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Hedging with Foreign Currency Options

Hedging with Foreign Currency Options. By Soeren Hansen. What is an Option?. A Currency Option is an option, but not an obligation to buy or sell currency during a specified time period (time to maturity, T) at a specified price (exercise/strike price, X)

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Hedging with Foreign Currency Options

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  1. Hedging with Foreign Currency Options By Soeren Hansen

  2. What is an Option? • A Currency Option is an option, but not an obligation to buy or sell currency during a specified time period (time to maturity, T) at a specified price (exercise/strike price, X) • The price or value of the option is called the premium, P • Two different Options: • Call Option • Put Option

  3. What is a Call -and a Put Option? • A currency Call option is an option but not an obligation to buy currency during a specified time period at a specified price • A currency Put option is an option but not an obligation to sell currency during a specified time period at a specified price

  4. What is an European -and an American Option? • An European currency option is an option, which can be exercised only on the maturity date • An American currency option is an option which can be exercised any time prior to the maturity date

  5. Why an Option? • Since the the holder of a Currency Option has the right but not the obligation to trade currency, it is beneficial to use options to hedge potential transactions (ex. bids not yet accepted) • The exercise/strike price and the premium together determine the the floor or ceiling established for the potential transaction

  6. Call Option • The Call Option establishes a ceiling for the exchange rate, and the option can be used to hedge foreign currency outflows (potential payments) • If S>X => Profit increases one-for-one with appreciation of the foreign currency. At (X+P) the holder of the option breaks even (ceiling price) • If S<X => The call option will not be exercised, because the holder is better off buying the foreign currency in the spot market. The holder will have a negative profit reflecting the premium, P

  7. Profit Profile for a Call Option Profit S X X+P -P

  8. Put Option • The Put Option establishes a floor for the exchange rate, and the option can be used to hedge foreign currency inflows • If S>X => The call option will not be exercised, because the holder is better off selling the foreign currency in the spot market. The holder will have a negative profit reflecting the premium, P If S<X => Profit increases one-for-one with depreciation of the foreign currency. At (X-P) the holder of the option breaks even (floor price)

  9. Profit Profile for a Put Option Profit S X-P X -P

  10. Option Pricing • For European options • Black-Scholes’ pricing model • Garman & Kohlhagen • For both European and American option: • Binomial pricing model • Implicit finite difference method I will not go into these different pricing models, but for the interested student see John C. Hull ”Options, Futures and other derivatives”

  11. Principles of pricing currency options • The value of an option on its maturity date is either its immediate exercise value or zero, whichever is higher • If two options are identical in all respects with the exception of the exercise price, a call option with a higher exercise price will always have a lower value and a put option with a higher exercise price will always have a greater value than the corresponding options with lower exercise prices

  12. Principles of pricing currency options • If two American options are identical in all respects with exception of the length of the contract, the longer contract will have a greater value at all times (more flexible) • Prior to expiration, an American option has a value at least as large as the corresponding European option (more flexible)

  13. Principles of pricing currency options • A larger (positive) difference between the domestic and foreign interest rate (i – i*), increases the price of a call and decreases the price of a put (expected appreciation of the home currency) • The value of the option increases as the volatility of the underlying currency increases

  14. Example • B.Lack & S.Choles Enterprises of Salem, OR imports French wine. The wine is really rare, so B.Lack & S.Choles have to bid for the wine. On November 2nd B.Lack & S.Choles bids €62,500, but the firm will not know until December 15th whether the bid is accepted or not. Recently the dollar tanked against the euro, so to protect against a further appreciation of the euro, the firm purchases a €62,500 call option. The strike price is 1.2750 $/€ and the option premium is one cent pr. euro. The ceiling price is therefore 1.2850 $/€, for a maximum payment of $80,312.5

  15. Example • If the euro appreciates to 1.3000 $/€, the payment without the option would be $81,250, so B.Lack & S.Choles will exercise the option and purchase the euro for 1.2750, which is a payment of $79,687.5 + premium of $625 • If the euro depreciates to 1.2000, B.Lack & S.Choles will be better of buying euro on the spot market, so they let the option expire unused. The payment is then $75,000 + premium of $625

  16. Questions? Thank you

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