Hedging with Foreign Currency Options

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Hedging with Foreign Currency Options

• By Soeren Hansen

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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

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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

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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

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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

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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 SgtX
• gt Profit increases one-for-one with
  appreciation of the foreign currency. At (XP)
  the holder of the option breaks even (ceiling
  price)
• If SltX
• gt 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

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Profit Profile for a Call Option
Profit
S
X
XP
-P
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Put Option

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

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

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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

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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)

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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

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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

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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

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Questions?

• Thank you