Terms

Generally in thinking about options, one assumes that one is buying an asset: for instance, you can have a call option on oil, which allows you to buy oil at a given price. One can consider this situation more symmetrically in FX, where one exchanges: a put on GBPUSD allows one to exchange GBP for USD: it is at once a put on GBP and a call on USD.

As a vivid example: people usually consider that in a fast food restaurant, one buys hamburgers and pays in dollars, but one can instead say that the restaurant buys dollars and pays in hamburgers.

There are a number of subtleties that follow from this symmetry.

Ratio of notionals
The ratio of the notionals in an FX option is the strike, not the current spot or forward. Notably, when constructing an option strategy from FX options, one must be careful to match the foreign currency notionals, not the local currency notionals, else the foreign currencies received and delivered don't offset and one is left with residual risk.
Non-linear payoff
The payoff for a vanilla option is linear in the underlying, when one denominates the payout in a given numéraire. In the case of an FX option on a rate, one must be careful of which currency is the underlying and which in the numéraire: in the above example, an option on GBPUSD gives a USD value that is linear in GBPUSD (a move from 2.0000 to 1.9000 yields a .10 * $2,000,000 / 2.0000 = $100,000 profit), but has a non-linear GBP value in GBPUSD. Conversely, the GBP value is linear in the USDGBP rate, while the USD value is non-linear in the USDGBP rate. This is because inverting a rate has the effect of x \mapsto 1/x, which is non-linear.
Change of numéraire
the implied volatility of an FX option depends on the numéraire of the purchaser, again because of the non-linearity of x \mapsto 1/x.

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Example

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 notionals are £1,000,000 and $2,000,000 (£1,000,000 from the eyes of a USD investor, $2,000,000 from the eyes of a GBP investor).

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, as it is a put on the exchange rate; it could equally be called a USDGBP call, but isn't, as market convention is to quote the 2.0000 number (normal quote), not the 0.5000 number (inverse quote).

If the rate is lower than 2.0000 GBPUSD come December 31 (say at 1.9000 GBPUSD), meaning that the dollar is stronger and the pound is weaker, 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 USD/GBP - 1.9000 USD/GBP)*1,000,000 GBP = 100,000 USD in the process. If they immediately exchanges their profit into GBP, this amounts to 100,000/1.9000 = 52,631.58 GBP.

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Foreign exchange option

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 and is lightly regulated, but a fraction is traded on exchanges like the Philadelphia Stock Exchange, or the Chicago Mercantile Exchange for options on futures contracts: 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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Currency correlation

Currency correlation is a statistical measure of the strength and direction of a linear relationship between two currency pairs. Currency correlation is computed as a correlation coefficient. In the broader sense, currency correlation can refer to the correlation between any currency pairs and the commodities, stocks and bonds markets.

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Spread

The quotation of a currency pair usually consists of two prices. The lower price (bid) is the price at which a market maker or a brokerage in general is willing to buy the first currency of a pair. The higher price (offer or ask) is the price at which a brokerage is willing to sell the first currency of a pair. The spread is the difference between the two prices. For example if the quotation of EUR/USD is 1.3607/1.3609, then the spread is EUR 0.0002 (or 2 pips). The more popular the pair is, the smaller the differences or spreads. Different brokerage firms have different spreads.

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Pips

A pip is the smallest number in a quotation of a currency.

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Cross Rates

Cross rate is a currency pair that does not include USD, such as GBP/JPY. Pairs that involve the EUR are called euro crosses, such as EUR/GBP. All other currency pairs (those that don't involve USD or EUR) are generally referred to as cross rates.

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