The term deep in-the-money refers to an option that has significant intrinsic value. The concept of moneyness helps an investor to understand the position of an underlying asset relative to an option's strike price.
When an investor holds an option, they are provided with the right, but not an obligation, to buy or sell the underlying asset at the strike price on or before the contract's expiration date. In the case of a call option, the holder has the right to buy the underlying asset, while a put option confers the right to sell the underlying.
An option that is deep in-the-money has an exercise price that is much higher, or lower, than the current market price of the underlying asset. An option that is deep in-the-money will trade at a significant premium that accounts not only for the time value of the option itself, since it can it increase in value over time, but also the fact that if the option were exercised, the holder would make a significant profit on the transaction.
The intrinsic value of a call can be calculated by subtracting the option's strike price from the current market price of the underlying asset, while the intrinsic value of a put is calculated by subtracting the current market value of the underlying asset from the option's strike price. The larger the spread between these two values, the deeper the option goes in-the-money.
At some point, the delta for a deep in-the-money call option will approach 1.00, which means for every one unit increase in the underlying asset's market price, the intrinsic value of the option will increase by one unit. In the same manner, the delta for a deep in-the-money put option will approach -1.00, which means for every one unit decrease in the underlying asset's market price, the intrinsic value of the option will increase by one unit.