An option is "deep in-the money" when it is so far in-the-money that it is unlikely to go out-of-the-money prior to expiration. It is an arbitrary term and can be used to describe different options by different people.
DEEP IN-THE-MONEY
Meaning of DEEP IN-THE-MONEY in English
A guide to futures and options market technology English dictionary. Английский словарь-руководство по фьючерсам и опционам рыночных технологий . 2012