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Foreign Exchange Options

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?. Option Hedge. CALL OPTION ON YEN. FORWARD

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Foreign Exchange Options

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  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 CALL OPTION ON YEN FORWARD CONTRACT

  4. 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?

  5. 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.

  6. 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

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

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

  9. 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

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

  11. 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

  12. Currency Option Pricing: the Famous Formula

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

  14. Delta Hedging

  15. The Effect of Increased Volatility

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

  17. Unconventional OptionsCan 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

  18. 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

  19. AVERAGE PRICE STRIKE PRICE

  20. 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.

  21. BARRIER STRIKE PRICE

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

  23. View on Direction, Volatility or Both?

  24. When Use What? • View on direction • View on volatility

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