Example

Suppose a United Kingdom manufacturing firm is expecting to be paid $100,000 for a piece of engineering equipment to be delivered in 90 days. If the exchange rate goes down over the next 90 days the UK firm will lose money, but if the rate goes up then the UK firm will make a profit. The UK firm can purchase an option (the right to sell part or all of their expected income for pounds sterling at a given rate near todays rate) to mitigate their risk of exchange rate fluctuation over the 90 days. Conversely another party may wish to have the reverse option for a similar reason. A Market maker will buy and sell these options with the aim of making a profit while not incurring too much risk.

In finance, a foreign exchange option (commonly shortened to just fx option) is a derivative security where the owner has the right but not the obligation to exchange money denominated in one currency into another currency at pre-agreed exchange rate on a specified date.

For example a USD/GBP FX option might be specified by a contract allowing the purchaser to exchange £1,000,000 into $2,000,000 on December 31st. In this case the pre-agreed exchange rate, or strike price, is 2USD/GBP or 0.5GBP/USD and the notional is £1,000,000. This type of contract may be called either a dollar call or a sterling put depending on the market convention. If the dollar is stronger than 0.5GBP/USD come December 31st (say at 0.55GBP/USD) then the option will be exercised, making a profit of (2 - 1/0.55)*1,000,000 = $181,818 or £100,000.

Valuing FX options : The Garman-Kohlhagen model

As in the Black-Scholes model for stock options and the Black model for certain interest rate options, the value of a european option on an FX rate is typically calculated by assuming that the rate follows a log-normal process. In 1983 Garman and Kohlhagen extended the Black-Scholes model to cope with the presence of two interest rates (one for each currency). Suppose that r_d is the risk-free interest rate to expiry of the domestic currency and r_f is the foreign currency risk-free interest rate (where domestic currency is the currency in which we obtain the value of the option; the formula also requires that FX rates - both strike and current spot be quoted in terms of "units of foreign currency per unit of domestic currency"). Then the value of a call option into the foreign currency has value

<math>exp(-r_f T) S N(d_1) - K exp(-r_d T) N(d_2)<math>

where

S is the current spot rate

K is the strike rate

N is the cumulative normal distribution function

<math>d_1 = \frac{log(S/K) + (r_d - r_f + \sigma^2/2)T}{\sigma^2T}<math>

<math>d_2 = d_1 - \sigma\sqrt{T}<math>

and <math>\sigma<math> is the volatility of the FX rate.

See also

• Foreign Exchange
• Put option
• Call option