1. Foreign Exchange Options
Prof. Ian Giddy
New York University

2. 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?

3. Option Hedge

4. Option Hedge
FORWARD
CONTRACT

5. Option Hedge
CALL
OPTION
ON YEN
FORWARD
CONTRACT

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?

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.

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.
Buy a Put
Gain
or Loss
Value of Swiss franc

9. Option Payoff Diagrams
Buy call: right to purchase foreign currency
Buy put: right to sell foreign currency

10. Put-Call Parity Gain or Loss Value of DM Buy a Call Plus:
Short the currency
Net effect:
Buy a put
Value of DM

11. Option Combinations
Four classic ways of combining an option with a futures to create the opposite option

12. Put-Call Parity Gain or Loss Value of Swiss franc Sell a Call Plus:
Buy a put
Net effect:
Short the currency
Value of Swiss franc

13. Put-Call Parity
Buying a call and selling a put can replicate a long futures
From this we get put-call parity for foreign exchange:
Thus if we know the put’s price, we can get the call’s price, and vice-versa

14. Put-Call Parity: Carmen’s Career
Calculate a put price, given a call price of $0.01 and futures=$ , at strike of $0.36:
P =1.00-( )/( )148/360
=1.68 cents per DM
(Locking in off-market futures:
Fee =( )/( )148/360 = .68 cents/DM)

15. Forward relative to strike Time to expiration Volatility Interest rate
Pricing a Call Option
Forward relative to strike
Time to expiration
Volatility
Interest rate
Option
Value
Currency Value

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

17. Value of Call Option
FORWARD
Equals present value of its expected intrinsic value at expiration, given that the forward is above the strike
STRIKE

18. EXPECTED VALUE OF PROFIT
Value of Call Option
SHADED AREA:
Probability distribution
of the log of the forward
rate on the expiration date
for values above the strike.
FORWARD
STRIKE
INTRINSIC VALUE
TIME VALUE
EXPECTED VALUE OF PROFIT
GIVEN EXERCISE

19. Currency Option Pricing: the Famous Formula

20. How a Change in the Forward Rate Changes the Currency Option’s Price

21. Delta Hedging

22. The Effect of Increased Volatility

23. Betting on Volatility Gain or Loss Value of Swiss franc Buy a Call
Plus:
Buy a put
Net effect:
Long Straddle
Value of Swiss franc

24. Unconventional Options Can be Cheaper
Examples
Asian
Knock-in
Knock-out
Digital
Lookback
These are priced using binomial models
2.56
Soles per US Dollar
2.54
2.52
2.55
2.5
2.53
2.51
2.54
2.52
2.53

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

26. AVERAGE PRICE
STRIKE PRICE

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.

28. BARRIER
STRIKE PRICE

29. Constraints - internal or imposed Credit aspects.
Client Situations...
View on:
Direction of rates
Volatility of rates
Relative rates
Constraints - internal or imposed
Credit aspects.

30. View on Direction, Volatility or Both?

31. When Use What?
View on direction
View on volatility

33. www.giddy.org Ian Giddy NYU Stern School of Business
Tel ;
Fax ;