management,
Introduction,
2nd7th
edition
edition
Jeff
Colin
Madura
Drury
and Roland Fox
ISBN 978-1-40803-213-9
ISBN 978-1-4080-3229-9
© 2011©Cengage
2011 Cengage
Learning
Learning
EMEAEMEA
£0.60
£0.62
Future
Spot
Rate
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
€ 150 000
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Profit and loss
Jim
Selling price of €
Purchase price of €
Premium paid for option
Net profit
Linda
Selling price of €
Purchase price of €
Premium received
Net profit
Per unit
Per contract
0,724
108 600
0,700
105 000
0,005
750
2 850
0,700
0,724
0,005
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
105 000
108 600
750
-2 850
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]
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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]
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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]
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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)
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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
+
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Time
Value
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
Intrinsic
ST
value
Time
value
Out-of-theIn-the-money
money
loss
X 7 edition
Cost and Management Accounting: An Introduction,
th
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Option Value Determinants
Exchange rate
Exercise price
Interest rate home currency
Interest rate in other country
Variability in exchange rate
Expiration date
Call
+
+
+
+
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Put
+
+
+
+
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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.
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Garman - Kohlhagen
Calls: C  S  e
 r *T
Puts: P  X  e
 rT
 N(d1 )  X  e  rT  N(d 2 )
 N(d 2 )  S  e
 r *T
where
ln(S / X)  (r  r   / 2)  T
d1 
 T
*
2
d 2  d1   T
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
 N(d1 )
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)
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Garman - Kohlhagen
Spot rate
Exercise rate
Risk free foreign
Risk free domestic
Volatility (SD)
E
Time to expiration
Time to expiration
d1
d2
N(d1)
N(d2)
N(-d1)
N(-d2)
Call option value
Put option value
S
X
r*
r
σ
days
T
1,4900
1,4500
3,70 %
5,00 %
20,00 %
2,718282
365
1,000
0,301063
0,101063
0,618317
0,540250
0,381683
0,459750
0,1427
0,0861
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Long straddle
Call option premium on dollar
Put option premium on dollar
Strike price
Option contract in dollar
0,03
0,02
0,60
50 000
Own a call
Own a put
Net
0,50
-0,03
0,08
0,05
0,55
-0,03
0,03
0
0,60
-0,03
-0,02
-0,05
0,65
0,02
-0,02
0
When do you make money?
What is the most you can lose?
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
0,70
0,07
-0,02
0,05
0,75
0,12
-0,02
0,10
Short straddle
Call option premium on dollar
Put option premium on dollar
Strike price
Option contract in dollar
0,03
0,02
0,60
50 000
Sell a call
Sell a put
Net
0,50
0,03
-0,08
-0,05
0,55
0,03
-0,03
0,00
0,60
0,03
0,02
0,05
0,65
-0,02
0,02
0,00
When do you make money?
What is the most you can lose?
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
0,70
-0,07
0,02
-0,05
0,75
-0,12
0,02
-0,10
Long currency strangle
•
•
•
•
•
•
Call option premium on $
Put option premium on $
Call option strike price
Put option strike price
One option contract
What is the profit or loss?
= £ 0.015
= £ 0.025
= £ 0.625/$
= £ 0,575/$
= A$ 50 000
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Long currency strangle
Call option premium on dollar
Put option premium on dollar
Call option strike price
Put option strike price
Option contract in dollar
Own a call
Own a put
Net
0,015
0,025
0,625
0,575
50 000
0,525
-0,015
0,025
0,01
0,575
-0,015
-0,025
-0,04
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
0,625
-0,015
-0,025
-0,04
0,675
0,035
-0,025
0,01
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
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
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$ 50 000
• 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?
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
Currency bull spread
Call option A exercise
Premium call A
Call option B exercise
Premium call B
Option contract in A$
Buy option A
Sell option B
Net
0,41
0,010
0,42
0,005
50 000
0,400
-0,010
0,005
-0,005
0,410
-0,010
0,005
-0,005
0,415
-0,005
0,005
0
0,420
0,000
0,005
0,005
Cost and Management Accounting: An Introduction, 7th edition
Colin Drury
ISBN 978-1-40803-213-9 © 2011 Cengage Learning EMEA
0,430
0,010
-0,005
0,005
0,440
0,020
-0,015
0,005