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Deep-in-the-money
Said of an option whose exercise price at a specific point in time is so far below the market price of the underlying in the case of a call option, or so far above the market price of the underlying in the case of a put option, that the option is unlikely to become out of the money before its maturity.
The premium to be paid on the purchase of a deep-in-the-money option is high since the intrinsic value of the option is high. The call option gives the holder the right to purchase the underlying at a price considerably below market value; the put option gives the holder the right to sell the underlying at a price well above market value.