[Fegu]

An Example

Imagine you are the holder of a GBP Call / USD Put Option with a strike of 1.50 that is about to expire and spot is higher than your option’s strike. If you exercise your right to buy, you can buy GBP at a cheaper rate than that currently available in the market – your option has some intrinsic value. It is In-The-Money. The intrinsic value (denominated in the term currency, USD) is the difference between the strike and the outright forward multiplied by the base (GBP) notional N of the option contract: N x (Outright Forward - Strike).

An option’s total cost is typically greater than its current intrinsic value, because the time remaining until expiration leaves a lot of uncertainty as to where the market rate will be at expiry. This uncertainty is known as time value and it is reflected in the premium, or total cost, of the option. The greatest amount of time value exists when the option is ATM, as here the uncertainty of whether or not the option will be exercised is greatest.

Most frequently the total value of an option is calculated using the Black-Scholes formula (BS). While it is not necessary to know exactly how the BS formula is calculated or derived, it is important to understand what the inputs are and how they can affect an option’s price.

The Inputs
1 – Currency pair
2 – Spot
3 – Strike
4 – Time remaining to expiry
5 – Interest rates of both currencies
6 – Strategy (Call or Put)
7 – Volatility

The price of an option is sensitive to each one of these inputs, and each sensitivity is quantified by a Greek (named after various letters of the Greek alphabet). There are four main Greeks: Delta, Gamma, Vega and Theta.

Aside from these sensitivities, it is important to know that the Black-Scholes model makes some incorrect assumptions, the two most important being that spot is normally distributed and that volatility of spot is constant over the life of an option. In reality extreme moves in spot are much more likely than suggested by the normal distribution. On some occasions spot can be very volatile, while on other occasions it is almost stationary.