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Why Do OTM Options Still Have a Small Amount of Time Value?

Out-of-the-money (OTM) options still have a small amount of time value because there is a non-zero probability that the underlying asset's price will move enough before expiration to make the option in-the-money. This possibility of future profit is the time value.

The longer the time to expiration and the higher the volatility, the greater this time value will be.

Why Are Out-of-the-Money Options Often Cheaper to Buy?
How Does the Time Remaining until Expiration Affect the Option’s Time Value?
Why Do Deep Out-of-the-Money Options on Bitcoin Often Have a Very Low Delta?
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