The two terms In the money and out of the money are used to indicate if an option is closed in profit or loss.
A binary option is in the money when it is profitable, that is, when it generates a profit. If at expiry, the trader’s prediction it’s correct, the binary option closes In the money.
A binary option is out of the money when it’s lost, that is when the invested capital is lost. If the trader’s prediction it’s not true, the option expired out of the money.
Let’s consider a binary option High / low, that is an option where you need to predict if the asset will close up (High) from purchase price or down (low).
1. Suppose to buy a High option, so we focus on the rising price.
In this case the option will be in the money at expiry only if the price of the asset will be greater than the purchase price.
The option is in the money and then pays a profit.
If the option ends with lowest price it’s out of the money, so it’s in loss.
2. Suppose to buy a Low option, so we focus on price reduction.
The option is in the money when at expiry the price of the asset is less than the purchase price of the same. Therefore the option is in the money and pays a profit. If the option closes with higher price it’s out of the money, that is a loss.
If on expiry, both for the High option that the low option, the purchase price of the asset it’s identical to the final price, it’s said that the option is At the money. In this case, the broker does not pay any profit and repay the entire investment without any loss.
Caution: A binary option is At-the-money when the purchase price and the price at expiry are identical. Identical means you don’t need to differentiate even a penny. That’s why doesn’t happened often that a binary option expires At the money.