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What Is the Term for an Option That Is Almost Worthless?

The term for an option that is almost worthless is a "penny option" or a "deep out-of-the-money" (DOTM) option. It is an option with a very low premium, consisting of minimal time value and zero intrinsic value.

How Does Skew Affect the Pricing of Deep In-the-Money versus Deep Out-of-the-Money Options?
How Does the Delta of a Deep Out-of-the-Money Option Behave When Gamma Is near Zero?
What Is the Approximate Delta of a Deep Out-of-the-Money Option?
What Is the Optimal Time to Cut Losses on a Deep Out-of-the-Money Option?