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) 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 The price or value of the option is called the premium, P Two different Options: Two different Options: 1. Call Option 2. Put Option

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 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 A currency Put option is an option but not an obligation to sell currency during a specified time period at a specified price

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 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 An American currency option is an option which can be exercised any time prior to the maturity date

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) 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 The exercise/strike price and the premium together determine the the floor or ceiling established for the potential transaction

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) 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 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 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

Profit Profile for a Call Option Profit S -P XX+P

Put Option The Put Option establishes a floor for the exchange rate, and the option can be used to hedge foreign currency inflows The Put Option establishes a floor for the exchange rate, and the option can be used to hedge foreign currency inflows If S>X 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 => 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) => Profit increases one-for-one with depreciation of the foreign currency. At (X-P) the holder of the option breaks even (floor price)

Profit Profile for a Put Option Profit S -P XX-P

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

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 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 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

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) 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) Prior to expiration, an American option has a value at least as large as the corresponding European option (more flexible)

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) 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 The value of the option increases as the volatility of the underlying currency increases

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 2 nd B.Lack & S.Choles bids €62,500, but the firm will not know until December 15 th 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 $/€ and the option premium is one cent pr. euro. The ceiling price is therefore $/€, for a maximum payment of $80,312.5 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 2 nd B.Lack & S.Choles bids €62,500, but the firm will not know until December 15 th 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 $/€ and the option premium is one cent pr. euro. The ceiling price is therefore $/€, for a maximum payment of $80,312.5

Example If the euro appreciates to $/€, the payment without the option would be $81,250, so B.Lack & S.Choles will exercise the option and purchase the euro for , which is a payment of $79, premium of $625 If the euro appreciates to $/€, the payment without the option would be $81,250, so B.Lack & S.Choles will exercise the option and purchase the euro for , which is a payment of $79, premium of $625 If the euro depreciates to , 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 If the euro depreciates to , 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

Questions? Thank you