## What is a Currency Option?

A **currency option** is an agreement between two compensations whereby the buyer of the option pays a premium to the seller for the right but not the obligation to buy or sell a specified quantity of currency on or before a fixed date ( called maturity or expiration) to a fixed exchange rate (called the "strike.") The buyer then chooses to exercise its right depending on the price of the currency.

**The risk profile of the buyer and seller are different:**** - The buyer has a limited risk to the premium and theoretically unlimited profit potential- The seller is in a theoretical unlimited risk and limited profit to the premium.**

The right to buy a currency is called "**call A**" the right to sell a currency is called a "**Put A**". A call is a buy option, a put an option to sell. This can therefore explain the four positions in the foreign exchange market as well:

** - Buyer of Call = buy the right to buy one currency A against currency B- Seller of Call = Sell the right to buy one currency A against currency B- Buyer of put = buy the right to sell a currency A against currency B- Seller of put = sell the right to sell a currency A against currency B**

__The different possible cases at the maturity of the option__

**There are 3 possible cases:**** - Strike = spot:** It is said that the option is at the money. There is no winner or loser.**- Strike> spot for a put or strike <spot for a call:** It is said that the option is in the money. The transaction is favorable to the buyer.**- Strike <spot price for a put or strike> spot for a call:** It is said that the option is out of the money. The transaction is favorable to the seller.

There are two types of options:

- **The American option:** The right to buy or sell can be made before or at maturity.

-** The European option:** The right to buy or sell can be made only at maturity

American options have a value which exceeds the European options. Indeed, for the issuer that is a additional risk because the buyer of the option can exercise his option at any time. It therefore has an additional right and the issuer make pay this right to the buyer and so, the value of the option is increasing.

## American options

An** American option** is calculated by the difference between the strike and the spot of the underlying. This is called intrinsic value. With American option, there is no time value because the option may be exercised at any time. There are then 3 cases:**- The option is in the money**, the value of the option is positive because the winner of the operation is the buyer. The risk of loss to the seller is unlimited.** - The option is out of the money**, the value of the option is negative because the winner of the operation is the seller. The loss for the buyer is then limited to the amount of the premium.** - The option at the money**, the value of the option is zero. It is said that the value is zero but in reality this is not the case because in fact the spot + premium paid is never less than the strike. Otherwise, arbitrage transactions could be made.

So, the intrinsic value corresponds to the profit realized by the investor in case of immediate exercise of the option.

## European options

A **European option** is calculated by 2 functions. The first one is the intrinsic value which is the difference between the strike and the forward price. Indeed, as the option can be exercised only at maturity, arbitration is only possible with the forward price.

The time value also comes into the calculation of the option. It is the difference between the premium and the intrinsic value. The time value is the right paid by the buyer to exercise or sell the option at a profit. It is the in fact the probability of exercise that we have is based on the lifetime of the option. It represents the speculative part of the option. That is why more the strike will be far from the spot, more the price of the option will be high. Indeed, a disaffection of the strike makes it less feasible the exercise of the option.

## Time Value

**In the time value, there are three components:**

- The **interest rate differential** between the base currency and the quoted currency: a currency can be in premium (interest rate lower than the quoted currency and which is expected on the rise by the market) or in discount (interest rate higher than the quoted currency and which is expected on the fall by the market).

The differential, however, has a minimal effect on the price of the option.

- The **maturity** of the option: more the maturity of the option is far away, more the buyer will have more probability that the strike will be exceeded. So, the time value will be higher.

- **Volatility:** The volatility is the amplitude and frequency of price changes of the underlying currency relative to the average. It is measured by the standard deviation. More this standard deviation is important, the more expensive the option will be.

**Trade options is therefore a triple bet:**** - On the moving of the price of the underlying:** The sensitivity of the option at the variation of 1 unit of the underlying price is given by the Delta. More an option is out of the money, more its delta will tend to 0%. More an option is in the money, more its delta will tend to 100%. An option in the money behaves almost like the underlying. The delta of this option will be close to 50% if the price of its underlying tends to the strike** - The evolution of the volatility: **The influence of a movement of volatility on the value of an option is given by the Vega.**- The time value:** The influence of time value on the value of the option is given by the Theta

### In practice

Today, some Brokers allow you to trade with **currency options**. The operation is conducted OTC. You can choose the parity, the amount, the maturity and the strike. You create your own option. The broker will quote this one after for you. Check the price by calculating its theoretical price (excluding commissions charged by the Broker) (calculated with the formulas of the forward exchange)

Although this service is available to all customers generally (when offered), only big customers use the currency option and it is usually to sell it to the broker (it is therefore limited in profit and unlimited in loss but they receive the premium at the beginning). Of course, the profit of the premium would be lower if the strike is far from the spot or that the maturity is short. The client will just monitor his options and hedge his positions in the case of the parity will not go in the right side.