Post on 18-Jan-2016
Foreign Exchange Options
Prof. Ian Giddy
New York University
Copyright ©1996 Ian H. Giddy Currency Options 2
Tools for Hedging
Petrobras has to pay for equipment from Japan, in Japanese yen, in 3 monthsLock in a forward priceOr use a call option on the Yen?How much will it cost?
Copyright ©1996 Ian H. Giddy Currency Options 5
Option Hedge
CALL
OPTION
ON YEN
FORWARD
CONTRACT
Copyright ©1996 Ian H. Giddy Currency Options 6
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 7
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 8
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.
Gain
or Loss
Buy a Put
Value of Swiss franc
Copyright ©1996 Ian H. Giddy Currency Options 9
Option Payoff Diagrams
Buy call: right to purchase foreign currency
Buy put: right to sell foreign currency
Profit
ForwardRate
+
0
_
BUYCALLOPTION
Strike
Premium
Profit
Forward
+
0
_SELLCALLOPTION
Profit
Forward
+
0
_
BUYPUTOPTION
Profit
Forward
+
0
_SELLPUTOPTION
Figure 2. Payoff at Expiration of Options. Eg. buying a call produces a gain if the currency (ie the futures price) risesabove the strike plus the premium; the call writer's profit profile is opposite.
Copyright ©1996 Ian H. Giddy Currency Options 15
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 16
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 17
Value of Call Option
Equals present value of its expected intrinsic value at expiration, given that the forward is above the strike
FORWARD
STRIKE
Copyright ©1996 Ian H. Giddy Currency Options 18
Value of Call Option
INTRINSIC VALUE TIME VALUE
EXPECTED VALUE OF PROFIT
GIVEN EXERCISE
STRIKE
FORWARDSHADED AREA:
Probability distribution
of the log of the forward
rate on the expiration date
for values above the strike.
Copyright ©1996 Ian H. Giddy Currency Options 19
Currency Option Pricing: the Famous Formula
C PV FN d KN d
where
dF K
d d
[ ( ) ( )]
ln( / )
1 2
1
2 1
2
Copyright ©1996 Ian H. Giddy Currency Options 20
Forwardmarket priceof currency
Profit(gain or loss)
+
0
_
K F
K F
Time Value
F-K
Time Value
E(FJ *FJ >K)
How a Change in the Forward Rate Changes the Currency Option’s Price
Copyright ©1996 Ian H. Giddy Currency Options 21
Delta Hedging
OptionValue
Forward orFuturesPrice
HEDGERATIO=50%
HEDGERATIO=80%
HEDGERATIO=15%
Copyright ©1996 Ian H. Giddy Currency Options 22
The Effect of Increased Volatility
Forwardmarket priceof currency
Profit(gain or loss)
+
0
_
K F
K F
Time Value
F-K
Time Value
E(FJ *FJ >K)
Copyright ©1996 Ian H. Giddy Currency Options 23
Gain
or Loss
Value of Swiss franc
Plus:
Buy a put
Betting on Volatility
Net effect:
Long Straddle
Buy a Call
Copyright ©1996 Ian H. Giddy Currency Options 24
Unconventional OptionsCan be Cheaper
Examples Asian Knock-in Knock-out Digital Lookback
These are priced using binomial models
2.562.54
2.52 2.552.5 2.53
2.51 2.542.52
2.53
Soles per US Dollar
Copyright ©1996 Ian H. Giddy Currency Options 25
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 26
STRIKE PRICE
AVERAGE PRICE
Copyright ©1996 Ian H. Giddy Currency Options 27
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 28
BARRIER
STRIKE PRICE
Copyright ©1996 Ian H. Giddy Currency Options 29
Client Situations...
View on:Direction of ratesVolatility of ratesRelative rates
Constraints - internal or imposed Credit aspects.
Copyright ©1996 Ian H. Giddy Currency Options 30
View on Direction, Volatility or Both?
Copyright ©1996 Ian H. Giddy Currency Options 31
When Use What?
View on direction View on volatility
Direction:
Volatility
Currencyrising
Currencyfalling
No trend
Volatilityincreasing
Buy call Buy put Buystraddle
Volatilityfalling
Sell put Sell call Sellstraddle
No trend involatility
Buyforward
Sellforward
Arbitrage
Copyright ©1996 Ian H. Giddy Currency Options 32