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Foreign Exchange

Exchange Rates Currency band Exchange rate Exchange rate regime Fixed exchange rate Floating exchange rate Linked exchange rate

Markets Foreign exchange market Futures exchange

Products Currency Currency future Non-deliverable forward Forex swap Currency swap Foreign exchange option

See also Bureau de change

In finance, a foreign exchange option (commonly shortened to just FX option or currency option) is a derivative financial instrument where the owner has the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date. The FX options market is the deepest, largest and most liquid market for options of any kind in the world. Most of the FX option volume is traded OTC but a fraction is traded on exchanges like the Philadelphia Stock Exchange, or the Chicago Mercantile Exchange for options on futures contracts.

For example a GBPUSD FX option might be specified by a contract allowing the owner to sell £1,000,000 and buy $2,000,000 on December 31. In this case the pre-agreed exchange rate, or strike price, is 2.0000 GBPUSD or 0.5000 USDGBP and the notional is £1,000,000. This type of contract is both a call on dollars and a put on sterling, and is often called a GBPUSD put by market participants. If the dollar is stronger than 2.0000 GBPUSD come December 31 (say at 1.9000 GBPUSD) then the option will be exercised, allowing the owner to sell GBP at 2.0000 and immediately buy it back in the spot market at 1.9000, making a profit of (2.0000 - 1.9000)*1,000,000 GBP = 100,000 USD in the process. If he immediately exchanges his profit, this amounts to 100,000/1.9000 = 52,631.58 GBP.

As in the Black-Scholes model for stock options and the Black model for certain interest rate options, the value of an european option on a FX rate is typically calculated by assuming that the rate follows a log-normal process.

Suppose a United Kingdom manufacturing firm is expecting to be paid US$100,000 for a piece of engineering equipment to be delivered in 90 days. If the GBP strengthen against the US$ over the next 90 days the UK firm will lose money, as it will receive less GBP when the US$100,000 is converted into GBP. However, if the GBP weaken against the US$,then the UK firm will gain additional money. In this case, to protect the GBP value that the firm will receive in 90 day's time, the UK firm can purchase a GBP call/ USD put option (the right to sell part or all of their expected income for pounds sterling at a given rate near today's 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.

The advantage of using an option instead is that it gives unlimited profit potential to the buyer at a limited cost (this cost is known as option premium).

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 domestic currency per unit of foreign currency"). Then the domestic currency value of a call option into the foreign currency is

The value of a put option has value

where :

S₀ is the current spot rate

K is the strike price

N is the cumulative normal distribution function

r_d is domestic risk free rate

r_f is foreign risk free rate

and σ is the volatility of the FX rate.

The global market for exchange-traded currency options is notionally valued by the Bank for International Settlements at $158,300 million in 2005...

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