What Is the Term for an Option That Is Significantly “In-the-Money”?

An option that is significantly "in-the-money" (ITM) is often referred to as a deep in-the-money option. An option is ITM when exercising it immediately would yield a positive payoff.

For a call, this means the underlying price is much higher than the strike price. For a put, it means the underlying price is much lower than the strike price.

Deep ITM options have a high intrinsic value and their price is highly correlated with the underlying asset price.