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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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Majors

Majors are the most liquid and widely traded currency pairs in the world. Trades involving majors make up about 90% of total Forex trading.

The Majors are: EUR/USD, GBP/USD, USD/JPY, USD/CHF, AUD/USD and USD/CAD.

GBP/USD is the only currency pair with its own name. It is known as "Cable", which has its origins from the days when a cable under the Atlantic synchronized the GBP/USD rate between the London and New York markets. But there are also lots of abbreviations for other currency pairs such as:
AUD/USD ... "Aussie"
EUR/USD ... "Euro"
GBP/JPY ... "Geppy"
GBP/USD ... "Cable"
NZD/USD ... "Kiwi"
USD/CAD ... "Loonie"
USD/CHF ... "Swissy"
USD/JPY ... "Gopher"
USD/CAD ... "Beaver"


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Currency pair

A currency pair depicts a quotation of two different currencies. The first currency in the pair is the base currency or transaction currency. The second currency in the pair is labelled quote currency, payment currency or counter currency. Such a quotation depicts how many units of the counter currency are needed to buy one unit of the base currency.

For example the quotation EUR/USD 1.2500 means that one euro is exchanged for 1.25 US dollar. If the quote moves from EUR/USD 1.2500 to EUR/USD 1.2510, the euro is getting stronger and the dollar weaker. On the other hand if the EUR/USD quote moves from 1.2500 to 1.2490 the euro is getting weaker while the dollar is getting stronger.

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Fluctuations in exchange rates

A market based exchange rate will change whenever the values of either of the two component currencies change. A currency will tend to become more valuable whenever demand for it is greater than the available supply. It will become less valuable whenever demand is less than available supply (this does not mean people no longer want money, it just means they prefer holding their wealth in some other form, possibly another currency).

Increased demand for a currency is due to either an increased transaction demand for money, or an increased speculative demand for money. The transaction demand for money is highly correlated to the country's level of business activity, gross domestic product (GDP), and employment levels. The more people there are unemployed, the less the public as a whole will spend on goods and services. Central banks typically have little difficulty adjusting the available money supply to accommodate changes in the demand for money due to business transactions.

The speculative demand for money is much harder for a central bank to accommodate but they try to do this by adjusting interest rates. An investor may choose to buy a currency if the return (that is the interest rate) is high enough. The higher a country's interest rates, the greater the demand for that currency. It has been argued that currency speculation can undermine real economic growth, in particular since large currency speculators may deliberately create downward pressure on a currency in order to force that central bank to sell their currency to keep it stable (once this happens, the speculator can buy the currency back from the bank at a lower price, close out their position, and thereby take a profit).