## FX Options Basics

A currency option is a transaction between two counterparts, 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 the currency on or before a fixed date (called maturity or expiration) at a prefixed exchange rate (called the exercise price or “strike.”) The buyer then chooses to exercise its right depending at what level the currency pair trades.

### Fx Options: the ABC

The risk profile of the buyer and seller are different:

1. – The buyer has a risk limited to the premium that he paid and theoretically an unlimited profit potential,

2. – The seller has the opposite risk/return profile, in particular infinite risk.

A “call” option gives the right to buy a given currency pair, whereas a “put” gives the right to sell that same pair. For example holding a call on the euro (EUR/USD) at strike price 1.50 gives the right to buy euros versus US dollars at a price of 1.50 dollar per euro.

There are two types of options:

1. – The **American option**: The right to buy or sell can be exercised at any time at or before maturity.

2. – The **European option**: The right to buy or sell can only be exercised at maturity.

Americans options always have more values than European options with the same characteristics, as the ability to exercise the option at any time has some value in itself.

Any unexpired option is always in one of three states:

1. – **At the money**: the exercise price = price spot (no benefit in exercising the option). The intrinsic value (the value of exercising the option) is zero.

2. – **In the money**: the exercise price > spot price for a put or exercise price < spot price for a call; exercising the option generates a positive cash flow, the intrinsic value is positive

3. - **Out of the money**: the exercise price < spot price for a put or exercise price > spot price for a call; the option should not be exercised, the intrinsic value is zero.

### The calculation of the premium of an FX option

Beyond intrinsic value, time to maturity comes into play in the calculation of price of a fx option. The time value is the difference between the premium (the price of the option) and its intrinsic value. It represents the probability of large price movements in the currency pair itself during the duration of the option.

The three main factors determining the value of a fx option are:

1. – The **interest rate differential** between the two currencies within the currency pair (this differential has a minimal effect on the option price).

2. – The maturity of the option. The longer the maturity of the option, the higher the chance that it will have a large intrinsic value at maturity, and the higher the option price.

3. – The **implied volatility**: this represents the expectation of price changes in the underlying currency pair during the duration of the option. The higher the volatility, the higher the expected price change and the higher the option price.

Trading fx options is therefore a threefold challenge depending on:

1. – the price level of the underlying currency pair: The sensitivity of the fx option to the change of 1 unit of the underlying currency is given by the so-called Delta. The more “out of money” an option, the closer the delta goes to 0%. The more it is “in the money”, the closer to 100%. The option delta is close to 50% if the currency price is close to the strike price.

2. – the changes in volatility: The influence of a movement of volatility on the value of an option is given by the Vega. The Vega shows the sensitivity of the option price with respect to change in implied volatility.

3. – the time factor: The influence of time on the value of the option is given by the Theta.