Foreign Exchange Options
Prof. Ian Giddy
New York University
Tools for Hedging

Petrobras has to pay for equipment from
Japan, in Japanese yen, in 3 months
Lock
in a forward price
Or use a call option on the Yen?
How much will it cost?
Copyright ©1996 Ian H. Giddy
Currency Options 2
Option Hedge
CALL
OPTION
ON YEN
FORWARD
CONTRACT
Copyright ©1996 Ian H. Giddy
Currency Options 5
Option Hedge
Questions about options:
 When should companies use them?
 Which options?
 How much do they cost,
 Are they worth paying for?
 What is the risk to the bank?
Copyright ©1996 Ian H. Giddy
Currency Options 6
Foreign Exchange Options
The right, but not the obligation, to
exchange currency at a predertermined
rate.
 The right to buy is a call; the right to
sell, a put.
 American options permit the holder to
exercise at any time before the
expiration date; European options, only
on the expiration date.

Copyright ©1996 Ian H. Giddy
Currency Options 7
Hockey Stick Diagrams
These show payoff at expiration of
options. Eg. buying a call produces a
gain if the currency rises above the
strike plus the premium; the call writer’s
profit profile is opposite.
Buy a Put
Gain
or Loss
Copyright ©1996 Ian H. Giddy
Value of Swiss franc
Currency Options 8
Option Payoff Diagrams

Buy call: right to
purchase
foreign currency
Profit
Profit
BUY
CALL
OPTION
+
+
Strike
0
0
Premium
Forward
Rate
_
Forward
_
SELL
CALL
OPTION

Buy put: right to
sell foreign
currency
Profit
Profit
BUY
PUT
OPTION
+
+
0
0
Forward
_
Forward
_
SELL
PUT
OPTION
Figure 2. Payoff at Expiration of Options. Eg. buying a call produces a gain if the currency (ie the futures price) rises
above the strike plus the premium; the call writer's profit profile is opposite.
Copyright ©1996 Ian H. Giddy
Currency Options 9
Pricing a Call Option
Forward relative to strike
 Time to expiration
 Volatility
 Interest rate

Option
Value
Currency Value
Copyright ©1996 Ian H. Giddy
Currency Options 15
Option Price is
“Present value of average-profit-given
exercise
 Underlying instrument has probability
distribution
 Probability of exercise is given by area under
curve to right of strike price
 Average-profit-given-exercise is mean of right
hand area under curve minus the strike price
(you buy at strike and sell at market)
Value of option is the present value of that profit
Copyright ©1996 Ian H. Giddy
Currency Options 16
Value of Call Option
FORWARD
Equals present value
of its expected
intrinsic value at
expiration, given
that the forward is
above the strike
STRIKE
Copyright ©1996 Ian H. Giddy
Currency Options 17
Value of Call Option
FORWARD
STRIKE
INTRINSIC VALUE
SHADED AREA:
Probability distribution
of the log of the forward
rate on the expiration date
for values above the strike.
TIME VALUE
EXPECTED VALUE OF PROFIT
GIVEN EXERCISE
Copyright ©1996 Ian H. Giddy
Currency Options 18
Currency Option Pricing:
the Famous Formula
C  PV [FN (d1 )  KN (d 2 )]
where
ln(F / K )  

d1 
2
 
d 2  d1   
Copyright ©1996 Ian H. Giddy
Currency Options 19
How a Change in the Forward Rate
Changes the Currency Option’s Price
Profit
(gain or loss)
Time Value
+
F-K
0
K
Forward
market price
of currency
F
_
Time Value
K
Copyright ©1996 Ian H. Giddy
F E(FJ*FJ>K)
Currency Options 20
Delta Hedging
Option
Value
HEDGE
RATIO
=80%
HEDGE
RATIO
=50%
HEDGE
RATIO
=15%
Forward or
Futures
Price
Copyright ©1996 Ian H. Giddy
Currency Options 21
The Effect of Increased Volatility
Profit
(gain or loss)
Time Value
+
F-K
0
K
Forward
market price
of currency
F
_
Time Value
K
Copyright ©1996 Ian H. Giddy
F E(FJ*FJ>K)
Currency Options 22
Betting on Volatility
Buy a Call
Gain
or Loss
Plus:
Buy a put
Net effect:
Long Straddle
Value of Swiss franc
Copyright ©1996 Ian H. Giddy
Currency Options 23
Unconventional Options
Can be Cheaper
Examples
Soles per US Dollar
 Asian
2.52
 Knock-in
2.5
2.51
 Knock-out
 Digital
 Lookback
These are priced using
binomial models
Copyright ©1996 Ian H. Giddy
2.56
2.54
2.55
2.53
2.54
2.52
2.53
Currency Options 24
Asian (Average Price) Options
Pays the difference between the strike
price on the expiry date and the average
price of the underlying instrument over a
certain time period.
 Used where the purchaser wants to cover
many spot transactions using one hedging
instrument.
 Since the volatility of an average is less
than the volatility for a spot price, average
price options are less expensive

Copyright ©1996 Ian H. Giddy
Currency Options 25
AVERAGE PRICE
STRIKE PRICE
Copyright ©1996 Ian H. Giddy
Currency Options 26
Knock-in and Knock-out Options
A knock-in option has the same payout
as a standard option if a certain barrier
level is reached before the option expiry
date, otherwise it pays nothing.
 A knock-out option becomes worthless if
the price of the underlying instrument
reaches a barrier level before the option
expiry date. If the barrier is not reached,
the payout is the same as a standard
option.

Copyright ©1996 Ian H. Giddy
Currency Options 27
BARRIER
STRIKE PRICE
Copyright ©1996 Ian H. Giddy
Currency Options 28
Client Situations...

View on:
Direction
of rates
Volatility of rates
Relative rates
Constraints - internal or imposed
 Credit aspects.

Copyright ©1996 Ian H. Giddy
Currency Options 29
View on Direction, Volatility or Both?
Copyright ©1996 Ian H. Giddy
Currency Options 30
When Use What?
View on direction
 View on volatility

Direction: Currency
No trend
rising
Currency
falling
Buy call
Buy put
Sell put
Sell call
Buy
forward
Sell
forward
Buy
straddle
Sell
straddle
Arbitrage
Volatility
Volatility
increasing
Volatility
falling
No trend in
volatility
Copyright ©1996 Ian H. Giddy
Currency Options 31
Copyright ©1996 Ian H. Giddy
Currency Options 32